JP5097102B2 - Hierarchical ID-based encryption device and decryption device, method thereof, program, and recording medium - Google Patents

Description

  The present invention relates to an apparatus for encrypting data, and more particularly, to a hierarchical ID-based encryption apparatus and decryption apparatus that use well-known user information as an encryption key for public key encryption, a method, a program thereof, and a recording medium.

  The ID-based encryption method is an application technique of public key encryption method that uses well-known personal information that can uniquely identify a recipient, such as a recipient's ID and email address, as a public key of the public key encryption method. Since well-known personal information is used as a public key, it is not necessary to confirm the authenticity of the public key (by a public key certificate) unlike a general public key cryptosystem, which is excellent in convenience. However, the ID-based encryption method is a method in which a key generation center (hereinafter referred to as “node”) is responsible for generating a secret key. Authentication of a recipient who requests generation of a secret key, generation of a secret key, and Since each node is responsible for each process, such as secure distribution of the private key to the recipients, the number of users will eventually reach the limit of the processing capacity due to the increase in users, and the number of users will no longer increase. There was a problem that.

  Therefore, by arranging a plurality of nodes hierarchically, it is possible to distribute the load on the nodes by appropriately assigning recipients (IDs) to each node, and it is possible to easily add nodes. An ID-based encryption scheme has been devised (see Non-Patent Document 1). The outline will be described below.

  In the hierarchical ID-based encryption method, the receiver's private key (corresponding to the ID) assigned to each node under the highest node (hereinafter referred to as “root”) is basically received. The parent node of the node to which the person is assigned generates from the ID of the receiver and the private key received from the parent node of the parent node, and distributes it to the receiver.

This series of processing will be described in detail with reference to the block diagram of FIG. 6 by taking as an example a case where the nodes are configured in three layers of a route, a first node, and a second node from the top. In this configuration, for example, when there is a use request from the receiver 2 belonging to the second node 12 to the first node 11 (here, the receiver 1), the receiver 1 first authenticates the receiver 2, The private key (S ₁ , Q ₀ ) is received from the route 10. Then, a secret key (S ₂ , Q ₁ ) of the receiver 2 is generated from the ID information set (id ₀ , id _1a , id _2a ) of the receiver 2 that is well-known information and distributed to the receiver 2 To do. Even when there is a layer below the third node, the secret key is distributed in the same manner. Note that when the recipient 1 there is usage request to the root 10 belonging to the first node 11, on the route 10 has authenticated the recipient 1, the recipient is a well-known information and the secret key s ₀ by itself holds 1 The secret key (S ₁ , Q ₀ ) of the receiver 1 is generated from the ID information set (id ₀ , id _1a ) and distributed to the receiver 1. When the sender 3 sends the plaintext M encrypted to the receiver 1, the sender 3 transmits the ID information set (id ₀ , id _1a ) of the receiver 1 as well-known information and the public parameters P ₀ , p of the route. , Q ₀ is used to create and transmit ciphertext m from plaintext M, and the receiver 1 who receives the ciphertext m receives his / her private key (S ₁ , Q ₀ ) distributed from the route 10. To decrypt plaintext M. In the configuration example of FIG. 1, only one user is allocated to each node, but a plurality of users may be allocated.

  A conventional hierarchical ID-based encryption scheme is composed of four functions: initial setting, key generation, encryption, and decryption. Hereinafter, an example of processing for each function will be described.

≪Initial setting≫
The initial setting is a root function, which generates a root secret key s ₀ and public parameters P ₀ , p, Q ₀ for all users. Also, id ₀ is set as route ID information. In the configuration of FIG. 6, the route 10 has the function.

In this method, in order to perform an operation on an elliptic curve, an elliptic curve E defined on the finite field F _q and a base point P ₀ (order: p) on the elliptic curve E are determined, and then Process.
(1) Generate a random integer s ₀ ε {0, 1, 2,..., P−1}.
(2) Q ₀ = s ₀ · P ₀ is calculated.
(3) Output P ₀ , p, Q ₀ .

≪Key generation≫
The key generation function is a function of the root and each node other than the root (each recipient belonging to), and issues a secret key corresponding to the ID information set of each recipient belonging to the lower node. Hereinafter, a process in which a node at the (t−1) -th layer issues a secret key for the recipient of the node at the t-th layer will be described (layer 0 is the root). Since the process is divided into three types depending on the value of t, each will be described. In the configuration of FIG. 6, the key generation devices 21 and 22 have the function.

<When t = 1>
The route is a process of issuing a secret key for the recipient of the first layer node (see FIG. 7).
[input]
-ID information set of receiver (well-known information, character string): id ₀ , id ₁
-Route public parameters (generated by default): Q ₀
-Root secret key (generated by default): s ₀
[Processing content]
(1) P ₁ is calculated by P ₁ = IDenc (id ₀ ‖id ₁ ).

(IDenc is a function that maps a character string onto an elliptic curve E, and ‖ represents concatenation)
(2) S ₁ is calculated by S ₁ = s ₀ · P ₁ .

