WO2006103851A1

WO2006103851A1 - Power value generation device

Info

Publication number: WO2006103851A1
Application number: PCT/JP2006/303253
Authority: WO
Inventors: Yuichi Futa; Takatoshi Ono; Natsume Matsuzaki
Original assignee: Matsushita Electric Industrial Co., Ltd.
Priority date: 2005-03-28
Filing date: 2006-02-23
Publication date: 2006-10-05

Abstract

A secret key generation unit (1102) of a key issuing server (1100) generates a power value used in power-residue calculation for a positive integer c and a modulus n and uses the generated power value as a secret key. Here, a random number generation unit (11021) generates a candidate value as a candidate for the power value. A humming weight judgment unit (11022) judges whether the humming weight of the candidate value belongs to a predetermined range. If it belongs to the predetermined range, the candidate value is set as a power value.

Description

Specification

Price generator

Technical field

[0001] The present invention relates to an attack method for analyzing a power value embedded in a module that executes a power residue calculation process by measuring power consumption when the power residue calculation process is executed. The present invention relates to a safe threshold generation device.

Background art

[0002] In recent years, there is hardware! /, A module that performs cryptographic processing (hereinafter referred to as a cryptographic module) implemented in software, and includes secondary information (hereinafter referred to as secondary information) when performing cryptographic processing. Various cryptanalysis methods have been devised to analyze cryptographic keys using the clue to "information".

[0003] For example, in an analysis method called a timing attack, the time required for cryptographic processing by a cryptographic module varies slightly depending on the value of the cryptographic key used for cryptographic processing. Analyze. That is, in the timing attack, the encryption key is decrypted by using the sub-information called the processing time when performing the encryption process (for example, see Non-Patent Document 1).

[0004] Furthermore, among these cryptanalysis methods, power consumption during cryptographic processing, such as Simple Power Analysis and Differential Power Analysis, is used as sub-information. Such cryptanalysis has been devised (see Non-Patent Document 2, for example).

[0005] These cryptanalysis methods have been used in recent years for high-performance measuring instruments at a low price, and even for actual products with encryption such as IC cards. It has been reported that analysis is possible. In the following description, the power consumption of the cryptographic module during the cryptographic processing as described above, that is, the decryption method for analyzing the cryptographic key using the power waveform as a clue is collectively referred to as the “power analysis attack”. .

[0006] Here, as an example, a simple power analysis attack on an RSA cipher will be described.

[0007] In the decryption process of RSA (Rivest—Shamir—Adelman) cipher, the product of prime numbers p and q n, the ciphertext c is a positive integer less than n, to the secret key d is a positive integer, as the calculation of "c ^d mod n" (for example, see non-patent document 3.) ₀ This calculation method, For example, a binary method is known (for example, non-Patent Document 4 reference.) ₀

[0008] In the noinari method, the following step (S) is performed using the secret key d expressed by the following mathematical formula (1).

Processes 1) to (S7) are performed.

[0009] [Equation 1]

(1)

{= 0 or l: i = 0, l 厂-, len-l}

Here, len indicates the number of bits of d, “X,” indicates multiplication of integers, and “x ^y ” indicates x to the power of y.

[0011] (SI): Execute “i len— 2, z ^ c” to initialize variable i and variable z.

[0012] (S2): “z ^ z ² mod n” is performed to update the variable z.

(S3): It is determined whether or not “d = 1”.

(S4): If the result of determination is “d = l”, “z ^ z X c mod n” is performed, and the variable z is updated.

[0015] (S5): Perform “i ^ i-1” to update variable i.

(S6): It is determined whether or not “i <0”.

(S7): If “i <0”, the value of variable z is output. Otherwise, return to step (S2) and repeat the process.

[0018] In the above method, the processing of steps (S2) to (S6) is repeatedly calculated as a loop.

FIG. 1 is a diagram showing an outline of calculation processing by a conventional binary method. As shown in Figure 1, within this loop, for (1 ^ = 1, 2, ..., len— 1), if "d = l" If "d = 0", perform only multiplication by z. n is a large number, for example, an integer of 1024 bits. Usually, the multiplication by 2 can be performed more quickly than the multiplication because the efficiency of the calculation process can be improved. In this case, the power waveform is different because 2 multiplication and multiplication are processed differently.

[0020] Therefore, by measuring the power waveform, it is possible to analyze the order of operations of multiplication and multiplication. Furthermore, using the fact that the processing in the loop differs depending on d, the order The value of d is obtained from the beginning. In summary, the simple power analysis attack can be performed by the following steps (S11) to (S13).

(S11): The ciphertext c is decrypted, and the power waveform in the processing is measured.

[0022] (S12): The order of the multiplication and multiplication operations is specified from the measured power waveform.

[0023] (S13): Bits d (i = l, 2,..., Len-l) are obtained from the specified order.

[0024] The simple power analysis attack described above utilizes the fact that the calculation processing is different between double multiplication and multiplication. Therefore, if the two multiplications are processed with the same value multiplication, the two multiplications cannot be distinguished from the multiplications, and the calculation order is insignificant, so the above simple power analysis attack cannot be performed. That is, the operation function of double multiplication with X as input and "X ² mod n" as output is Sqr (x), x and y as input, and x Xy mod n as output is Mul (x, When y), Sqr (x) should be calculated as Mul (x, x).

Non-Patent Literature 1: Paul Kocher. Timing attacks on implementations of Di ffie— Hellman, RSA, DSS, and other systems. In Neal Koblitz, editor, CRYPTO '96, LNCS 1109, Springer-Verlag, 1996, pp. 104- 113 .

Non-Patent Document 2: P. Kocher, J. Ja_e, and B. Jun, "Di- erential Pow er Analysis," Advances in Cryptology -CRYPTO '99, LNCS, 1

666, Springer— Verlag, 1999, pp. 388— 397.

Non-patent literature 3: Tatsuaki Okamoto, Hiroshi Yamamoto, “Modern cryptography”, industrial books (1997)

Non-Patent Document 4: H. Cohen, "A Course in Computational Algebraic Number Theory", GTM 138, Springer -Verlag, 1996, p9

Disclosure of the invention

Problems to be solved by the invention

[0025] With the above-mentioned RSA encryption simple power analysis attack countermeasures, two multiplications and multiplications cannot be distinguished, but the total number of operations of two multiplications and multiplications can be analyzed. In the above binary method, the power of 2 multiplication is always executed len-l times. The multiplication is executed w (d) times for w (d) which is the Hamming weight of d. Therefore, the number of operations is “len−l + w (d)”, and if the number of operations can be analyzed, the Hamming weight of d is obtained. Depending on the value of d, the attacker uses this hamming weight. The search for d may be easier.

[0026] Due to the ming weight, the search space for d is "C (len, w (d)) = len! / ((Len-w (d))!

X w (d)! ) ", Where C (x, y) is the number of combinations of X and y to choose y. R SA cipher security is generally a force that depends on the computation time of the factoring of n n and if d is 10 24-bit, the calculation time is about the same as the computation time for searching a value from the search space size of 2 ⁸ °. here, if, C (len, w (d )) is if falls below the 2 ⁸ °, than the computation time of the prime factorization of n, the search time of the d is reduced, the safety of the RSA encryption is lowered by simple power analysis attack.

[0027] Therefore, if d is selected at random, C (len, w (d)) may be less than ^28Q . In this case, if safety is lowered, there is a problem. .

Therefore, the present invention has been made in view of the above problems, and provides a threshold value generating apparatus that executes a power residue calculation process so that safety is not reduced by a simple power analysis attack. With the goal.

Means for solving the problem

[0029] In order to achieve the above object, a threshold value generating apparatus according to the present invention is (a) a threshold value generating apparatus that generates a threshold value used for a power-residue calculation for positive integer c and modulus n. (Al) generating means for generating candidate values that are candidates for the threshold value; (a2) determining means for determining whether or not the hamming weight of the candidate value falls within a predetermined range; and (a3 And a setting unit configured to set the candidate value as the saddle value when it is determined by the determination unit to be within a predetermined range.

[0030] For example, for a simple power analysis attack, if the hamming weight is small, the search time is shortened and the safety is lowered. However, by limiting the threshold value and the ming weight to a predetermined range, a threshold value having a threshold value that is smaller than the predetermined range is not generated, so that it is possible to prevent the safety from being lowered. Furthermore, even if the Hamming weight of the threshold value is leaked, it is possible to prevent the safety from being lowered.

[0031] Further, (b) the generating means calculates the power value d given in advance, the modulus n of the power-residue operation, the random number!:, And the Carmichael function (n) or the Euler function φ (n). By using this, d + r X λ (η) or d + r X φ (η) may be generated as the candidate value. [0032] Alternatively, (c) the determination means is determined on the basis of the safety against the brute force brute force attack with a combination of the number of bits of the modulus n and a predetermined positive integer as a first value When the value is the second value, the predetermined positive integer determined under the condition that the first value exceeds the second value may be determined as the lower limit in the predetermined range.

