CN1777100A - Method for reducing RSA key varible storage space - Google Patents

Abstract

Using modulus N, relation among public key PK and private key SK, two pieces of large prime number P and Q, and nine variables, the invention creates nine variables with total length as 106 bits. The method reduces memory space of key variable in RSA cryptographic system to the degree so that key variable in RSA cryptographic system is applicable to magnetic strip card with 106 bits. Thus, magnetic strip card can be in use as EFT of user's ID authentication and in use for POS device. Advantages are: using created nine variables stored on magnetic strip card with 106 bits prepares user's ID authentication card or information authentication card, which is suitable to both of EFT and POS device, and is capable of resisting attack of small exponent.

Description

A kind of method that reduces RSA key variable storage space

Technical field

The present invention relates to a kind of method that reduces RSA key variable storage space, belong to the technical field of information security and network security.

Background technology

Along with the appearance of global IT wave, information security and network security are subjected to people's attention day by day.That the application of information security and network security technology has been deep into is large-scale, critical operation system such as EFT and POS machine system (electronic fund transfer and point of salessystems) etc.Yet for for the system of low capacity memory device, because the restriction of computing capability and the physical characteristic that the storage device medium can not be stored big data, these The Application of Technology are restricted.

Public key algorithm is that Difte and Hellman proposed in 1976.They utilize a kind of special mathematic(al) manipulation, and power operation proposes the key distribution protocol based on a discrete logarithm difficult problem.The user carries out Montgomery Algorithm twice, just can obtain a relative side's identical key.Because this conversion is unidirectional, so can't be used for encryption and decryption.

In U.S. Pat 4,218, in 582, Hellman and Merkle utilize the result of Difte and Hellman to propose a kind of method of eliminating secure infomation passageway.1978, Rivest, Shanir and Adleman propose public key encryption algorithm RSA, also propose digital signature simultaneously, i.e. Dian Ziqianming notion.Their United States Patent (USP) that has been this algorithm application, and obtain the authorization, the patent No. is US 4,405,829.This algorithm is to utilize two big prime numbers to multiply each other, and draws a modulus N, gets a PKI e, calculates private key d by these two big prime numbers then, open PKI e and modulus N.Like this,, then only need carry out Montgomery Algorithm to message M, obtain ciphertext C with modulus N and PKI e if user A will be that e and modulus are the user B transmission message M of N to PKI.After user B received ciphertext C, d was decrypted with private key.The reverse computing of said process just in time can be used for doing electronic signature, and with integrality, confirmability and the non-repudiation of acknowledgement message M, one people knows because private key d has only user B.

Because the size of key of public key cryptography is huge, public key cryptography is not expected always in Verification System on the card.In U.S. Pat 4,438, in 824, Mueller-Schloer has proposed an authentication system with the way of additional data card.In this system, a plurality of terminals link to each other with the security service station, and each terminal all has CPU, internal memory, a card reader and closes digital-to-analogue.CPU is by closing the encryption and decryption of digital-to-analogue control data.And the work at security service station is also similar, verifies with this, this system is compatible simultaneously Data Encryption Standard algorithm DES and public key encryption algorithm RSA.

But commercial, this system is not accepted by EFT and POS machine system so far yet.Because these systems adopt the very little magnetic stripe card of capacity to make storage medium, store private identify (PIN), with the legitimacy of authenticated user identity.At the end of the eighties and the beginning of the nineties, people begin to seek to solve key variable are stored in way on the low capacity storage medium.

In U.S. Pat 4,408, in 203, Canpbell has proposed one and has solved the method scheme with the algorithm of symmetric cryptography (private key password).In addition, in U.S. Pat 4,423, in 287, Zeidler solves the authenticating user identification problem of EFT and POS machine system with the method for a secondary key.Because be subjected to the capacity limit of magnetic stripe card, people's (comprising Canpbell and Zeidler) fail that all the time safer RSA is applied to EFT and POS machine system gets on.