[output]
-Secret key for the recipient's ID: (S ₁ , Q ₀ )

<When t = 2>
This is a process in which the first layer node issues a secret key for the recipient of the second layer node (see FIG. 8).
[input]
・ Recipient ID information set (well-known information, character string): id ₀ , id ₁ , id ₂
-Route public parameters (public information): P ₀
First layer private key (obtained from root): (S ₁ , Q ₀ )
[Processing content]
(1) Generate a random integer s ₁ ε {0, 1, 2,..., P−1}.
(2) P ₂ is calculated by P ₂ = IDenc (id ₀ ‖id ₁ ‖id ₂ ).
(3) S ₂ is calculated by S ₂ = S ₁ + s ₁ · P ₂ .
(4) Q ₁ is calculated by Q ₁ = s ₁ · P ₀ .
[output]
- secret key for the ID of the recipient: (S _2, Q ₁₎

<When t>2>
This is a process in which each node in the second and subsequent layers (t-1 layer) issues a secret key for the recipient of the node in the lower layer (t layer) (see FIG. 9: the node in the second layer is the first layer) An example of issuing to a node of three layers).
[input]
ID information set of receiver (well-known information, character string): id ₀ , id ₁ ,..., Id _t
-Route public parameters (public information): P ₀
-T-1 layer private key (obtained from layer t-2)
: (S _t , Q ₁ , Q ₂ ,..., Q _t-2 )
[Processing content]
(1) Generate a random integer s _t-1 ε {0, 1, 2,..., P−1}.
(2) P _t, is calculated by _{P t = IDenc (id 0 ‖id} 1 || ··· ‖id _t).
(3) S _t is calculated by S _t = S _t−1 + s _t−1 · P _t .
(4) Q _t−1 is calculated by Q _t−1 = s _t−1 · P ₀ .
[output]
A secret key for the recipient ID: (S _t , Q ₁ , Q ₂ ,..., Q _t-1 )

≪Encryption≫
The encryption function is a function for the sender, and generates a ciphertext c in which the plaintext M is encrypted using the receiver's ID information set and the route public parameter. 6 to 9, the hierarchical ID-based encryption device 300 corresponds to this.
(1) Generate and output a random value rε {0, 1, 2,..., P−1}.
(2) ID information set _{id 0, id 1, id 2} , ···, based on the _{id t, P 1, P 2} , ···, the P _t respectively,
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (1 ≦ i ≦ t)
Calculate according to
_{(3) P 0, P 2} , P 3, ···, and a P _t and _{r, U 0, U 2,} U 3, ···, a U _t, respectively,
U _j = r · P _j (j = 0 or 2 ≦ j ≦ t)
Calculate according to
(4) Q is calculated from Q ₀ , P _1, and r using an arbitrary pairing function e by Q = e (Q ₀ , P ₁ ) ^r . The pairing function e is a two-input one-output function, and e (aP, bQ) = e (P, Q) ^ab = e (bP, aQ) for two points P and Q on the elliptic curve E. This function establishes such bilinearity.
(5) Q ′ and plaintext M are input, and c ′ is calculated using an arbitrary one-way function hash that outputs a data string of a predetermined length.
c '= Mxor hash (Q)
(Xor represents an exclusive OR operation).
(6) U ₀ , U ₂ , U ₃ ,..., U _t and c ′ are input, U _j is converted into a data string,
c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′
Calculate and output by

≪Decryption≫
The decryption function is a function for the receiver, and decrypts the plaintext M from the ciphertext c using a secret key corresponding to the ID information set of the receiver. 6 to 9, the hierarchical ID-based encryption device 400 corresponds to this.
(1) the ciphertext c is input, as a c = U ₀ ‖U ₂ ‖U ₃ ‖ _{··· ‖U t ‖c', U 0,} U 2, U 3, ···, and U _t c ′.
_{(2) U 0, U 2} , U 3, ···, U t and the secret key _{S t, Q 1, Q 2} , ···, from Q _t-1 Metropolitan, the point on the elliptic curve E and U _j And Q using the pairing function e

Calculate according to
(3) From c ′ and Q, the plaintext M is calculated using the one-way function hash,
M = c'xor hash (Q)
Calculate and output by In the calculation, Q is converted into a data string.
Craig Gentry and Alice Silverberg, "Hierarchical ID-Based Criptography", ASIACRYPT2002, LNCS 2501, 2002, p.548-566 Nippon Telegraph and Telephone Corporation, "PSEC-KEM specification version 2.2", [online], April 14, 2008, [November 26, 2008 search], Internet <URL: http: //info.isl .ntt.co.jp / crypt / psec / dl / iso / psec-kem_v2.2_20080414j.pdf>

  FIG. 10 simply shows an encryption processing form for plaintext M in the conventional hierarchical ID-based encryption method described above. As can be seen from the above functional description and this figure, the conventional hierarchical ID-based encryption method is a very general method in which plaintext M is directly encrypted by public parameter P and ciphertext m is decrypted using secret key S. Based on a simple public key cryptosystem.

  Among various public key cryptosystems, the application method to the hierarchical ID-based cryptosystem has been established at present only in a scheme using elliptic curve cryptography (see Non-Patent Document 1). However, in the method using elliptic curve cryptography, the plaintext data is encrypted in correspondence with the points on the elliptic curve, so the length of plaintext (data amount) that can be encrypted in one process is on the elliptic curve. There is a problem that the number of points (for example, 160 bits) is limited.

  PSEC-KEM (Provably Secure Elliptic Curve Encryption-Key Encapsulation Mechanisms) has been realized as a method that enables efficient encryption of plaintexts of arbitrary length while taking advantage of the advantages of public key cryptography by elliptic curve cryptography. (See Non-Patent Document 2). The outline will be described below.