Alternatively, (d) the determination unit may determine a positive integer determined under a condition that the processing time of the power-residue calculation is shorter than a predetermined time as an upper limit in the predetermined range. .

Alternatively, (e) the power generation unit may include power residue calculation means for performing the power residue calculation using the power value.

[0035] Further, (f) the threshold value generating apparatus includes threshold value storing means for storing the threshold value, and the power residue calculating means performs the power value every time the power residue calculation is executed. You may use the value stored in the storage means.

Alternatively, (g) the setting means may update the power value every time the power-residue calculating means executes the power-residue calculating.

[0037] It should be noted that the present invention may be realized as the following (1) to (5) as well as being realized as a threshold value generating apparatus.

[0038] (1) A method for controlling the threshold value generating apparatus (hereinafter referred to as a threshold value generating method), and a program for causing a computer system or the like to execute the threshold value generating method (hereinafter referred to as a threshold value generating program). ), A recording medium on which a threshold value generation program is recorded, an integrated circuit having the function of the threshold value generation device, or the like.

[0039] (2) A key issuing device that has the same function as the threshold value generating device, uses the threshold value as a secret key, and generates a public key that is paired with the secret key, and a method for controlling the key issuing device (hereinafter referred to as ), A program for causing a computer system or the like to execute the key issuing method (hereinafter referred to as a key issuing program), a recording medium storing the key issuing program, and a function of the key issuing device. It may be realized as an integrated circuit or the like.

[0040] (3) A decryption device that has the same function as the saddle value generation device, uses the saddle value as a secret key, performs a power-residue operation, and decrypts the ciphertext, and a method for controlling the decryption device (hereinafter, Called a decryption method), and a program for causing a computer system or the like to execute the decryption method (hereinafter referred to as a decryption method) This is called a decryption program. ), A recording medium in which a decoding program is recorded, an integrated circuit having a function of a decoding device, or the like.

[0041] (4) A signature generation device that has the same function as the threshold value generation device, uses the threshold value as a secret key, performs a power-residue operation, and generates signature data, and a method for controlling the signature generation device (hereinafter referred to as ), A program for causing a computer system or the like to execute the signature generation method (hereinafter referred to as a signature generation program), a recording medium on which the signature generation program is recorded, and a function of the signature generation apparatus. It may be realized as an integrated circuit provided.

[0042] (5) An encryption system comprising a plurality of devices, at least one of the plurality of devices being a decryption device, a key issuing device, and a signature generation device, and a method for controlling the encryption system (hereinafter referred to as encryption) Called a system control method), a program for causing a plurality of computer systems to execute the cryptographic system control method (hereinafter referred to as a cryptographic system control program), a recording medium on which the cryptographic system control program is recorded, and the like. This is fine.

The invention's effect

[0043] According to the present invention, by limiting the Hamming weight of the saddle value to a predetermined range, a saddle value having a no-mining weight smaller than the predetermined range is not generated, so that safety is reduced. And can prevent. Furthermore, even if the threshold value or the ming weight is leaked, it is possible to prevent the safety from deteriorating. Its value is great.

Brief Description of Drawings

[0044] FIG. 1 is a diagram showing an outline of calculation processing by a conventional binary method.

[FIG. 2] FIG. 2 is a diagram showing a configuration of a cryptographic system according to the first embodiment of the present invention.

FIG. 3 is a diagram showing a configuration of a key issuing server according to the first embodiment of the present invention.

FIG. 4 is a diagram showing a configuration of terminal apparatus A according to Embodiment 1 of the present invention.

[FIG. 5] FIG. 5 shows the calculation of the first power-residue calculating unit in Embodiment 1 according to the present invention. FIG. 3 shows a flowchart of the method.

[Fig. 6] Fig. 6 is a diagram showing a flowchart of a calculation method of the second power-residue calculating unit in the first embodiment according to the present invention.

FIG. 7 is a diagram showing a configuration of terminal apparatus B in the first embodiment according to the present invention.

[FIG. 8] FIG. 8 is a diagram showing an operation at the time of key issuance of the cryptographic system according to the first embodiment of the present invention.

[FIG. 9] FIG. 9 is a diagram showing operations during cryptographic communication of the cryptographic system according to the first embodiment of the present invention.

FIG. 10 is a diagram showing a configuration of a cryptographic system according to the second embodiment of the present invention.

[11] FIG. 11 is a diagram showing the configuration of the key issuing server in the second embodiment according to the present invention.

FIG. 12 is a diagram showing a configuration of terminal apparatus A in the second embodiment according to the present invention.

FIG. 13 is a diagram showing a configuration of terminal apparatus B in the second embodiment according to the present invention.

FIG. 14 is a flowchart showing an operation at the time of key issuance in the cryptographic system according to the second embodiment of the present invention.

FIG. 15 is a diagram showing an operation at the time of generating a first used secret key of the terminal device A in Embodiment 2 according to the present invention.

FIG. 16 is a diagram showing an operation at the time of generating a second used secret key of the terminal device B in the second embodiment according to the present invention.

FIG. 17 is a diagram showing an operation at the time of cryptographic communication of the cryptographic system according to the second embodiment of the present invention.

FIG. 18 is a diagram showing a conventional distribution of the number of multiplications.

FIG. 19 is a diagram showing a distribution of the number of multiplications in the present invention.

FIG. 20 is a diagram showing a distribution of appearance frequencies of the minimum number of multiplications in the present invention. The

FIG. 21 is a diagram showing a configuration of a terminal device A in a modified example according to the present invention.

FIG. 22 is a diagram showing a configuration of a terminal device B in a modified example according to the present invention. Explanation of symbols

1000, 2000 cryptosystem

1100, 2100 Key issuing sano

1101 Prime number generator

1102, 2102 Secret key generator

11021 random number generator

11022 Hamming weight judgment unit

1103, 2103 public key generator

1104, 2104 Key setting part

1200, 2200 terminal device A

1201 Transmitter

1202 Encryption section

12021 First power residue calculation unit

1203, 2203 Signature generator

12031, 22031

12032, 22032 Second power residue calculation unit

1204, 2204 First private key storage

1205 First public key storage

1206 Second public key storage

1300, 2300 Terminal device B

1301 Receiver

1302, 2302 Decryption section

13021 Second power residue calculation unit

1303 Signature Verification Department

13031 Hash calculator 13032 First power residue calculation unit

13033 Signature judgment part

1304, 2304 Second private key storage

1305 Second public key storage

1306 First public key storage

1400 communication channel

2207 First used secret key generator

22071 random number generator

22072 Used secret key candidate generator

22073 Hamming weight judgment part

2208 First private key storage

2307 Second used secret key generator

23071 Random number generator

23072 Used secret key candidate generator

23073 Hamming weight judgment part

2308 Second private key storage

BEST MODE FOR CARRYING OUT THE INVENTION

[Embodiment 1]

Embodiment 1 of the present invention will be described below with reference to the drawings.

[0047] The threshold value generating apparatus according to the present embodiment includes the following features (a) to (c).

[0048] (a) A power generation device that generates power used for power-residue calculation for positive integer c and modulus n, and (al) generation that generates candidate values that are candidates for power A function, (a2) a judgment function that determines whether the hamming weight of the candidate value falls within a predetermined range, and (a3) a candidate value if the judgment function determines that it belongs to the predetermined range. And a setting function for setting as a threshold value.

[0049] (b) The determination function uses a combination of the number of bits of modulus n and a predetermined positive integer as a first value, and determines a value determined based on the safety against brute force brute force attacks as a second value. In the case of a value, a predetermined positive integer determined under the condition that the first value exceeds the second value is within a predetermined range. The lower limit is determined.

[0050] (c) The determination function determines a positive integer determined under the condition that the processing time of the power-residue calculation is smaller than the predetermined time as the upper limit in the predetermined range.

Based on the above points, the threshold value generating apparatus in the present embodiment will be described. Here, the threshold value generating device is a key issuing device that uses the threshold value as a secret key and generates a public key that is paired with the secret key.

FIG. 2 is a diagram showing a configuration of the cryptographic system in the present embodiment. As shown in FIG. 2, the cryptographic system 1000 includes a key issuing server 1100, a terminal device A1200, a terminal device B1300, and a communication path 1400. Here, the key issuing server 1100 is a value generating device, that is, a key issuing device having a public key generating function for generating a public key that is paired with a secret key by using the value as a secret key.

The cryptographic system 1000 generates a key pair including a secret key and a public key for the terminal device A1200 and the terminal device B1300 at the key issuing server 1100, and generates the key pair generated for each of the terminal device A1200 and the terminal device B1300. Is issued. Further, the terminal device A1200 encrypts the first message, generates a signature of the second message, and transmits it to the terminal device B1300 via the communication path 1400. The terminal device B1300 receives the ciphertext of the first message, the second message, and its signature data via the communication path 1400, decrypts the ciphertext, and obtains the decrypted text of the first message. To verify the signature data of the second message.