At present the RSA of safety closes the integer that digital-to-analogue is 1024 bits, and 3 magnetic tracks on the magnetic stripe card of mechanisms such as bank can only be deposited the information of 316,160 and 432 bits, and this is that close digital-to-analogue, PKI, the private key of 1024 bits all is far from being enough for length.U.S. Pat 4,736, though 423 disclose the algorithm of one 400 bit, but because the limitation of this algorithm itself, this algorithm can't be generalized on the RSA that length is 1024 bits, and the little finger of toe technology of counting attack did not occur at that time, and in today, this method may be unsafe fully.

So to the application of common key cryptosystem, depend primarily on the development of two factors, promptly or jumbo memory technology occurs, or find a kind of technology that reduces the key memory space in bank or financial sector.Because the limitation of memory technology, main outlet are the technology that development reduces the key memory space.From angle practical and safety, this is again a pair of contradiction.Therefore not only key generation technique that safety but also key memory space the are little most important thing especially.

Summary of the invention

The technical problem to be solved in the present invention is to propose a kind of method that reduces RSA key variable storage space, promptly reduces the algorithm in RSA key variable storage space.This method is a technology that generates not only safety, key memory space but also little key, following advantage is arranged: can be for using small-capacity memory, the Electronic Finance system of magnetic stripe card is used for the required high strength password of authentication, discriminating and message authentication as generations such as EFT and POS machine systems.

The present invention makes above-mentioned technical problem be resolved by the following technical solutions.According to the characteristics that present EFT and POS machine system carry out authentication with magnetic stripe card, for satisfying the requirement of RSA fail safe: the length of RSA key variable should be 3072 bits, and wherein, PKI PK, private key SK and modulus N respectively account for 1024 bits; Key: PKI PK and private key SK should be able to resist the little finger of toe number and attack.The authentication information that technical scheme of the present invention will be stored in 106 bits on the magnetic stripe card earlier is divided into 9 variablees, and wherein the length of two variablees is respectively 16 and 20 bits, and the length of remaining variables is 10 bits; The algorithm that then utilizes technical scheme of the present invention to provide generates described 9 variablees and obtains two big prime P and Q; Product with two big prime P and Q can obtain modulus N=P*Q and two key K P that can resist the attack of little finger of toe number: PKI PK and private key SK.To sum up, technical scheme of the present invention is utilized modulus N, PKI PK and private key SK, two big prime P and Q, and the relation between 9 variable threes, and generating the length summation is 9 variablees of 106 bits.Technical scheme of the present invention reduces to the memory space of rsa cryptosystem system key variable that it can be used in memory capacity is that the magnetic stripe card of 106 bits is as the degree in the systems such as the EFT of authenticating user identification and POS machine.

About the authentication of EFT and POS machine system, RSA realizes with public key algorithm, need use the technology of the memory space that reduces key variable, and three main bodys of this technology is subscriber card (CARD), terminal (EFT) and host process center (HPC) respectively.

Suppose that the user registers in bank or other financial institution, then he has a basic number of the account (PAN).And the user inserts when information is read on the card of terminal, and the identification card number (PIN) that the user only need import the individual confirms the basic number of the account (PAN) of oneself.If PIN and PAN check correctly, then system will start business service.

But user's authentication is actually the individual subscriber identity information that utilizes on the card: personal key KP, wait as RSA by cryptographic algorithm and to protect.

Fig. 1 has explained the application of RSA system in EFT and POS machine system.The capacity of magnetic stripe card can not be stored the RSA key variable of safe enough, becomes a urgent problem.Before explaining the method that reduces RSA key variable storage space in detail, look at the structure of whole system first.

At first, establish user's identity ID _i, personal key KP _iAnd modulus N _iAll be read into terminal EFT, and individual's identification card number PIN _iAlso read in terminal EFT, at this moment user's identity information ID _iIdentity information TID with terminal _jBe sent to host process center HPC.