  KEM (Key Encapsulation Mechanism) is a framework that uses a public key cryptosystem for the generation and distribution of session keys used in a common key cryptosystem, and a common key cryptosystem that encrypts and decrypts plaintext using the session key Hybrid encryption is realized in combination with DEM (Data Encapsulation Mechanisms), which is a framework based on the system. By using such a KEM-DEM configuration, the public key cryptosystem's “key management and distribution is easy” and the common key cryptosystem's “encryption / decryption processing is high-speed and encryption It is possible to enjoy both of the advantages that there is no restriction on the length of plaintext that can be converted. FIG. 11 shows an encryption processing form for plain text in the KEM-DEM configuration. In this configuration, first, the sender's KEM encryption apparatus 500 generates a session key k, which is a common key, using the receiver's public key P, and also generates a ciphertext c including the session key k. To send. Then, the receiver's KEM decryption apparatus 600 receives the ciphertext c, decrypts it using the secret key S, and extracts the session key k. After sharing the session key k in this way, the sender's DEM encryption apparatus 700 encrypts and transmits the plaintext M using the session key k, and the receiver's DEM decryption apparatus 800 receives the received ciphertext m. Is decrypted using the session key k to extract plaintext M.

  PSEC-KEM is a method of constructing KEM with elliptic curve cryptography. In addition to the above merits, "it is possible to configure key length to be short while maintaining security", "high speed key generation processing", etc. Benefits can also be enjoyed. PSEC-KEM is composed of three functions: key generation, encryption, and decryption. Each function will be briefly described below.

[Key generation function]
In PSEC-KEM, in order to perform an operation on an elliptic curve, first, an elliptic curve E defined on a finite field F _q and a base point P ₀ (order: p) on the elliptic curve E are determined, and then The base point P ₀ and its order p, the public key P = Q ₀ , and the secret key S = s ₀ are output.
(1) Generate a random integer s ₀ ε {0, 1, 2,..., P−1}.
(2) Q ₀ = s ₀ · P ₀ is calculated.
(3) The base point P ₀ and its order p, the public key P = Q ₀ , and the secret key S = s ₀ are output.

[Encryption function]
The base point P ₀ , its order p, and the public key P = Q ₀ are input, and the ciphertext c and the session key k are output.
(1) Generate a random value rε {0, 1, 2,..., P−1} having a predetermined length hLen octets.
(2) Generate h = KDF (0x00000000‖r) of length zLen + keyLen octets. Here, zLen and keyLen are predetermined octet lengths, KDF () is an arbitrary key derivation function, and ‖ represents concatenation of octet sequences.
(3) As h = z‖k, h is divided into z of length zLen octets and k of length keyLen octets.
(4) After converting z into an integer, α = z mod p is calculated. Calculation is performed.
(5) U ₀ = α · P ₀ and Q = α · Q ₀ are calculated.
(6) After converting U ₀ and Q into an octet string, h ′ of length hLen octets is calculated by h ′ = KDF (0x00000001‖U ₀ ‖Q).
(7) c ′ of length hLen octets is calculated by c ′ = r xor h ′. Here, xor represents an exclusive OR operation.
(8) After converting U ₀ into an octet string, ciphertext c = U ₀ ‖c ′ and session key k are output.

[Decryption function]
The secret key S = s ₀ , the ciphertext c, the base point P ₀ and its order p are input, and the session key k (or information indicating decryption failure) is output.
(1) The ciphertext c = U ₀ ‖c ′ is divided into U ₀ and c ′ of length hLen octets.
(2) After converting U ₀ to a point on the elliptic curve E, Q = s ₀ · U ₀ is calculated.
(3) After converting Q into an octet string, the length hLen octet h ′ is calculated by h ′ = KDF (0x00000001‖U ₀ ‖Q).
(4) Calculate r of length hLen octets by r = c′xor h ′.
(5) Calculate the length zLen + keyLen octet h by h = KDF (0x00000000‖r).
(6) With h = z‖k, divide h into z of length zLen octets and k of length keyLen octets.
(7) After converting z into an integer, α = z mod p is calculated.
(8) It is checked whether U ₀ = α · P ₀ is established. If it is established, the session key k is output, and if it is not established, information indicating a decryption failure such as “INVALID” is output.

  The PSEC-KEM described above is a technology that makes a general public key cryptosystem based on elliptic curve cryptography correspond to a KEM-DEM configuration, that is, a KEM technology. If the hierarchical ID-based encryption method can also be converted to KEM as shown in FIG. 1, since plaintext encryption is performed by common key encryption, it is possible to encrypt plaintext of arbitrary length. An object of the present invention is to apply a PSEC-KEM to a hierarchical ID-based encryption method and realize a hierarchical ID-based encryption device and a decryption device that are converted into a KEM.

  The hierarchical ID-based encryption apparatus according to the present invention includes a random number generator, a first hash calculator, a divider, an α calculator, a P calculator, a U calculator, a Q calculator, a second hash calculator, and a ciphertext calculation. It consists of parts.

  The random number generator generates and outputs a random value rε {0, 1, 2,..., P−1} having a predetermined length hLen octets.