Here, the RSA (Rivest-Shamir-Adelman) code system and RSA signature system used in the cryptographic system 1000 will be described.

[0055] RSA encryption is described on pages 110 to 113 of Reference Document 1 below. The RSA signature is described on pages 175 to 176 of this document. Here, the outline is explained.

[0056] [Reference 1]

Tatsuaki Okamoto, Hiroshi Yamamoto, "Contemporary Cryptography", Industrial Books (1997)

First, in the RSA encryption method, the following (1) to (3) are performed.

[0057] (1) Generate a key. [0058] As shown in the following (a) to (d), the public key and the secret key are calculated.

(A) Randomly large prime numbers p and q are selected, and the product “n = p X q” is calculated.

[0060] (b) The least common multiple of “p—1” and “q—1” “L = LCM (p—1, q—1)” is calculated.

[0061] (c) As shown in "l≤e≤L—l," and "GCD (e, L) = 1," a natural number e that is relatively prime to L and smaller than L is chosen at random. GCD (e, L) indicates the greatest common divisor of e and L.

(D) Calculate d that satisfies “e X d = 1 mod L”. From "GCD (e, L) = 1", such d always exists. Thus, the obtained integer e and integer n are public keys. The integer d is a secret key. Here, “X mod y” indicates the remainder when X is divided by y.

(2) Generate ciphertext.

[0064] As shown in Equation (11) below, ciphertext c is calculated by performing cryptographic operations on plaintext m using integer e and integer n, which are public keys.

[0065] [Equation 2]

(1-1) c = m ^e mod n

(3) Generate a decrypted text.

[0067] As shown in the following formula (12), decryption text m 'is calculated by performing decryption operation on ciphertext c using integer d that is a secret key. The decrypted text m ′ matches the plain text m.

[0068] [Equation 3]

(1-2) m '= c ^d mod n

= (m ^e ) ^d mod n

= ( _m exd mod L) mod n

= m ¹ mod n

= m mod n

[0069] In the RSA signature method, the following (1) to (3) are performed.

[0070] (1) Generate a key.

The key generation method is the same as that shown in (1) of the RSA encryption method.

(2) Generate a signature.

[0073] For message data D, calculate signature data S as shown in (a) and (b) below. To do.

[0074] (a) First, using the hash function Hash, the hash value of the message data D "h = Hash

(D) Calculate “.

[0075] (b) As shown in the following formula (13), the signature data S is calculated by using the integer d, which is a secret key, to multiply the dash value h by the d power.

[0076] painting

(1-3) S = h ^d mod n

[0077] (3) The signature is verified.

[0078] Whether the signature data S is correct and the signature of the message data D is verified as shown in (a) and (b) below.

[0079] (a) Check whether Hash (D) and "S ^e mod n" are equal.

(B) If they are equal, the signature data S is accepted as a correct signature. If they are not equal, the signature data S is rejected as an incorrect signature.

[0081] Next, the configuration of the key issuing server 1100 in the present embodiment will be described.

FIG. 3 is a diagram showing a configuration of the key issuing server 1100 in the present embodiment. As shown in FIG. 3, the key issuing server 1100 includes a prime number generation unit 1101, a secret key generation unit 1102,

A public key generation unit 1103 and a key setting unit 1104.

The prime number generation unit 1101 generates prime numbers p and q, which are secret information of RSA encryption. Note that prime generation is explained in Reference 2 below. Here, the explanation is omitted.

[0084] [Reference 2]

JP 2003-5644

The secret key generation unit 1102 generates a secret key d in the RSA encryption method.

Public key generation section 1103 calculates product n of prime numbers p and q, and further calculates “e = d− ¹ mod L”. Here, “L = LCM (p—1, q—1),” and “d— ¹ mod L” is an inverse element of d in mod.

[0086] The calculation method of the inverse element is described on pages 16 to 19 in Reference 3 below. Therefore, the description is omitted here.

[0087] [Reference 3]

H. Cohen, A Course in omputational Algebraic Number Theory, GTM 138, Springer— Verlag, 1996, p9

The key setting unit 1104 stores the secret key d generated by the secret key generation unit 1102 in the secret key storage unit of the terminal device Al 200 or the terminal device B 1300. Further, n and e generated by the public key generation unit 1103 are stored as public keys in the public key storage unit of the terminal device A1200 or the terminal device B1300.

[0088] Next, a detailed configuration of secret key generation section 1102 in the present embodiment will be described.

[0089] As shown in FIG. 3, secret key generation section 1102 generates a threshold value used in the power-residue calculation for positive integer c and modulus n, and uses the generated threshold value as a secret key. . At this time, a candidate value that is a candidate for the saddle value is generated, and it is determined whether or not the hamming weight of the candidate value is within a predetermined range. To do. Here, as an example, a random number generation unit 11021 and a no-ming weight determination unit 11022 are provided.

The random number generation unit 11021 generates a random number k.

[0091] The mingming weight determination unit 11022 calculates the hamming weight of the random number k, and determines whether the hamming weight is equal to or greater than a predetermined value tl and less than th. The ming weight is the number of bits whose bit value is 1 when the random number k is a bit string. For example, a Hamming weight of 5 is 2 because the 5 bit string is "101".

Then, secret key generation section 1102 generates random number k in random number generation section 11021.

In the ming weight determination unit 11022, it is determined whether the humming weight of the random number k is greater than or equal to tl and less than th. The Otherwise, the process returns to the random number generation unit 11021.

[0093] Here, tl is determined based on the security level against the brute force attack of the secret key. Specifically, for example, when the number of bits of n is 1024, X that becomes “2 ^8Q C (1024, x)” may be tl. Here, C (x, y) is the number of combinations to select x power y, and is expressed by the following formula (14). [0094] [Equation 5]

(1-4) C (x, y) = x! / {(X-y)! XY!}

[0095] Also, th is determined, for example, from the upper limit value of the processing time of a predetermined second power residue calculation unit 12032 (described later). In second power residue calculation section 12032, the number of multiplication Mul operations is “len−l + w (d)”. When the calculation time of the multiplication Mul is TMul, the processing time of the second power residue calculation unit 12032 is “(len−l + w (d)) XTMul”. If TH is the upper limit of processing time, set th to a value satisfying "th <TH / TMul-len + 1" from "(len-l + th) XTMuKTH"!

[0096] Next, the configuration of terminal apparatus A1200 in the present embodiment will be described.

FIG. 4 is a diagram showing a configuration of terminal apparatus A1200 in the present embodiment. As shown in FIG. 4, terminal device A1200 includes transmission unit 1201, encryption unit 1202, signature generation unit 1203, first secret key storage unit 1204, and first public key storage unit. 1205 and a second public key storage unit 1206 are provided.

Transmitting section 1201 transmits data to terminal apparatus B 1300 via communication path 1400.

[0099] Encryption unit 1202 encrypts first message ml using public key nB, eB of terminal device B1300 stored in second public key storage unit 1206 to generate ciphertext cl .

[0100] For the second message m2, the signature generation unit 1203 stores the secret key dA of the terminal device A1200 stored in the first secret key storage unit 1204 and the first public key storage unit 1205. Signature data S is generated using nA, which is a part of the public key of terminal device A1200 stored. Here, signature data S is generated based on the RSA signature method.

[0101] First secret key storage section 1204 stores secret key dA of terminal device A1200.

[0102] First public key storage section 1205 stores public keys nA and eA of terminal device A1200.

The second public key storage unit 1206 stores the public keys nB and eB of the terminal device B1300.

[0104] Next, the detailed configuration of the encryption key unit 1202 in the present embodiment will be described.

[0105] As shown in FIG. 4, encryption key unit 1202 includes first power residue calculation unit 12021.

[0106] The first power-residue calculating unit 12021 has an input value x, e represented by the following mathematical formula (1-5), Calculate "x ^e mod n" for n and n.

[0107] [Equation 6]

(1-5)

= e ₀ + e ₁ X2 + e ₂ X2 ² + ~ + e _len _ ₁ X2i ^en - ¹

Here, len is the number of bits of d, “X” is an integer multiplication, and “x ^y ” is x to the power of y.

FIG. 5 shows a flowchart of the calculation method of the first power residue calculation unit 12021.

FIG. 5 is a diagram showing a flow chart of the calculation method of first power residue calculation unit 12021 in the present embodiment. As shown in FIG. 5, the first power-residue calculating unit 12021 performs the following steps (S101) to (S107).

[0111] (S101): "i ^ len-2, z x" is performed to initialize variable i and variable z.

[0112] (S102): "z ^ Sqr (z) mod n" is performed to update the variable z.