Then, host process center HPC produces random number T by randomizer (GEN RN) ₁, and be sent to terminal EFT, then terminal EFT is with random number T ₁TRM does concatenation operation with business need message, simultaneously also individual's identification card number PIN _iWith personal key KP _iDo mould 2 and add computing, produce private key SK _iUse private key SK _iAnd modulus N _iTo business need message TRM ‖ random number T ₁Do decrypt operation, obtain dSK _i(TRM, T ₁).Terminal EFT produces random number T by the randomizer of oneself ₂, with it and dSK _i(TRM, T ₁) send to host process center HPC together.

In the HPC of host process center, by the subscriber identity information ID of terminal EFT transmission _i, terminal identity information TID _j, find user's individual's identification card number PAN _i, modulus N _iWith PKI PK _i, use PKI PK _iAnd modulus N _iTo dSK _i(TRM, T ₁) carry out encryption, recover business need message TRM and random number T ₁'.If random number T ₁'=random number T ₁, then by checking, continue, otherwise the refusal business need.Checking above supposing is passed through, then the host process center HPC modulus N of bank _bWith private key SK _bTo random number T ₂Be decrypted processing, with dSK _b(T ₂) send back to terminal EFT.Fig. 2 and Fig. 3 are respectively deciphering and ciphering process.

At last, terminal EFT is with the dSK that receives _b(T ₂) the disclosed modulus N of usefulness bank _bWith PKI PK _bCarry out encryption.If encrypted result is T ₂', just in time with original T ₂Unanimity, then authenticated user is a validated user, and by business need message TRM transacting business.

The operation of said system is enough can store N with the capacity of card (CARD) _iAnd KP _iFor prerequisite.Since magnetic stripe card capacity little, have no idea they are directly stored on the magnetic stripe card, so the present invention utilizes certain precomputation with N _iAnd KP _iThe compression capacity of being stored in be on the magnetic stripe card of 106 bits, make magnetic stripe card can with above-mentioned system's coupling.

It below is to utilize the information that is stored in 106 bits on the magnetic stripe card to produce the RSA key variable of safe enough: modulus N _iWith personal key KP _i

106 bits shown in Figure 4 are divided into 9 groups of variable: D ₁..., D ₉, all variablees are all stored with binary form.Wherein, D ₂And D ₉Length be respectively 20 and 16 bits, the length of remaining variables is 10 bits.

Now specify technical scheme of the present invention in conjunction with Fig. 5 a and Fig. 5 b.

A kind of method that reduces RSA key variable storage space is characterized in that, the concrete operations step:

The first step is chosen variables D ₁, make Z=2 ⁴⁸⁸-2D ₁+ 1 is a prime number that length is 488 bits, will utilize Z to produce other parameter below, and used computing and symbol thereof are enumerated as follows:

OR: binary number ' or ' computing,

Mod: the modular arithmetic of number,

[K]: be no more than the maximum integer of K,

A*b: expression a and b's multiplies each other,

L (Q): get two of Q and advance the left side 373 bits of expression, promptly preceding 373 bits constitute a new number,

Other computing of below not enumerating is common integer arithmetic;

(annotate: variables D ₁Generate, its length is 10 bits.)

Second step was chosen D ₂, D ₃, ${\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="A200510111351.000171.png"\; state="\{\{state\}\}">X</figure-callout>}}_1={D_2}^{(D_3+1)}\mathrm{mod}Z,$ "=(the X that makes P ₁) OR (2 ⁴⁸⁷+ 1) is a prime number that length is 488 bits;

(annotate: variables D ₂And D ₃Generate variables D ₂And D ₃Length be respectively 20 and 10 bits.)

The 3rd step was chosen D ₄, make P '=2 (D ₄+ 2 ¹⁰) "+1 is a prime number that length is 500 bits to P;

(annotate: variables D ₄Generate, its length is 10 bits.)