The first hash calculation unit receives r and uses an arbitrary one-way function hash ₁ to calculate the length zLen + keyLen octet h,
h = hash ₁ (r)
(ZLen and keyLen are predetermined octet lengths) and output.

  The dividing unit divides the data into z of length zLen octets and a session key k of length keyLen octets and outputs them, assuming that h is input and h = z‖k (‖ represents concatenation).

  The α calculation unit receives z and the public parameter p, converts z to an integer, calculates α by α = z mod p, and outputs it.

The P calculation unit receives ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t , and uses a function IDenc that maps a character string to a point on the elliptic curve E, P ₁ , P ₂ , ..., P _t
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (1 ≦ i ≦ t)
Calculate and output by

U calculator, P _2, P _3, · · ·, and the P _t and α and public parameter P ₀ is input, U _0, U _2, U _3, · · ·, a U _t, respectively,
U _j = α · P _j (j = 0 or 2 ≦ j ≦ t)
Calculate and output by

The Q calculation unit receives P ₁ , α, and the public parameter Q _0, and uses an arbitrary pairing function e to calculate Q,
Q = e (Q ₀ , P ₁ ) ^α
Calculate and output by

Second hash calculation unit, r and _{U 0, U 2, U 3} , ···, ID information of the recipients and U _t and Q sets _{id 0, id 1, id 2} , ···, and the id _t Input U ₀ , U ₂ , U ₃ ,..., U _t and Q into an octet sequence, and then c ′ of a length hLen octet using an arbitrary one-way function hash ₂ ,
c ′ = rxor hash ₂ (U ₀ ‖U ₂ ‖ ... ‖ U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
(Xor represents exclusive OR operation) and output.

The ciphertext calculation unit receives U ₀ , U ₂ , U ₃ ,..., U _t and c ′ and converts U ₀ , U ₂ , U ₃ ,..., U _t into an octet string. The ciphertext c above,
c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′
Calculate and output by

  The hierarchical ID-based decoding apparatus of the present invention includes a first dividing unit, a Q calculating unit, a second hash calculating unit, a first hash calculating unit, a second dividing unit, an α calculating unit, a P calculating unit, and a verifying unit. It consists of.

The first division unit receives the ciphertext c and assumes that c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′, c ′ of length hLen octets, the rest is t, etc. Divided into divided U ₀ , U ₂ , U ₃ ,..., U _t .

Q calculation _{unit, U 0, U 2, U} 3, ···, U t and a predetermined secret key are previously generated by the process _{S t, Q 1, Q 2} , ···, and a Q _t-1 Is inputted, converted U ₀ , U ₂ , U ₃ ,..., U _t to a point on the elliptic curve E, and then used Q for the pairing function e,

により計算して出力する。

Calculate and output by

Second hash calculation _{unit, U 0, U 2, U} 3, ···, c' the U _t and Q and ID information set _{id 0, id 1, id 2} , ···, and the id _t is input , U ₀ , U ₂ , U ₃ ,..., U _t and Q are converted into an octet sequence, and r of length hLen octet is calculated using a one-way function hash ₂ .
r = c'xor hash ₂ (U ₀ ‖U ₂ ‖U ₃ ‖ ・ ・ ・ ‖U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
(Xor represents exclusive OR operation, and ‖ represents concatenation).

The first hash calculator receives r and an ID information set id ₀ , id ₁ , id ₂ ,..., Id _t, and uses the one-way function hash ₁ to set the length zLen + keyLen octet h,
h = hash ₁ (r)
(ZLen and keyLen are predetermined octet lengths) and output.

  The second dividing unit divides and outputs z of length zLen octets and session key k of length keyLen octets, assuming that h is input and h = z‖k.

  The α calculation unit receives z and p, converts z to an integer, calculates α by α = z mod p, and outputs it.

The P calculation unit receives ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t , and uses a function IDenc that maps a character string to a point on the elliptic curve E, P ₂ , P ₃ , ..., P _t
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (2 ≦ i ≦ t)
Calculate and output by

The verification unit receives P ₀ , P ₂ , P ₃ ,..., _Pt , α, and the session key k, and α · P ₀ , α · P ₂ , α · P ₃ ,. Calculate P _t and verify whether it matches U ₀ , U ₂ , U ₃ ,..., U _t , respectively. If they match, the session key k is output, and if they do not match, information indicating decryption failure is output.

  Since the hierarchical ID-based encryption apparatus and the decryption apparatus of the present invention can KEM the hierarchical ID-based encryption method, it is possible to encrypt plain text of any length.

  As described in the background art above, the hierarchical ID-based cryptosystem is configured such that a plurality of nodes that issue secret keys to assigned recipients are arranged hierarchically with the root at the top in terms of topology. In terms of functions, it is characterized by comprising four functions of initial setting, key generation, encryption, and decryption, but these characteristics are also the same in the present invention.

  Of the four functions, the parts related to KEM are an encryption function and a decryption function, and the present invention applies the technology of PSEC-KEM to these functions. Each function will be described below. Note that the initial setting function and the key generation function are the same as those in the prior art, and input / output and processing in those functions are as described in the background art above, and thus description thereof is omitted here.