(S103): It is determined whether or not “e = 1”, and if not (S103: e ≠ 1), step (S105) is performed.

(S104): If “e = 1” is determined as a result of the determination (S103: e = 1), “z Mul (z, c) mod n” is performed, and the variable z is updated.

[0115] (S105): "i ^ i-1" ^ TV \ Variable i is updated.

[0116] (S106): It is determined whether or not "i is 0". If not (S106: i≥0), step (S

102) Repeat the following steps.

[0117] (S107): If the result of determination is “i <0” (S106: i <0), the value of variable z is output and the process ends.

[0118] Here, Sqr (x) represents the result of performing x multiplication by two. Mul (x, y) indicates the result of multiplying x and y.

[0119] Then, in the first power residue calculation unit 12021, the encryption key unit 1202 inputs the first message ml as x, inputs eB which is a part of the public key as e, and makes it public as n Input nB that is part of the key, calculate "ml ^eB mod nB", and use the result as ciphertext cl.

Next, a detailed configuration of signature generation section 1203 in the present embodiment will be described. As shown in FIG. 4, signature generation section 1203 includes hash calculation section 12031 and second power residue calculation section 12032.

[0122] The first hash calculator 12031 calculates a hash value h for the second message m2. Here, the Noush function to be used only needs to have one-way property that it is difficult to obtain the input value of the hash function corresponding to the Nosh value. For example, the SHA-1 hash function. The one-way hash function is described in detail on pages 189 to 195 of Reference 1 above.

Second power-residue calculating unit 12032 calculates “x ^d mod n” for input value x, d indicated by the following mathematical formula (1-6), and n.

[0124] [Equation 7]

(1-6) 0 = ∑6 _t X2 0 or l: i = 0, l, "', len-l}

= d ₀ + d ₁ X2 + d.X2 ² + ---)-d _{| en} _ ₁ X2 ^len - ¹

FIG. 6 shows a flowchart of the calculation method of the second power residue calculation unit 12032.

FIG. 6 is a diagram showing a flow chart of a calculation method of second power residue calculation unit 12032 in the present embodiment. As shown in FIG. 6, the second power residue calculation unit 12032 performs the following steps (S 111) to (S 117).

[0127] (Sill): Perform "i ^ len-2, z x" to initialize the variable i and the variable z.

[0128] (S112): "z ^ Mul (z, z) mod n" is performed to update the variable z.

(S113): It is determined whether or not “d = l”. If not (S113: d ≠ l), step (S115) is performed.

(S114): If “d = 1” is determined as a result of the determination (S113: d = 1), “z Mul (z, c) mod n” is performed, and the variable z is updated.

[0131] (S115): “i ^ i—1” is performed to update the variable i.

(S116): It is determined whether or not “i <0”. If not (S116: i≥0), the steps after step (S112) are repeated.

[0133] (S117): If the result of determination is "i <0" (S116: i <0), the value of variable z is output and the process ends. [0134] Here, in step (S112), the square remainder of z may be calculated, but in Embodiment 1, the "multiplication" is explicitly performed so that the same number of multiplications are performed and the remainder is taken. use. This is because calculation is generally different between multiplication by two and multiplication is faster than multiplication by two. Here, the multiplication by the same number of multiplications by the calculation by two multiplications is realized. Means.

In the second power residue calculation unit 12032 described above, the multiplication is always executed len−1 times in step (S 112). However, in step (S114), multiplication is executed w (d) times for w (d) which is the Hamming weight of d. As a result, the total number of computations is “len− 1 + w (d)” times.

First, signature generation section 1203 calculates a no-shash value h for second message m 2 at noush calculation section 12031. Next, in the second power residue calculation unit 12032, the hash value h is input as X, the secret key dA is input as d, and nA that is a part of the public key is input as n, thereby calculating “h ^dA mod nA”. The result is signature data S.

[0137] Next, the configuration of terminal apparatus B1300 in the present embodiment will be described.

FIG. 7 is a diagram showing a configuration of terminal apparatus B1300 in the present embodiment. As shown in FIG. 7, the terminal device B 1300 includes a receiving unit 1301, a decrypting unit 1302, a signature verifying unit 1303, a second secret key storage unit 1304, and a second public key storage unit 1305. And a first public key storage unit 1306.

The receiving unit 1301 receives data from the terminal device A1200 via the communication path 1400.

[0140] The decryption key unit 1302 stores the secret key dB of the terminal device B 1300 stored in the second secret key storage unit 1304 and the public key stored in the second public key storage unit 1305. Using nB which is a part, decrypt ciphertext cl and generate decrypted text ml '.

[0141] The signature verification unit 1303 is the terminal device A120 stored in the first public key storage unit 1305.

Using the public key eA of 0, verify that the signature data S is the correct signature of the second message m2.

[0142] Second secret key storage section 1304 stores secret key dB of terminal apparatus B 1300.

The second public key storage unit 1305 stores the public keys nB and eB of the terminal device B1300.

The first public key storage unit 1306 stores the public keys nA and eA of the terminal device A1200. [0145] Next, a detailed configuration of decryption unit 1302 in the present embodiment will be described.

[0146] As shown in Fig. 7, decryption unit 1302 includes second power residue calculation unit 13021.

The second power residue calculation unit 13021 has the same function as the second power residue calculation unit 12032 included in the signature generation unit 1203 of the terminal device A1200, and thus description thereof is omitted.

Then, the decryption unit 1302 inputs the ciphertext cl as x, the secret key dB as d, and nB which is a part of the public key as n in the second power residue calculation unit 13021. cl ^dB mod nB "is calculated, and the result is the decrypted text ml.

[0149] Regarding the decryption method, the RSA encryption method "(2) Processing for generating ciphertext" is used.

[0150] Next, the detailed configuration of signature verification section 1303 in the present embodiment will be described.

As shown in FIG. 7, signature verification section 1303 includes hash calculation section 13031, first power residue calculation section 13032, and signature determination section 13033.

Since the node calculation unit 13031 has the same function as the hash calculation unit 12031 included in the signature generation unit 1203 of the terminal device A1200, the description thereof is omitted.

[0153] First power residue calculation unit 13032 has the same function as first power residue calculation unit 12021 included in encryption unit 1202 of terminal apparatus A1200, and thus the description thereof is omitted.

The signature determination unit 13033 determines whether or not the hash value h calculated by the hash calculation unit 13031 and the verification value h ′ calculated by the first power residue calculation unit 13032 are equal.

[0155] Then, signature verification section 1303 first calculates hash value h for second message m2 in node calculation section 13031. Next, in the first power residue calculation unit 13032, the signature data S is input as X, eA which is a part of the public key as e, and nA which is a part of the public key as n, and “S ^eA mod nA "is calculated, and the result is used as the verification value. In the signature judgment unit 13033, it is confirmed whether or not the hush value h and the verification value h are equal. If they are equal, OK is output as a correct signature, and NG is output as an incorrect signature if they are not equal.

Next, the operation of the cryptographic system 1000 in the present embodiment will be described. [0157] The operation of the cryptographic system 1000 is an operating force for "key issuance" for issuing a key and for "cipher communication" for performing cipher communication between the terminal device A1200 and the terminal device B1300.

[0158] At the time of “key issuance”, the key issuing server 1100 generates secret keys and public keys of the terminal device A1200 and the terminal device B1300, and stores them in the respective devices. At the time of “encryption communication”, the ciphertext of the first message ml and the signature data of the second message m2 are received in the terminal device A1200 for the input first message ml and second message m2. Is transmitted to the terminal device B 1300 via the communication path 1400, received by the terminal device B 1300, decrypted and signed, and decrypted text ml 'and the signature verification result (OK or NG ) Is output.

[0159] In the following, a flowchart of "at the time of key issuance" is shown in FIG.

[0160] Fig. 8 is a diagram showing an operation at the time of key issuance of the cryptographic system 1000 according to the present embodiment. As shown in FIG. 8, at the time of key issuance, the key issuing server 1100 generates prime numbers pA and qA in the prime number generation unit 110 1 (S201). The secret key generation unit 1102 generates a secret key dA (S202). The public key generation unit 1103 calculates “nA = pAX qA” and calculates “eA = dA− ¹ mod nA” (S203). The key setting unit 1104 stores the secret key dA in the first secret key storage unit 1204 of the terminal device A 1200 (S204). NA and eA are stored as public keys in the first public key storage unit 1205 of the terminal device A1200 (S205). NA and eA are stored in the first public key storage unit 1306 of the terminal device B 1300 (S206).

Furthermore, the key issuing server 1100 generates prime numbers pB and qB in the prime number generation unit 1101 (S207). The secret key generation unit 1102 generates a secret key dB (S208). The public key generation unit 1103 calculates “nB = pB X qB” and calculates “eB = dB— ¹ mod nB” (S209). In the key setting unit 1104, the secret key dB is stored in the second secret key storage unit 1304 of the terminal device B1300 (S210). N B and eB are stored as public keys in the second public key storage unit 1305 of the terminal device B 1300 (S211). NB and eB are stored in the second public key storage unit 12 06 of the terminal device A1200 (S212). And it ends.