The 4th step was chosen D ₅, make P=2 (D ₅+ 2 ¹⁰) P '+1 is a prime number that length is 512 bits;

(annotate: variables D ₅Generate, its length is 10 bits.)

The 5th step was calculated X ₂=[2 ¹⁰²⁴/ P], with X ₂Last pressure of binary representation change 1 into, X ₃

The 6th step was chosen D ₆, "=2 (D that make Q ₆+ 2 ¹⁰) X ₃+ 1 is a prime number that length is 488 bits;

(annotate: variables D ₆Generate, its length is 10 bits.)

The 7th step was chosen D ₇, make Q '=2 (D ₇+ 2 ¹⁰) "+1 is a prime number that length is 500 bits to Q;

(annotate: variables D ₇Generate, its length is 10 bits.)

The 8th step was chosen D ₈, make Q=2 (D ₈+ 2 ¹⁰) Q '+1 is a prime number that length is 512 bits;

(annotate: variables D ₈Generate, its length is 10 bits.)

The 9th step was calculated modulus N=P*Q, and this moment, the length of N was 1024 bits;

The tenth step was chosen D ₉, calculate d=2 ³⁷⁴+ 2 (D ₉+ L (Q))+1, make e 〉=2 of e*d ≡ 1 mod (P-1) in (Q-1) ¹⁷+ 1;

(annotate: variables D ₉Generate, its length is 16 bits.E and d are called encryption exponent and decryption exponent.In the method for attacking the rsa cryptosystem system now, if decryption exponent d＜N ^0.365, the rsa cryptosystem system is broken easily.N ^0.365＜2 ³⁷⁴So the d that chooses here is greater than 2 ³⁷⁴Be safe.Meanwhile, also be unsafe about less encryption exponent e, so the e that chooses necessary 〉=2 ¹⁷+ 1.)

The 11 step made PKI PK=e, private key SK=d, and this moment, the length of PKI PK and private key SK was 1024 bits;

The 12 goes on foot so far variables D ₁, D ₂, D ₃, D ₄, D ₅, D ₆, D ₇, D ₈And D ₉All generate, wherein, variables D ₂And D ₉Length be respectively 20 and 16 bits, remaining length is 10 bits.

With variables D ₁, D ₂, D ₃, D ₄, D ₅, D ₆, D ₇, D ₈And D ₉The length that is stored on the magnetic stripe card is on the memory space of 106 bits.

The magnetic stripe card of recording with method of the present invention is particularly suitable for and system's couplings such as EFT and POS machine, for systems such as EFT and POS machine provide not only safe but also can resist authenticating user identification or the authentification of message that the little finger of toe number is attacked.

The advantage of method of the present invention:

1, because the data length that is used for authentication or data authentication that method of the present invention generates is 106 bits,, this method carries out among the EFT and POS machine system of authentication with magnetic stripe card at present so being suitable for use in.

2, the length that generates of method of the present invention is after the data of the authentication of 106 bits or data authentication are read in EFT and POS machine system, EFT and POS machine system can produce modulus N, PKI PK and the private key SK that length is 1024 bits, and PKI PK and private key SK can resist the little finger of toe number and attack, in other words, this method can produce can resist the attack of little finger of toe number, the modulus N that can not be decomposed, PKI PK and private key SK again.

Above-mentioned performance has increased substantially present EFT and the authentication fail safe of POS machine system and the popularity of application.

Description of drawings

Primary structure of the present invention, algorithm and technical step be mainly by accompanying drawing 1, Fig. 2, and Fig. 3, Fig. 4 and Fig. 5 form.

Fig. 1 is application structure and the algorithm of rsa cryptosystem algorithm in EFT and POS machine system, and the schematic diagram of authenticated user legitimacy and bank's legitimacy.

Fig. 2, Fig. 3 are respectively decipherment algorithm and the cryptographic algorithm among Fig. 1.