≪Encryption≫
FIG. 2 shows an example of the functional configuration of the hierarchical ID-based encryption apparatus 100 of the present invention, and FIG. 3 shows an example of the processing flow. The hierarchical ID-based encryption apparatus 100 of the present invention includes a random number generation unit 101, a first hash calculation unit 102, a division unit 103, an α calculation unit 104, a P calculation unit 105, a U calculation unit 106, a Q calculation unit 107, and a first calculation unit 107. It consists of a 2-hash calculation unit 108 and a ciphertext calculation unit 109.

  The random number generation unit 101 generates and outputs a random value rε {0, 1, 2,..., P−1} having a predetermined length hLen octets (S1). In order to ensure safety, hLen should be 16 octets or more, but if possible, it should be 32 octets or more.

The first hash calculation unit 102 receives r, calculates h of length zLen + keyLen octet using h = hash ₁ (r) using an arbitrary one-way function hash ₁ (S2). Here, zLen and keyLen are predetermined octet lengths, respectively. In order to ensure safety, zLen should be 36 octets or more, but if possible, it should be 48 octets or more. In addition, keyLen corresponding to the session key length is preferably 32 octets or more.

Note that h may be calculated by h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖... ‖Id _t ). In this case, the ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t of the receiver are further input to the first hash calculation unit 102, and the first hash calculation unit 204 on the decryption side H is calculated by h = hash ₁ (r (id ₀ ‖id ₁ ‖id ₂ ‖... ‖Id _t ).

  Dividing section 103 divides the data into z of length zLen octets and session key k of length keyLen octets and outputs it, assuming that h is input and h = z‖k (S3). The session key k output here is a session key shared with the recipient.

  The α calculation unit 104 receives z and the public parameter p, converts z to an integer, calculates α by α = z mod p, and outputs it (S4).

P calculation unit 105, the recipient's ID information set _{id 0, id 1, id 2} , ···, id t is input, P ₁ by using the function IDenc mapping the string to a point on the elliptic curve E , P ₂ ,..., P _t respectively
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (1 ≦ i ≦ t)
Is calculated and output (S5).

U generator 106, P _2, P _3, · · ·, and the P _t and α and public parameter P ₀ is input, U _0, U _2, U _3, · · ·, a U _t, respectively,
U _j = α · P _j (j = 0 or 2 ≦ j ≦ t)
Is calculated and output (S6).

The Q calculation unit 107 receives P ₁ , α, and the public parameter Q ₀ , calculates Q using an arbitrary pairing function e by Q = e (Q ₀ , P ₁ ) ^α , and outputs it ( S7).

Second hash calculation section 108, r and _{U 0, U 2, U 3} , ···, ID information of the recipients and U _t and Q sets _{id 0, id 1, id 2} , ···, and id _t Is input, and after converting U _j and Q into an octet sequence, c ′ of a length hLen octet is obtained using an arbitrary one-way function hash ₂ ,
c ′ = rxor hash ₂ (U ₀ ‖U ₂ ‖ ... ‖ U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
(Xor represents an exclusive OR operation) is calculated and output (S8).

The ciphertext calculation unit 109 receives U ₀ , U ₂ , U ₃ ,..., U _t and c ′, converts U _j into an octet string,
c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′
Is calculated and output (S9).

≪Decryption≫
FIG. 4 shows an example of the functional configuration of the hierarchical ID-based decoding apparatus 200 of the present invention, and FIG. 5 shows an example of the processing flow. The hierarchical ID-based decoding apparatus 200 of the present invention includes a first dividing unit 201, a Q calculating unit 202, a second hash calculating unit 203, a first hash calculating unit 204, a second dividing unit 205, an α calculating unit 206, and a P. A calculation unit 207 and a verification unit 208 are included. Hierarchical ID-based decryption apparatus 200 uses a secret key (S _t , Q ₁ , Q ₂ ,..., Q _t-1 ) generated in advance by the key generation function described in the background art above as an upper node. Obtain from and process.

The first dividing unit 201 receives the ciphertext c, assumes that c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′, and c ′ of length hLen octets and the rest t Divided into equally divided U ₀ , U ₂ , U ₃ ,..., U _t (S11).

Q calculation unit _{202, U 0, U 2, U} 3, ···, U t and secret key S _t, Q _1, Q _2, · · ·, and a Q _t-1 is inputted, ellipse U _j Q is converted into a point on the curve E, and the pairing function e is used.

により計算して出力する（Ｓ１２）。

Is calculated and output (S12).

Second hash calculation unit _{203, U 0, U 2, U} 3, ···, c' the U _t and Q and ID information set _{id 0, id 1, id 2} , ···, and an id _t input After converting Q to an octet sequence, the one-way function hash ₂ is used to set the length hLen octet r,
r = c'xor hash ₂ (U ₀ ‖U ₂ ‖U ₃ ‖ ・ ・ ・ ‖U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
Is calculated and output (S13).

The first hash calculation unit 204 receives r, and uses the one-way function hash ₁ to calculate the length zLen + keyLen octet h,
h = hash ₁ (r)
Is calculated and output (S14).

When h is calculated by h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖... ‖Id _t ) in the first hash calculation unit 102 on the transmission side, the second hash calculation unit In 204, the receiver ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t are further input, and h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖. Calculate by ‖id _t ).

  The second dividing unit 205 divides the data into a length zLen octet z and a length keyLen octet session key k, assuming that h is input and h = z‖k (S15).

  The α calculation unit 206 receives z and the public parameter p, converts z into an integer, calculates α by α = z mod p, and outputs it (S16).