[0162] Fig. 9 is a diagram showing an operation during cryptographic communication of the cryptographic system 1000 according to the present embodiment. As shown in FIG. 9, at the time of encrypted communication, the terminal device A1200 uses the encryption key unit 120. In 2, the ciphertext cl of the first message ml is generated (S301). The signature generation unit 1203 generates the signature data S of the second message m2 (S302). Transmitter 1201 transmits ciphertext cl, second message m2 and signature data S to terminal device B 1300 via communication path 1400 (S303).

[0163] On the other hand, terminal apparatus B1300 receives ciphertext cl, second message m2 and signature data S at receiving section 1301 (S304). In the decryption key unit 1302, the ciphertext cl is decrypted to obtain the decrypted text ml ′ (S305). The signature verification unit 1303 verifies the signature data S (S306). If the signature data S is correct and the signature of the second message (S306: S is correct), the signature verification result is OK (S307), and if it is not correct (S306: S is invalid), the signature verification result Is NG (S308).

Then, terminal apparatus B 1300 outputs the decrypted text ml ′ and the signature verification result (S309).

[0165] As described above, in the cryptographic system 1000 according to Embodiment 1, the key issuing server 1100 generates the secret key dA, dB having a Hamming weight not less than tl and less than th and generated the secret key dA. Is used by terminal device A1200, and secret key dB is used by terminal device B 1300. Terminal device A1200 and terminal device B1300 perform power-residue calculation using secret keys dA and dB, respectively. The power-residue calculation is executed by realizing the second multiplication by the same number of multiplications in the second power-residue calculation unit 12032. Therefore, it is difficult to analyze the secret key dA, dB by a power analysis attack that analyzes the order of two multiplications and multiplications. Furthermore, the key issuing server 1100 generates the Hamming weight of the secret key dA, dB so that it is greater than or equal to tl, and tl is longer than the processing time required for factoring the prime factor of n. Therefore, the terminal devices A 1200 and B 1300 of the first embodiment are safe against an attack that narrows the search space for the secret power of the number of operations.

[Embodiment 2]

Next, Embodiment 2 according to the present invention will be described with reference to the drawings.

[0167] The threshold value generating apparatus according to the present embodiment includes the characteristics shown in the following (a) to (c).

[0168] (a) The generation function has a given value d, a power-residue modulus n, a random number! And d + r X λ (η) or d + r X φ (η) are generated as candidate values using the Carmichael function (n) or Euler function φ (n). [0169] (b) The power generation device has a power-residue calculation function for performing power-residue calculation using the power.

[0170] (c) The threshold value generating apparatus has a threshold value storing function for storing a threshold value, and the power residue calculation function is stored in the threshold value storing function every time the power residue calculation is executed. Use saddle value

[0171] Based on the above points, the threshold value generating apparatus according to the present embodiment will be described. Note that the same constituent elements as those in the first embodiment are denoted by the same reference numerals, and description thereof is omitted. Also, here, the saddle value generating device uses the saddle value as a secret key, performs a power surplus operation, decrypts the ciphertext, and uses the saddle value as a secret key to perform a power surplus operation. A signature generation device that generates signature data.

FIG. 10 is a diagram showing a configuration of the cryptographic system in the present embodiment. As shown in FIG. 10, the cryptographic system 2000 includes a key issuing server 2100, a terminal device A 2200, a terminal device B 2300, and a communication path 1400. Here, the terminal device A 2200 is a threshold value generating device that generates signature data by performing a power residue calculation using the threshold value as a secret key, that is, a signature generating device. The terminal device B2300 is a threshold value generating device that decrypts a ciphertext by performing a power residue operation using the threshold value as a secret key, that is, a decryption device.

The cryptographic system 2000 generates a key pair consisting of a secret key and a public key for the terminal device A 2200 and the terminal device B 2300 using the key issuing server 2100, and generates the key pair generated for each of the terminal device A 2200 and the terminal device B 2300. Issue. Further, the terminal device A2200 encrypts the first message, generates a signature of the second message, and transmits it to the terminal device B2300 via the communication path 1400. The terminal device B2300 receives the ciphertext of the first message, the second message, and its signature data via the communication path 1400, decrypts the ciphertext, and obtains the decrypted text of the first message. To verify the signature data of the second message.

[0174] In the cryptographic system 2000, the RSA encryption method and the RSA signature method are used as in the first embodiment.

Subsequently, the configuration of the key issuing server 2100 in the present embodiment will be described.

FIG. 11 is a diagram showing a configuration of the key issuing server 2100 in the present embodiment. Fig 11 As shown in FIG. 4, the key issuing server 2100 differs from the key issuing server 1100 in the following points (1) to (3).

(1) A secret key generation unit 2102 is provided instead of the secret key generation unit 1102.

The secret key generation unit 2102 calculates “d = e− ¹ mod L” for the prime numbers p and q generated by the prime number generation unit 1101 and “e = 17”. Here, "L = LCM (p— 1, q— 1),” and “e mod L” is the inverse element of e at mod L. Note that e is only 17 and for example, “2 ^It may be ¹⁶ + 1 ".

(2) A public key generation unit 2103 is provided instead of the public key generation unit 1103.

Public key generation section 2103 calculates product n of prime numbers p and q, further sets “e = 17”, and uses n and e as public keys.

(018) A key setting unit 2104 is provided instead of the key setting unit 1104.

[0182] The key setting unit 2104 uses the primes p and q generated by the prime number generation unit 1101 and d generated by the secret key generation unit 2102 as a secret key in the secret key storage unit of the terminal device A2200 or the terminal device B2300. Store. Further, n and e generated by the public key generation unit 2103 are stored as public keys in the public key storage unit of the terminal device A2200 or the terminal device B2300.

Next, the configuration of terminal apparatus A 2200 in the present embodiment will be described.

FIG. 12 is a diagram showing a configuration of terminal apparatus A2200 in the present embodiment. As shown in FIG. 12, the terminal device A2200 differs from the terminal device A1200 in the following points (1) to (4).

(1) A signature generation unit 2203 is provided instead of the signature generation unit 1203.

[0186] The signature generation unit 2203 stores the used secret key dA stored in the first used secret key storage unit 2208 and the first public key storage unit 1205 for the second message m2. The signature data S is generated using nA that is part of the public key. For the signature generation method, use the (2) signature generation process of the RSA signature method. Here, the used secret key dA is a secret key generated from the secret key dA and used only within the terminal device A 2200 (hereinafter also referred to as a first used secret key).

(2) A first secret key storage unit 2204 is provided instead of the first secret key storage unit 1204.

[0188] The first secret key storage unit 2204 stores the secret keys pA, qA, dA of the terminal device A2200. (3) A first use secret key generation unit 2207 is newly provided.

[0190] The first used secret key generation unit 2207 uses the secret keys pA, qA, dA stored in the first secret key storage unit 2204 to use the used secret key dA 'Is generated only once and stored in the first used secret key storage unit 2208.

(4) A first use private key storage unit 2208 is newly provided.

[0192] The first used secret key storage unit 2208 stores the used secret key dA 'used in the power-residue calculation.

[0193] Next, a detailed configuration of the signature generation unit 203 in the present embodiment will be described.

As shown in FIG. 12, signature generation section 2203 includes hash calculation section 22031 and second power residue calculation section 22032.

Since the hash calculation unit 22031 has the same function as the hash calculation unit 12031 in the first embodiment, the description thereof is omitted.

[0196] Second power residue calculation unit 22032 has the same function as second power residue calculation unit 12032 in the first embodiment, and a description thereof will be omitted.

Then, signature generation section 2203 first calculates hash value h for second message m 2 at node calculation section 22031. Next, in the second power residue calculation unit 22032, X is a hash value h, d is a used secret key dA ′, and n is a part of the public key n

Input A, calculate “h ^dA 'mod nA”, and set the result as signature data S.

Next, a detailed configuration of the first used secret key generation unit 2207 in the present embodiment will be described.

[0199] As shown in FIG. 12, the first used secret key generation unit 2207 generates a threshold value used in the power-residue calculation for the positive integer c and modulus n, and generates the generated threshold value. Is used as the first used private key. At this time, a candidate value that is a candidate for the threshold value is generated, it is determined whether the hamming weight of the candidate value is within a predetermined range, and if it is within the predetermined range, the candidate value is set as the threshold value To do. Here, as an example, a random number generation unit 22071, a used secret key candidate generation unit 22072, and a ming weight determination unit 22073 are provided.

[0200] The random number generation unit 22071 generates a random number r that is a positive integer. The number of bits of the random number is, for example, 32.