Fig. 4 is the RSA compression key that is stored in 106 bits on the magnetic stripe card.

Fig. 5 (a) and Fig. 5 (b) generate the precomputation process of RSA key variable safely and effectively for 9 groups of variablees with 106 bits.This algorithm is the technological core of method of the present invention, can satisfy that RSA is up-to-date to prevent the specification requirement of attacking, and can produce the very high key of fail safe again.

Embodiment

The method in the minimizing RSA key variable storage space that illustrates in detail in the superincumbent summary of the invention is exactly embodiment.

Operation principle.

Can realize by precomputation in the said process.At present, existing a lot of algorithms that detect the integer disposition are so above-mentioned operating procedure all is attainable.

The data of 106 bits by prior precomputation and the inverse process of aforesaid operations step can recover modulus N, key K P easily: PKI PK and private key SK.Known: authenticating user identification data, its length are 106 bits, and 9 groups of variable: D ₁, D ₂, D ₃, D ₄, D ₅, D ₆, D ₇, D ₈And D ₉Below be to recover modulus N, key K P: the process of PKI PK and private key SK:

1、Z＝2 ⁴⁸⁸-2D ₁+1

With D ₁The substitution following formula gets Z.

2、

${\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="A200510111351.000171.png"\; state="\{\{state\}\}">X</figure-callout>}}_1={D_2}^{(D_3+1)}\mathrm{mod}Z$

With D ₂, D ₃With Z substitution following formula, get X ₁

3、P″＝(X ₁)OR(2 ⁴⁸⁷+1)

With X ₁The substitution following formula gets P ".

4、P′＝2(D ₄+2 ¹⁰)P″+1

With D ₄" the substitution following formula gets P ' to and P.

5、P＝2(D ₅+2 ¹⁰)P′+1

With D ₅And P ' substitution following formula, get P.

6、X ₂＝[2 ¹⁰²⁴/P]

7、

8、Q″＝2(D ₆+2 ¹⁰)X ₃+1

With D ₆And X ₃The substitution following formula gets Q ".

9、Q′＝2(D ₇+2 ¹⁰)Q″+1

With D ₇" the substitution following formula gets Q ' to and Q.

10、Q＝2(D ₈+2 ¹⁰)Q′+1

With D ₈And Q ' substitution following formula, get Q.

11、N＝P*Q

With P and Q substitution following formula, get N.

12、d＝2 ³⁷⁴+2(D ₉+L(Q))+1

With D ₉And L (Q) substitution following formula, get d.

13、e*d≡1?mod(P-1)(Q-1)

With d, P and Q substitution following formula get e.

14、PK＝e，SK＝d

So far, the modulus that recovers, PKI and private key are respectively N, PK and SK, modulus N, the length of PKI PK and private key SK is 1024 bits.

Claims (3)

1, a kind of method that reduces RSA key variable storage space is characterized in that, the concrete operations step:

The first step is chosen variables D ₁, make Z=2 ⁴⁸⁸-2D ₁+ 1 is a prime number that length is 488 bits, will utilize Z to produce other parameter below, and used computing and symbol thereof are enumerated as follows:

OR: binary number ' or ' computing,

Mod: the modular arithmetic of number,

[K]: be no more than the maximum integer of K,

A*b: expression a and b's multiplies each other,

L (Q): get two of Q and advance the left side 373 bits of expression, promptly preceding 373 bits constitute a new number,

Other computing of below not enumerating is common integer arithmetic;

Second step was chosen D ₂, D ₃, $X_1={D_2}^{(D_3+1)}\mathrm{mod}Z,$ "=(the X that makes P ₁) OR (2 ⁴⁸⁷+ 1) is a prime number that length is 488 bits;

The 3rd step was chosen D ₄, make P '=2 (D ₄+ 2 ¹⁰) "+1 is a prime number that length is 500 bits to P;

The 4th step was chosen D ₅, make P=2 (D ₅+ 2 ¹⁰) P '+1 is a prime number that length is 512 bits;