P calculation unit 207, the recipient's ID information set _{id 0, id 1, id 2} , ···, id t is input, P ₂ using a function IDenc mapping the string to a point on the elliptic curve E , P ₃ ,..., P _t respectively
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (2 ≦ i ≦ t)
Is calculated and output (S17).

The verification unit 208 receives P ₂ , P ₃ ,..., P _t and α, the public parameter P _0, and the session key k. First, α · P ₀ , α · P ₂ , α · P ₃ , ... Α · P _t is calculated (S18a). Then, it is verified whether or not each of U ₀ , U ₂ , U ₃ ,..., U _t matches, and if they match, it is determined that the session key is authentic and a session key k is output. If they do not match, it is determined that the ciphertext is an authentic ciphertext, and information indicating decryption failure such as “INVALID” is output without outputting the session key k (S18b).

  By configuring as described above, the hierarchical ID-based encryption device and the decryption device can be converted to KEM, and the session key k can be shared by both the sender and the receiver. Therefore, by encrypting plaintext using this session key k, it is possible to eliminate the restriction on the length of plaintext to be encrypted while taking advantage of the hierarchical ID-based encryption.

  The hierarchical ID-based encryption device and decryption device, the method, the program, and the recording medium in the present invention are not limited to the above-described embodiments, and can be appropriately changed without departing from the present invention. . In addition, the processes described above are not only executed in time series according to the order of description, but may be executed in parallel or individually as required by the processing capability of the apparatus that executes the processes.

  Further, when the processing functions in the hierarchical ID-based encryption device and the decryption device are realized by a computer, the processing contents of the functions that the hierarchical ID-based encryption device and the decryption device should have are described by a program. Then, by executing this program on a computer, the processing functions of the hierarchical ID-based encryption device and the decryption device are realized on the computer.

  The program describing the processing contents can be recorded on a computer-readable recording medium. As the computer-readable recording medium, for example, any recording medium such as a magnetic recording device, an optical disk, a magneto-optical recording medium, and a semiconductor memory may be used. Specifically, for example, as a magnetic recording device, a hard disk device, a flexible disk, a magnetic tape or the like, and as an optical disk, a DVD (Digital Versatile Disc), a DVD-RAM (Random Access Memory), a CD-ROM (Compact Disc Read Only Memory). ), CD-R (Recordable) / RW (ReWritable), etc., magneto-optical recording medium, MO (Magnet-Optical disc), etc., semiconductor memory, EEP-ROM (Electronically Erasable and Programmable-Read Only Memory), etc. Can be used.

  The program is distributed by selling, transferring, or lending a portable recording medium such as a DVD or CD-ROM in which the program is recorded. Further, the program may be distributed by storing the program in a recording device of the server computer and transferring the program from the server computer to another computer via a network.

  A computer that executes such a program first stores, for example, a program recorded on a portable recording medium or a program transferred from a server computer in its recording device. When executing the process, this computer reads the program stored in its own recording medium and executes the process according to the read program. As another execution form of the program, the computer may directly read the program from a portable recording medium and execute processing according to the program, and the program is transferred from the server computer to the computer. Each time, the processing according to the received program may be executed sequentially. Further, the program may not be transferred from the server computer to the computer, and the above processing may be executed by a so-called ASP (Application Service Provider) type service that realizes the processing function only by the execution instruction and result acquisition. Good. Note that the program in this embodiment includes information that is used for processing by an electronic computer and that conforms to the program (data that is not a direct command to the computer but has a property that defines the processing of the computer). In this embodiment, the hierarchical ID-based encryption device and the decryption device are configured by executing a predetermined program on the computer. However, at least a part of these processing contents is realized by hardware. It is good to do.

The image figure of the encryption processing form at the time of applying a KEM-DEM structure to a hierarchical ID base encryption system. The figure which shows the function structural example of the hierarchical ID base encryption apparatus 100 of this invention. The figure which shows the example of a processing flow of the hierarchical ID base encryption apparatus 100 of this invention. The figure which shows the function structural example of the hierarchical ID base decoding apparatus 200 of this invention. The figure which shows the example of a processing flow of the hierarchical ID base encryption apparatus 200 of this invention. The figure which shows the relationship between the component of the conventional hierarchical ID base encryption system. The figure which shows the mutual relationship between the components at the time of the issuance of a secret key in case the number of hierarchies t = 1. The figure which shows the relationship between the components at the time of secret key issue in case the number of hierarchies t = 2. The figure which shows the relationship between the components at the time of the issuance of a secret key in case of the number of hierarchies t> 2. The figure explaining the encryption processing form with respect to the plaintext in the conventional hierarchical ID base encryption system. The figure explaining the encryption processing form with respect to the plaintext in a KEM-DEM structure.