[0201] Use secret key candidate generation section 22072 generates use secret key candidate dA 'represented by the following equation (2-1) using random number r and secret keys pA, qA, dA.

[0202] [Equation 8]

(2-1) dA '= dA + rX A CnA)

[0203] [Equation 9]

(2-2) λ (nA) = LCM (pA-l, qA-l)

[0204] Here, λ (ηΑ) shown in the above equations (2-1) and (2-2) is a Carmichael function. Instead of the Carmichael function (ηΑ), the Euler function φ (ηΑ) represented by the following equation (2-3) may be used.

[0205] [Equation 10]

(2-4) φ (ηΑ) = (ρΑ-1) X (qA-1)

[0206] The ming weight determination unit 22073 determines whether the ming weight of the used secret key candidate dA 'is equal to or greater than a predetermined value tl and less than th.

Then, first use secret key generation section 2207 generates random number r in random number generation section 22071. The used secret key candidate generation unit 22072 calculates a used secret key candidate dA, using the random number r and the secret keys pA, qA, dA. The ming weight determination unit 22073 determines whether the ming weight of the used secret key candidate dA ′ is greater than or equal to tl and less than th. If it is greater than or equal to tl and less than th, the used secret key candidate dA ′ (candidate value) ) Is set as the first used secret key (value) and stored in the first used secret key storage unit 2208. Otherwise, the process returns to the random number generation unit 22071.

[0208] tl is determined based on the security level against the brute force attack of the secret key.

[0209] Specifically, for example, when the number of bits of n is 1024, X that satisfies "2 ^8Q <C (1024, x)" may be set to tl. Where C (x, y) is the number of combinations that select x and y forces.

It is indicated by (1 4). [0210] th is determined from, for example, a predetermined upper limit value of the processing time of the second power residue calculating unit 22032, which is determined in advance. In second power residue calculation section 22032, the number of operations of multiplication Mul is “le n−l + w (d)”. When the calculation time of the multiplication Mul is TMul, the processing time of the second power residue calculation unit 22032 is “(len−l + w (d)) XTMul”. If TH is the upper limit of the processing time, set th to a value that satisfies "th> TH / TMul—len + 1" from "(len— 1 + th) XTMuKTH".

[0211] Here, the relationship between dA, which is a part of the secret key, and the used secret key dA will be described.

When the used secret key dA is generated as described above, “dA ′ = dA + r X λ (nA)” or “dA ′ = dA + r X φ (nA)” is satisfied. Euler's theorem satisfies the following formulas (2-4) and (2-5) for any nA and a positive integer x that is relatively prime.

[0213] [Equation 11]

(2-4) χ ^λ ( ^πΑ ) = 1 [0214] [ ^Equation 12]

(2-5) χ Ψ ( ^ηΑ ) = 1

[0215] Therefore, as indicated by the following mathematical formula (2-6), the power of dA in the mod nA of the second message m2 is equal to the power of dA. The same is true for φ (nA).

[0216] [Equation 13]

(2-6 m2 ^dA '= m2 ( ^{dA + rx A} ( ^nA ))

= (m2 ^dA ) x (m2 ^A ( ^nA )) ^r

= m2 ^dA mod nA

Therefore, the signature data generated using the secret key dA is equal to the signature data generated using the used secret key dA ′ as in the present embodiment. As a result, the signature can be generated without any problem even if the used secret key dA 'is used instead of the secret key dA without changing the public key.

[0218] Next, the configuration of terminal apparatus B2300 in the present embodiment will be described.

[0219] FIG. 13 is a diagram showing a configuration of terminal apparatus B in the present embodiment. Shown in Figure 13 As described above, the terminal device B2300 differs from the terminal device B1300 in the following points (1) to (4).

(1) A decoding key unit 2302 is provided instead of the decoding key unit 1302.

[0221] The decryption key unit 2302 includes the used secret key dB 'of the terminal device B2 300 stored in the second used secret key storage unit 2308 and the public key stored in the second public key storage unit 1305. Using nB, which is a part of the key, the ciphertext cl is decrypted to generate a decrypted text ml '. Here, the used secret key dB ′ is a secret key generated from the secret key dB and used only in the terminal apparatus B 2300 (hereinafter also referred to as a second used secret key).

(2) A second secret key storage unit 2304 is provided instead of the second secret key storage unit 1304.

[0223] Second secret key storage section 2304 stores secret keys pB, qB, dB of terminal device B2300

(3) A second use secret key generation unit 2307 is newly provided.

[0225] The second used secret key generation unit 2307 uses the secret key pB, qB, dB stored in the second secret key storage unit 2304 to use the used secret key dB used in the power-residue calculation dB 'Is generated only once and stored in the second used secret key storage unit 2308.

(4) A second used secret key storage unit 2308 is newly provided.

[0227] The second used secret key storage unit 2308 stores the used secret key dB 'used in the power-residue calculation.

[0228] Next, a detailed configuration of decoding section 2302 in the present embodiment will be described.

As shown in FIG. 13, decryption unit 2302 includes second power residue calculation unit 23021.

[0230] The second power residue calculation unit 23021 has the same function as the second power residue calculation unit 13021 in Embodiment 1, and thus the description thereof is omitted.

[0231] Then, the decryption unit 2302 inputs the ciphertext cl as x, the used secret key dB 'as x, and nB that is a part of the public key as n in the second power residue calculation unit 23021, "cl ^dB 'mod nB" is calculated, and the result is the decrypted text ml.

[0232] Next, a detailed configuration of the second used secret key generation unit 2307 in the present embodiment will be described. [0233] As shown in Fig. 13, the second used secret key generation unit 2307 generates a threshold value used for the power-residue calculation for the positive integer c and modulus n, and the generated threshold value is the second value. Use as a private key. At this time, a candidate value that is a candidate for the threshold value is generated, it is determined whether the hamming weight of the candidate value is within a predetermined range, and if it is within the predetermined range, the candidate value is set as the threshold value. Set. Here, as an example, a random number generation unit 23071, a used secret key candidate generation unit 23072, and a half-ming weight half IJ definition 23073 are provided.

[0234] The random number generation unit 23071 generates a random number r that is a positive integer. The number of bits of the random number is, for example, 32.

Use secret key candidate generation section 23072 generates use secret key candidate dB ′ represented by the following equation (2-7) using random number r and secret keys pB, qB, dB.

[0236] [Equation 14]

(2-7) dB '= dB + rx λ (ηΒ)

[0237] [Equation 15]

(2-8) λ (nB) = LCM (pB-l, qB-l)

Where λ (ηΒ) is the Carmichael function. Instead of the Carmichael function λ (ηΒ), the Euler function φ (ηΒ) represented by the following equation (2-9) may be used.

[0239] [Equation 16]

(2-9) (ηΒ) = (ρΒ-1) Χ (ςΒ-1)

[0240] The ming weight determination section 23073 determines whether the hamming weight of the used secret key candidate dB 'is greater than or equal to a predetermined value tl and less than th.

Then, second used secret key generation section 2307 generates random number r in random number generation section 23071. The used secret key candidate generation unit 23072 calculates the used secret key candidate dB ′ using the random number r and the secret keys pB, qB, dB. In the ming weight determination unit 23073, it is determined whether the hamming weight power of the used secret key candidate dB ′ is ¾1 or more and less than th, and if it is tl or more and less than th, the used secret key candidate dB ′ (candidate value) is determined. Set it as the second private key (low value) Stored in the second used secret key storage unit 2308. Otherwise, the process returns to the random number generator 23071.

[0242] Here, the relationship between dB, which is a part of the secret key, and the used secret key dB 'will be described.

When the used secret key dB is generated as described above, “dB ′ = dB + r X λ (nB)” or “d B ′ = dB + rX (nB)” is satisfied. Euler's theorem satisfies the following formulas (2-10) and (2-11) for any nB and a positive integer x that is relatively prime.

[0244] [Equation 17]

(2-10) χ ^λ ( ^πΒ ) = 1

[0245] [Equation 18]

(2-11) χΦ ( ^πΒ ) = 1

[0246] Therefore, as shown in the following formula (2-12), the power of dB in mod nB of the ciphertext cl is equal to the power of dB. The same is true for φ (nB).

[0247] [Equation 19]

(2-l2) cl ^dB '='"1 ^{dB + rX λ} (nB)

= (Cl ^dB ) X (Cl ^A ( ^nB )) ^r

= cl ^dB mod nB Therefore, the decrypted text generated using the secret key dB is equal to the decrypted text generated using the used secret key dB ′ as in the present embodiment. As a result, decryption can be performed without any problem even if the used private key dB ′ is used instead of the private key dB without changing the public key.

[0248] Next, the operation of the cryptographic system 200 in the present embodiment will be described.