The 5th step was calculated X ₂=[2 ¹⁰²⁴/ P], with X ₂Last pressure of binary representation change 1 into, X ₃

The 6th step was chosen D ₆, "=2 (D that make Q ₆+ 2 ¹⁰) X ₃+ 1 is a prime number that length is 488 bits;

The 7th step was chosen D ₇, make Q '=2 (D ₇+ 2 ¹⁰) "+1 is a prime number that length is 500 bits to Q;

The 8th step was chosen D ₈, make Q=2 (D ₈+ 2 ¹⁰) Q '+1 is a prime number that length is 512 bits;

The 9th step was calculated modulus N=P*Q, and this moment, the length of N was 1024 bits;

The tenth step was chosen D ₉, calculate d=2 ³⁷⁴+ 2 (D ₉+ L (Q))+1, make e 〉=2 of e*d ≡ 1 mod (P-1) in (Q-1) ¹⁷+ 1;

The 11 step made PKI PK=e, private key SK=d, and this moment, the length of PKI PK and private key SK was 1024 bits;

The 12 goes on foot so far variables D ₁, D ₂, D ₃, D ₄, D ₅, D ₆, D ₇, D ₈And D ₉All generate, wherein, variables D ₂And D ₉Length be respectively 20 and 16 bits, remaining length is 10 bits.

2, method according to claim 1 is characterized in that, with 9 variables D of this method generation ₁, D ₂, D ₃, D ₄, D ₅, D ₆, D ₇, D ₈And D ₉The length that is stored on the magnetic stripe card is on the memory space of 106 bits, makes to be suitable for system's couplings such as EFT and POS machine, not only safe but also can resist authenticating user identification card or the authentification of message card that the little finger of toe number is attacked.

3, described authenticating user identification card of claim 2 or authentification of message card are used for the method for systemic effect family authentications such as EFT and POS machine, it is characterized in that, the data of 106 bits by prior precomputation and the inverse process of aforesaid operations step can recover modulus N, key K P easily: PKI PK and private key SK.Known: authenticating user identification data, its length are 106 bits, and 9 groups of variable: D ₁, D ₂, D ₃, D ₄, D ₅, D ₆, D ₇, D ₈And D ₉, below be to recover modulus N, key K P: the process of PKI PK and private key SK:

1、Z＝2 ⁴⁸⁸-2D ₁+1

With D ₁The substitution following formula gets Z;

2、 $X_1={D_2}^{(D_3+1)}\mathrm{mod}Z$

With D ₂, D ₃With Z substitution following formula, get X ₁

3、P″＝(X ₁)OR(2 ⁴⁸⁷+1)

With X ₁The substitution following formula gets P ";

4、P′＝2(D ₄+2 ¹⁰)P″+1

With D ₄" the substitution following formula gets P ' to and P;

5、P＝2(D ₅+2 ¹⁰)P′+1

With D ₅And P ' substitution following formula, get P;

6、X ₂＝[2 ¹⁰²⁴/P]

8、Q″＝2(D ₆+2 ¹⁰)X ₃+1

With D ₆And X ₃The substitution following formula gets Q ";

9、Q′＝2(D ₇+2 ¹⁰)Q″+1

With D ₇" the substitution following formula gets Q ' to and Q;

10、Q＝2(D ₈+2 ¹⁰)Q′+1

With D ₈And Q ' substitution following formula, get Q;

11、N＝P*Q

With P and Q substitution following formula, get N;

12、d＝2 ³⁷⁴+2(D ₉+L(Q))+1

With D ₉And L (Q) substitution following formula, get d;

13、e*d≡1mod(P-1)(Q-1)

With d, P and Q substitution following formula get e;

14、PK＝e，SK＝d

So far, the modulus that recovers, PKI and private key are respectively N, PK and SK, modulus N, the length of PKI PK and private key SK is 1024 bits.

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