Claims (9)

A point P ₀ on the elliptic curve E defined on the finite field F _q and its order p, and Q ₀ = s ₀ · P ₀ (s ₀ ∈ {0, 1, 2,..., P−1} and Q ₀ calculated by), ID information set id ₀ is an arbitrary _{string, id 1, id 2, ···} , id t (t hierarchy number of nodes to which the ID information set belongs, t ≧ 1 ), And outputs a ciphertext c and a session key k.
A random number generator for generating and outputting a random value rε {0, 1, 2,..., P−1} of a predetermined length hLen octets;
The above r is input, and the length zLen + keyLen octet h is set using an arbitrary one-way function hash ₁ .
h = hash ₁ (r)
(Where zLen and keyLen are predetermined octet lengths)
Assuming that h is input and h = z‖k (‖ represents concatenation), a dividing unit that divides and outputs z of length zLen octets and session key k of length keyLen octets,
An α calculation unit that inputs z and p, converts z to an integer, calculates α by α = z mod p, and outputs it;
The ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t are input and P ₁ , P ₂ ,..., Using the function IDenc that maps the character string to a point on the elliptic curve E. P _t respectively
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (1 ≦ i ≦ t)
A P calculation unit that calculates and outputs according to
The _{P 0, P 2, P 3} , ···, are inputted and P _t and the _{α, U 0, U 2,} U 3, ···, a U _t, respectively,
U _j = α · P _j (j = 0 or 2 ≦ j ≦ t)
A U calculation unit that calculates and outputs by
Q ₀ , P _1, and α are input, and Q is set using an arbitrary pairing function e.
Q = e (Q ₀ , P ₁ ) ^α
A Q calculation unit that calculates and outputs according to
The r and the _{U 0, U 2, U 3} , ···, U t and the Q and the ID information set _{id 0, id 1, id 2} , ···, and the id _t is input, U _0, U ₂ , U ₃ ,..., U _t and Q are converted into an octet sequence, and an arbitrary one-way function hash ₂ is used to set c ′ of a length hLen octet,
c ′ = rxor hash ₂ (U ₀ ‖U ₂ ‖ ... ‖ U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
(Where xor represents an exclusive OR operation)
Said _{U 0, U 2, U 3} , ···, and U _t and the c'are _{input, U 0, U 2, U} 3, ···, ciphertext on converting the U _t octet string c
c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′
A ciphertext calculation unit that calculates and outputs by
A hierarchical ID-based encryption apparatus comprising: In the hierarchical ID-based encryption device according to claim 1,
The first hash calculator further receives the ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t , and sets h to
h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖ ・ ・ ・ ‖id _t )
A hierarchical ID-based encryption apparatus characterized by the following calculation: A point P ₀ on the elliptic curve E defined on the finite field F _q and its order p, and an ID information set id ₀ , id ₁ , id ₂ ,..., Id _t (t Is the number of hierarchies of the node to which the ID information set belongs, t ≧ 1), and secret keys _St , Q ₁ , Q ₂ ,..., Q corresponding to the ID information set generated in advance by a predetermined method. Hierarchical ID-based decryption that receives _t-1 (S _t , Q ₁ , Q ₂ ,..., Q _t-1 are points on the elliptic curve E) and ciphertext c and outputs a session key k Device.
The ciphertext c is input, and c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′ (where ‖ represents concatenation), c ′ of length hLen octets, and the rest Is divided into U equal parts t, U ₀ , U ₂ , U ₃ ,..., U _t ;
The secret keys S _t , Q ₁ , Q ₂ ,..., Q _t-1 and the U ₀ , U ₂ , U ₃ ,..., U _t are input, and U ₀ , U ₂ , U ₃ are input. ,..., U _t is converted to a point on the elliptic curve E, and Q is set using an arbitrary pairing function e.