[0249] The operation of the cryptographic system 2000 is as follows: "When issuing a key" for issuing a key, "When generating a first used secret key" for generating a first used secret key in the terminal device A2200, In B2300, the operation power is “at the time of generating the second used secret key” for generating the second used secret key and “at the time of encrypted communication” for performing the encrypted communication between the terminal device A2 200 and the terminal device B2300.

[0250] When the key is issued, the key issuing server 2100 uses the terminal device A2200 and the terminal device B2 300 private keys and public keys are generated and stored in each device. In “when the first used secret key is generated”, the terminal device A2200 generates the first used secret key from the secret key of the terminal device A2200. In “when the second used secret key is generated”, the terminal device B2300 generates the second used secret key from the secret key of the terminal device B2300. At the time of “encryption communication”, the ciphertext of the first message ml and the signature data of the second message m2 are generated in the terminal device A2200 for the first message ml and the second message m2 that are input. The data is transmitted to the terminal device B2300 via the communication path 1400, received by the terminal device B2300, decrypted and signed, and the decrypted text ml 'and the signature verification result (OK or NG) are output. To do.

[0251] Fig. 14 shows the flowchart for "when issuing a key", Fig. 15 shows the flowchart for "when generating a first used secret key", and Fig. 16 shows the flowchart for "when generating a second used secret key". Fig. 17 shows the flowchart for "Cryptographic communication".

FIG. 14 is a diagram showing an operation at the time of key issuance of the cryptographic system 2000 in the present embodiment. As shown in FIG. 14, at the time of key issuance, the key issuing server 2100 generates prime numbers pA and qA in the prime number generation unit 1101 (S401). The secret key generation unit 2102 generates a secret key dA (S402). The public key generation unit 2103 calculates “nA = pAX qA” and calculates eA (S403). In the key setting unit 2104, the secret keys pA, qA, dA are stored in the first secret key storage unit 2204 of the terminal device A2200 (S404). NA and eA are stored as public keys in the first public key storage unit 1205 of the terminal device A2200 (S405). NA and eA are stored in the first public key storage unit 1306 of the terminal device B2300 (S406).

Furthermore, the key issuing server 2100 generates prime numbers pB and qB in the prime number generation unit 1101 (S407). The secret key generation unit 2102 generates a secret key dB (S408). The public key generation unit 2103 calculates “nB = pB X qB” and calculates eB (S409). The key setting unit 2104 stores the secret keys pB, qB, and dB in the second secret key storage unit 2304 of the terminal device B2300 (S410). NB and eB are stored as public keys in the second public key storage unit 1305 of the terminal device B2300 (S411). NB and eB are stored in the second public key storage unit 1206 of the terminal device A2200 (S412). And it ends.

FIG. 15 shows the operation at the time of generating the first used secret key of terminal device A 2200 in the present embodiment. It is a figure which shows work. As shown in FIG. 15, when the first used secret key is generated, the terminal device A 2200 generates a random number r in the first used secret key generation unit 2207 (S421). Using the secret keys pA, qA, dA stored in the one secret key storage unit 2204, a secret key candidate dA ′ to be used is calculated (S422). If the nominating weight of the used secret key candidate dA, obtained by calculation is greater than or equal to tl and less than th (S423: Yes), the first used secret key is used as the first secret key used dA '. Is stored in the used secret key storage unit 2208 (S424). On the other hand, when the ming weight is not less than tl and less than th (S423: No), the process is again executed from the process (S421) for generating the random number r.

[0255] FIG. 16 is a diagram showing an operation when the second used secret key is generated by terminal apparatus B2300 in the present embodiment. As shown in FIG. 16, when generating the second used secret key, the terminal device B 2300 generates a random number r in the second used secret key generation unit 2307 (S431), and the generated random number r and Using the secret keys pB, qB, dB stored in the second secret key storage unit 2304, a secret key candidate dB ′ is calculated (S432). If the value of the used secret key candidate dB 'obtained by calculation is greater than or equal to tl and less than th (S433: Yes), the second used secret key is used as the second used secret key. It is stored in the used secret key storage unit 2308 (S434). On the other hand, if the ming weight is not less than tl and less than th (S433: No), the process is again executed from the process (S431) for generating the random number r.

[0256] FIG. 17 is a diagram showing an operation at the time of cryptographic communication of the cryptographic system 2000 in the present embodiment. As shown in FIG. 17, at the time of encrypted communication, the terminal device A 2200 generates the ciphertext cl of the first message ml in the encryption unit 1202 (S501). The signature generation unit 2203 generates the signature data S of the second message m2 (S502). Transmitter 1201 transmits ciphertext cl, second message m2 and signature data S to terminal device B2300 via communication path 1400 (S503).

On the other hand, terminal apparatus B 2300 receives ciphertext cl, second message m 2 and signature data S at receiving section 1301 (S 504). In the decryption key section 2302, the ciphertext cl is decrypted to obtain the decrypted text ml ′ (S505). The signature verification unit 1303 verifies the signature data S (S506). If the signature data S is correct and the signature of the second message (S506: S is correct), the signature verification result is OK (S507), and if the signature is incorrect (S506: S is invalid), and the signature verification result is NG (S508).

Then, the terminal device B 2300 outputs the decrypted text ml ′ and the signature verification result (S509).

[0259] As described above, in the cryptographic system 2000 according to the second embodiment, in the terminal device A2 200 and the terminal device B2300, the used secret keys dA ′ and dB ′ having a hamming weight not less than tl and less than th are used. The generated private key dA ′ is generated and used by the signature generation unit 2203 of the terminal device A2200, and the used private key dB ′ is used by the decryption unit 2302 of the terminal device B2300. The terminal device A2200 and the terminal device B2300 perform the power-residue calculation using the used secret keys dA ′ and dB ′, respectively. The power-residue calculation is executed by realizing the second multiplication by the same number of multiplications in the second power-residue calculating unit 22032 and the second power-residue calculating unit 23021.

[0260] Therefore, it is difficult to analyze the secret key dA, dB by a power analysis attack that analyzes the order of two multiplications and multiplications. In addition, the terminal device A2200 and the terminal device 2300 generate the ming weights of the used secret keys dA 'and dB' to be tl or more, and tl is the processing time required for the brute force attack of the secret key n Therefore, the terminal device A2200 and terminal device B2300 of the second embodiment are safe even against attacks that narrow the secret key search space from the number of computations. .

That is, as shown in FIG. 18, the threshold value used in the conventional power-residue calculation may be generated when the humming weight is small or large. If the weight is small, the safety is low. If the Hamming weight is large, the calculation time is long.

On the other hand, as shown in FIG. 19, the power value used in the power-residue calculation of the present invention is generated so that the weighting weights are within a certain range. And since the Hamming weights fall within a certain range, it is safe and the calculation time is not prolonged.

[0263] As a result, the key issuing server 1100 in the first embodiment and the terminal device A2200, the terminal device B2300, etc. in the second embodiment ensure the security of the RSA encryption against a simple power analysis attack! RU

[0264] For the 512-bit threshold value d, a random number r that minimizes the Hamming weight of the used secret key d, among the numbers with tl = 15 or more, is searched in the 8-bit range, and the used secret key d 'may be generated. Fig. 20 is a graph plotting the frequency of occurrence of multiplication when such a used secret key d is generated. From this graph, after application of the present invention, it is multiplied about 20 times before application. It is shown that the number of times is reduced, and calculation time is about 3% faster.

[0265] (Modification)

The embodiment described above is an example of the implementation of the present invention, and the present invention is not limited to this embodiment in any way, and can be implemented in various modes without departing from the scope of the invention. It is possible. For example, the following cases (1) to (14) are also included in the present invention.

(1) In Embodiments 1 and 2, the key issuing server sends the generated public key and secret key to the first secret key storage unit and the second secret key of the terminal device A and the terminal device B, respectively. The private key storage unit, the first public key storage unit, and the second public key storage unit are directly stored and issued, but may be issued via a communication channel or a recording medium.

[0267] (2) In Embodiment 1, after determining the secret key d, e is determined. However, after e is determined as in Embodiment 2, d is determined. May be. In that case, the Hamming weighting force of the secret key d is ¾1 or more and less than th using the Carmichael function or the Euler function, as is done in the terminal device A2200 and the terminal device B2300 of the second embodiment. You can correct it to ヽ. Also in the second embodiment, e may be determined after fixing the secret key d without fixing e.

(3) In Embodiment 2, the used secret keys dA ′ and dB ′ may be generated every time during encrypted communication. That is, the used secret key used for the power residue calculation instead of the secret key may be changed every time the power residue calculation is executed in the terminal device. At this time, the used secret key is generated using random numbers so that the Hamming weight of the used secret key falls within a certain range.

[0269] For example, as shown in FIG. 21, the signature generation unit 3203 includes a first used secret key generation unit 3207, and is used every time a modular exponentiation operation is performed. You can also use to generate the signature generation process.