A Q calculation unit that calculates and outputs according to
It said _{U 0, U 2, U 3} , ···, and U _t, and the c', and the Q, the ID information set _{id 0, id 1, id 2} , ···, and the id _t is input , U ₀ , U ₂ , U ₃ ,..., U _t and Q are converted into octet sequences, and an arbitrary one-way function hash ₂ is used to calculate r of length hLen octets,
r = c'xor hash ₂ (U ₀ ‖U ₂ ‖U ₃ ‖ ・ ・ ・ ‖U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
(Where xor represents an exclusive OR operation)
The above r is input, and the length zLen + keyLen octet h is set using an arbitrary one-way function hash ₁ .
h = hash ₁ (r)
(Where zLen and keyLen are predetermined octet lengths)
Assuming that h is input and h = z‖k, a second dividing unit that divides and outputs z of length zLen octets and session key k of length keyLen octets,
An α calculation unit that inputs z and p, converts z to an integer, calculates α by α = z mod p, and outputs it;
The ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t are input, and P ₂ , P ₃ ,..., Using a function IDenc that maps a character string to a point on the elliptic curve E. P _t respectively
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (2 ≦ i ≦ t)
A P calculation unit that calculates and outputs according to
P ₀ , P ₂ , P ₃ ,..., P _t , α and the session key k are input, and α · P ₀ , α · P ₂ , α · P ₃ ,. P _t is calculated, and it is verified whether or not it matches U ₀ , U ₂ , U ₃ ,..., U _t . A verification unit that outputs information indicating decryption failure in the case,
A hierarchical ID-based decoding device comprising: The hierarchical ID-based decoding device according to claim 3,
The first hash calculator further receives the ID information sets id ₀ , id ₁ , id ₂ ,..., Id _t , and sets h to
h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖ ・ ・ ・ ‖id _t )
A hierarchical ID-based decoding device characterized by the following calculation: A point P ₀ on the elliptic curve E defined on the finite field F _q and its order p, and Q ₀ = s ₀ · P ₀ (s ₀ ∈ {0, 1, 2,..., P−1) and Q ₀ calculated by}), ID information set id ₀ is an arbitrary _{string, id 1, id 2, ···} , id t (t hierarchy number of nodes to which the ID information set belongs, t ≧ 1), a hierarchical ID-based encryption method for obtaining a ciphertext c and a session key k,
A random number generation step in which a random number generation unit generates a random value rε {0, 1, 2,..., P−1} of a predetermined length hLen octets;
The first hash calculator uses an arbitrary one-way function hash ₁ to calculate the length zLen + keyLen octet h,
h = hash ₁ (r)
Or h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖ ・ ・ ・ ‖id _t )
A first hash calculation step calculated by (zLen and keyLen are respectively predetermined octet lengths and ‖ represents concatenation);
A dividing step in which the dividing unit divides the above h into z of length zLen octets and session key k of length keyLen octets, assuming that h = z‖k;
an α calculating step in which an α calculating unit converts z to an integer and then calculates α by α = z mod p;
The P calculation unit converts P ₁ , P ₂ ,..., P _t using the function IDenc that maps the character string to a point on the elliptic curve E, respectively.
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (1 ≦ i ≦ t)
A P calculation step to calculate according to
U calculation unit, U _0, U _2, U _3, · · ·, a U _t, respectively,
U _j = α · P _j (j = 0 or 2 ≦ j ≦ t)
A U-calculation step to calculate according to
The Q calculation unit calculates Q using an arbitrary pairing function e,
Q = e (Q ₀ , P ₁ ) ^α
Q calculation step to calculate according to
The second hash calculator converts U ₀ , U ₂ , U ₃ ,..., U _t and Q into an octet sequence, and then uses the arbitrary one-way function hash ₂ to calculate c ′ of the length hLen octet. ,
c ′ = rxor hash ₂ (U ₀ ‖U ₂ ‖ ... ‖ U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
A second hash calculation step to calculate by (xor represents an exclusive OR operation);
The ciphertext calculation unit converts U ₀ , U ₂ , U ₃ ,..., U _t into an octet string, and then converts the ciphertext c to
c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′
A ciphertext calculation step calculated by
A hierarchical ID-based encryption method comprising: A point P ₀ on the elliptic curve E defined on the finite field F _q and its order p, and an ID information set id ₀ , id ₁ , id ₂ ,..., Id _t (t Is the number of hierarchies of the node to which the ID information set belongs, t ≧ 1), and secret keys _St , Q ₁ , Q ₂ ,..., Q corresponding to the ID information set generated in advance by a predetermined method. A hierarchical ID-based decryption method for obtaining a session key k from _t-1 (S _t , Q ₁ , Q ₂ ,..., Q _t-1 is a point on the elliptic curve E) and ciphertext c. There,
The first dividing unit assumes that the ciphertext c is c = U ₀ ‖U ₂ ‖U ₃ ‖... ‖U _t ‖c ′ (where ‖ represents concatenation) and c ′ of length hLen octets. When a first division step of dividing the remaining U that t equal _0, U _2, U _3, · · ·, to the U _t,
The Q calculation unit converts U ₀ , U ₂ , U ₃ ,..., U _t into points on the elliptic curve E, and then uses an arbitrary pairing function e to calculate Q,

Q calculation step to calculate according to
The second hash calculator converts U ₀ , U ₂ , U ₃ ,..., U _t and Q into an octet sequence, and then uses an arbitrary one-way function hash ₂ to calculate r of length hLen octets,
r = c'xor hash ₂ (U ₀ ‖U ₂ ‖U ₃ ‖ ・ ・ ・ ‖U _t ‖Q‖id ₀ ‖id ₁ ‖id ₂ ‖ ... ‖id _t )
A second hash calculation step to calculate by (xor represents an exclusive OR operation);
The first hash calculator uses the one-way function hash ₁ to calculate the length zLen + keyLen octet h,
h = hash ₁ (r)
Or h = hash ₁ (r‖id ₀ ‖id ₁ ‖id ₂ ‖ ・ ・ ・ ‖id _t )
A first hash calculation step of calculating according to (zLen and keyLen are respectively predetermined octet lengths);
A second dividing step in which the second dividing unit divides z into a length zLen octet z and a length keyLen octet session key k, assuming that h is h = z‖k;
an α calculating step in which an α calculating unit converts z to an integer and then calculates α by α = z mod p;
The P calculation unit converts P ₂ , P ₃ ,..., P _t using the function IDenc that maps the character string to a point on the elliptic curve E, respectively.
P _i = IDenc (id ₀ ‖id ₁ ‖... ‖Id _i ) (2 ≦ i ≦ t)
A P calculation step to calculate according to
Verification _{unit, α · P 0, α ·} P 2, α · P 3, ···, to calculate the α · P _t, respectively _{U 0, U 2, U 3} , ···, consistent with U _t A verification step of outputting the session key k if they match, and outputting information indicating decryption failure if they do not match,
A hierarchical ID-based decoding method characterized by executing:   A set of the hierarchical ID-based encryption device according to claim 1 and the hierarchical ID-based decryption device according to claim 3, or the hierarchical ID-based encryption device according to claim 2 and claim 4. A hierarchical ID-based encryption system including any of the pair with the hierarchical ID-based decryption device described in 1.   A program for causing a computer to function as the apparatus or system according to claim 1.   A computer-readable recording medium on which the program according to claim 8 is recorded.

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