Here, the first used secret key generation unit 3207 generates the used secret key dA ′ every time the second power residue calculation unit 32032 executes the power residue calculation. At this time, similarly to the first used secret key generation unit 2207 in the second embodiment, the secret key dA is used to generate a used secret key dA ′ having a hamming weight not less than tl and less than th. Second power residue calculation unit 320 32 uses the used secret key dA ′ generated each time the power-residue calculation is executed, and performs the power-residue calculation in the same way as the second power-residue calculation unit 22032 in the second embodiment.

[0271] Also, as shown in FIG. 22, the decryption unit 3302 includes a second used secret key generation unit 3307, and uses the used secret key dB ′ that is updated each time a power-residue operation is performed. You may use it to perform the decryption process.

Here, the second used secret key generating unit 3307 generates the used secret key dB ′ every time the second power residue calculating unit 33021 executes the power residue calculation. At this time, similarly to the second used secret key generation unit 2307 in the second embodiment, the secret key dB is used to generate a used secret key dB ′ having a ming weight of less than tl and less than th. The second power residue calculation unit 33021 uses the used secret key dA ′ generated each time the power residue calculation is performed, and is similar to the second power residue calculation unit 23021 in the second embodiment. Performs power-residue operation.

[0273] Or, it is assumed that the used private keys dA 'and dB' are generated only once after the process of key issuance.

(4) In Embodiments 1 and 2, RSA encryption may be used as the encryption method, or an encryption method that performs a power-residue operation, for example, ElGamal encryption. In ElGamal cryptography, the secret key is a value x, and the public key is "g ^x mod p" using the prime p given in advance in the whole system and g which is an integer from 1 to p—1. And get. These secret keys and public keys are generated by the key issuing server. At this time, the secret key generation unit 1102 of the first embodiment may use the random number k generated for the terminal device B 1300 as the secret key X of the ElGamal encryption. Also, in the secret key generation unit 2102 of the second embodiment, the random number k generated for the terminal device B2300 is set as the ElGamal encryption secret key X, and in the second use secret key generation unit 2307, “g ^x> mod P” If the order of is q, "x '= x + r X q" and a random number r is generated until the Hamming weight is greater than or equal to tl and less than th. 'May be generated as a used private key.

[0275] (5) The present invention may be a threshold value generating device that generates a threshold value so as to be a Hamming weight force ¾1 or more and less than th, and performs a power-residue calculation using the threshold value. This threshold generator is D H (Diffie-Hellman) key agreement or DSA (Digital Signature Algorithm) signature method may be used.

(6) Specifically, each of the above devices is a microprocessor, a ROM (Read Only Memory), a RAM (Random Access Memory), a node disk unit, and a Tisf. It is a computer system that also includes power such as a ray unit, keyboard, and mouse. A computer program is stored in the RAM or hard disk unit. Each device achieves its functions through the microprocessor's operation according to the computer program. Here, the computer program is configured by combining a plurality of instruction codes indicating instructions for the computer in order to achieve a predetermined function.

(7) A part or all of the constituent elements constituting each of the above devices may be constituted by one system LSI (Large Scale Integration). A system LSI is an ultra-multifunctional LSI that is manufactured by integrating multiple components on a single chip. Specifically, it is a computer system that includes a microprocessor, ROM, RAM, and so on. It is. A computer program is stored in the RAM. Microprocessor power The system LSI achieves its functions by operating according to the computer program.

[0278] (8) A part or all of the components constituting each of the above devices may be configured as an IC card that can be attached to and detached from each device or a single module force. An IC card or module is a computer system composed of a microprocessor, ROM, RAM, and so on. The IC card or module may include the above-mentioned super multifunctional LSI. The IC card or module achieves its functions by the microprocessor operating according to the computer program. This IC card or this module may be tamper resistant.

(9) The present invention may be the method described above. Also, it may be a computer program that realizes these methods by a computer, or it may be a digital signal that also serves as a computer program.

[0280] (10) The present invention also provides a computer program or a digital signal stored in a computer. A readable recording medium such as a flexible disk, hard disk, CD-RO

It may be recorded on M, MO, DVD, DVD-ROM, DVD-RAM, BD (Blu-ray Disc), semiconductor memory, or the like. It may also be a digital signal recorded on these recording media! /.

[0281] (11) Further, the present invention may transmit a computer program or a digital signal via a telecommunication line, a wireless or wired communication line, a network represented by the Internet, a data broadcast, or the like. .

[0282] (12) Further, the present invention may be a computer system including a microprocessor and a memory, wherein the memory stores a computer program, and the microprocessor operates according to the computer program.

[0283] (13) Also, the program or digital signal may be recorded on a recording medium and transferred, or the program or digital signal may be transferred via a network or the like by another independent computer system. You can do it.

[0284] (14) The above embodiment and the above modifications may be combined! /, Respectively.

Industrial applicability

[0285] The present invention can be used as an encryption device that is safe against an attack method that analyzes an encryption key embedded in an encryption module by measuring the power consumption when executing encryption processing. Can be used for IJ.

Claims

The scope of the claims

[1] A threshold value generating device for generating a threshold value used in the power-residue calculation for positive integer c and modulus n,

Generating means for generating candidate values that are candidates for the saddle value;

A determination unit that determines whether or not the hamming weight of the candidate value falls within a predetermined range; and a setting that sets the candidate value as the saddle value when the determination unit determines that the hamming weight is within the predetermined range. Means and

An apparatus for generating saddle values, comprising:

[2] The generation means uses the power value d given in advance, the power-modulation remainder method n, the random number!:, And the Carmichael function (n) or the Euler function φ (n), and d + r X λ (η) or d + r X φ (η) is generated as the candidate value

The threshold value generating apparatus according to claim 1, wherein:

[3] The determination means uses a combination of the number of bits of the modulus η and a predetermined positive integer as a first value, and is a value determined based on the safety against the brute force attack of the above value! Is determined to be the lower limit of the predetermined range determined by the condition that the first value exceeds the second value.

The threshold value generating apparatus according to claim 1, wherein:

[4] The determination unit determines a positive integer determined under a condition that a processing time of the power-residue calculation is smaller than a predetermined time as an upper limit in the predetermined range.

The threshold value generating apparatus according to claim 1, wherein:

[5] The power generation device further performs power residue calculation means for performing the power residue calculation using the power value.

The threshold value generating apparatus according to claim 1, comprising:

[6] The threshold value generating device further includes threshold value storage means for storing the threshold value,

The power-residue calculating means uses the power value stored in the power-value storing means every time the power-residue operation is executed.

The threshold value generating apparatus according to claim 5, wherein:

[7] The setting means updates the power value every time the power-residue calculation is executed by the power-residue calculating means.

The threshold value generating apparatus according to claim 5, wherein:

[8] The threshold value generating device further uses the threshold value as a secret key to generate a public key pairing with the secret key.

The threshold value generating apparatus according to claim 1, comprising:

[9] The generation unit generates the threshold used as the secret key based on an RSA encryption method.

The threshold value generating apparatus according to claim 8, wherein:

[10] The power-residue calculating means decrypts the ciphertext by performing the power-residue calculation using the power value as a secret key.

The threshold value generating apparatus according to claim 5, wherein:

11. The threshold value generating apparatus according to claim 10, wherein the power-residue calculating unit decrypts the ciphertext based on an RSA encryption method.

[12] The power-residue calculating unit generates signature data by performing the power-residue calculation using the power value as a secret key.

The threshold value generating apparatus according to claim 5, wherein:

13. The threshold value generating apparatus according to claim 12, wherein the power-residue calculating unit generates the signature data based on an RSA signature method.

[14] A threshold value generation method for generating a threshold value used in a power residue operation on a positive integer c and modulus n,

Generating a candidate value that is a candidate for the threshold;

A determination step for determining whether or not the hamming weight of the candidate value falls within a predetermined range;

A setting step for setting the candidate value as the above-described value when it is determined in the determination step that it falls within a predetermined range;

A threshold value generating method characterized by comprising:

[15] An integrated circuit that generates a power value used for a power-residue operation on positive integer c and modulus n. About

A determination unit that determines whether or not the hamming weight of the candidate value is within a predetermined range; and a setting that sets the candidate value as the saddle value when the determination unit determines that the hamming weight is within the predetermined range. Means and

An integrated circuit comprising:

[16] A computer-readable recording medium recording a program for generating a power value used for a power-residue operation on a positive integer c and modulus n,

Generating a candidate value that is a candidate for the threshold;

A setting step for setting the candidate value as the preceding value when it is determined in the determination step that the value falls within a predetermined range;

A computer-readable recording medium on which a program for causing a computer system to execute is recorded.

[17] A program for generating a power value used in a power residue operation on a positive integer c and modulus n,

Generating a candidate value that is a candidate for the threshold;

A program characterized by causing a computer system to execute.