CN106612182A - Method for implementing SM2 white-box digital signature based on residue number system - Google Patents

Method for implementing SM2 white-box digital signature based on residue number system Download PDF

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CN106612182A
CN106612182A CN201611202646.3A CN201611202646A CN106612182A CN 106612182 A CN106612182 A CN 106612182A CN 201611202646 A CN201611202646 A CN 201611202646A CN 106612182 A CN106612182 A CN 106612182A
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client
sbox1
private key
residue number
number system
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CN106612182B (en
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白健
周洁
安红章
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CETC 30 Research Institute
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H04L9/3249—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using RSA or related signature schemes, e.g. Rabin scheme
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves

Abstract

The invention provides a method for implementing an SM2 white-box digital signature based on a residue number system. The method carries out research in allusion to problems that a key is unsafe in operation in an incredible environment and that a malicious attacker can acquire the key of the system through a means of white-box attacks. Splitting of a big number is realized through using the residue number system, so that the size of a key table is reduced; an intermediate result is ensured to be invisible to the attacker through using scrambling and confounding; and the uncertainty of a terminal key operation relation is ensured through using a random factor of the cloud, the safety of a signature private key in the terminal signature operation process is realized, and verification can be performed by using a standard SM2 signature verification algorithm at the same time. The method provided by the invention is small in required storage space, high in calculation efficiency, good in safety and high in practicability.

Description

A kind of SM2 whitepack digital signature implementation methods based on residue number system
Technical field
The present invention relates to field of information security technology, more particularly to a kind of SM2 whitepacks numeral label based on residue number system Name implementation method.
Background technology
Existing software cryptography algorithm, key is that among the internal memory for occurring directly in calculating platform, attacker can be by disliking Meaning software etc. realizes stealing for key, it is impossible to tackle existing white-box attack means；Existing hardware encryption algorithm, can be preferably Ensure the safety of cipher key calculation, but relative usage is relatively costly, and versatility is poor, relatively low for Partial security requirement Application scenarios cannot use；Simultaneously also part research institution proposes and adds end part of key and key dispersion storage based on cloud The software cryptography algorithm of strategy, but the strategy of Yun Jiaduan cannot resist the leakage of local private key, also store the mirror in high in the clouds and terminal Power problem, key dispersion storage strategy must synthesize key when key computing is carried out, and key be equally existed in internal memory completely bright Text.
The content of the invention
To solve the above problems, the invention provides a kind of SM2 whitepack digital signature implementation methods based on residue number system, The applicable system of methods described includes client and server, and the system modulus of the system is n, and submodule is mrIt is selected The basic point of elliptic curve is G, and signature information is M characterized in that, comprising the steps：
Step one：Client chooses public key d, private key P.A residue number system is selected, prime number base is β=(p1, p2..., pt), the dynamic range of base β meets ω=p1p2p3…pt≥2768。
Step 2：Client generates the first private key look-up table, the second private key look-up table.Concrete grammar is：
Step 2.1：Two non-linear replacement of keys tables are randomly selected, Sbox1, Sbox2 are designated as respectively, and by server Public key oneself client id and Sbox1 be sent to into server preserved.
Step 2.2：Public key P is converted into into P using residue number systemi, wherein i=1 ..., t, r, and generate the first private key and look into Look for table Table1, i(i=1 ..., t, r), generation method is：Random ergodic produces two random number Ns1And N2, wherein N2, N1∈ [1, n-1], by residue number system N is separately converted to1iAnd N2i, calculate ui=sbox2 (N1, i×sbox1-1(sbox1 (N2, i))modpi), all u that traversal is producediAs table Table1, iThe element of (i=1 ..., t, r).
Step 2.3：The second private key look-up table Table is generated using private key d and residue number system2, i(i=1 ..., t, r), it is raw It is into method：Random ergodic produces two random number L1And L2, wherein L2, L1∈ [1, n-1], is distinguished by residue number system It is converted into L1iAnd L2i, while private key d is converted to into di, calculate si=di×(sbox2-1(L1i)-L2i×di)mod pi, will travel through The all s for producingiAs table Table2, iThe element of (i=1 ..., t, r)；
Step 3：Client is signed, and concrete grammar is：
Step 3.1：Client calculates M '=M | | ZA；Wherein, M is signature information, ZAFor the identity of client.
Step 3.2：Client calculates eap-message digest e=H with hash functionv(M’)。
Step 3.3:Client produces the first random number k1∈ [1, n-1]；
Step 3.4：Client calculates elliptic curve point Q1=[k1] * G, and by e and Q1It is sent to server；Wherein,
Step 3.5:Server produces the second random number k2∈ [1, n-1]；
Step 3.6:Server calculates elliptic curve point (x1, y1)=[k2]*Q1；
Step 3.7：Server calculates Part I signature r=(x1+ e) mod n, by the second random number k2Based on base β | prK is expressed as with residue number system2=(k2,1..., k2, t|k2, r), obscured by Sbox1, then by r and Sbox1 (k2) =[sbox1 (k2,1), sbox1 (k2,2) ..., sbox1 (k2, t)|sbox1(k2, r)] it is sent to client.
Step 3.8：Client is by the first random number K1With r based on base β | prK is expressed as with residue number system1=(k1,1, k1,2..., k1, t|k1, r) and r=(r1, r2..., rt|rr)；
Step 3.9：Client uses the first private key look-up table Table1, i(i=1 ..., t, r) calculates intermediate value ui= sbox2(k1, i×sbox1-1(sbox1(k2, i))modpi)。
Step 4.0:Client uses the second private key look-up table Table2, i(i=1 ..., t, r) calculates si=di× (sbox2-1(ui)-ri×dA, i)mod pi, wherein private key dAIt is hidden in the second private key look-up table Table2, iIn.
Step 4.1：Client recovers s using Chinese remainder theorem.
Step 4.3：Client calculates s '=s mod n, and s ' is Part II signature value.
Step 5：Output message M and signature.
Further, each random number is produced using randomizer.
Beneficial effects of the present invention are：
(1) client is not in the complete plaintext of private key in the hardware device such as internal memory in signature calculating process is carried out, Guarantee the white-box attack safety that cryptographic algorithm runs.
(2) realize that this method only needs the internal layer size of 207.5MB, memory space to require less.
(3) the signature efficiency of this implementation method and original SM2 algorithms is basically identical, and practicality is higher.
(4) realize that the use cost of commercial cipher algorithm can be reduced by using whitepack software, expand commercial cipher algorithm Use range.
(5) using whitepack software algorithm while guaranteeing that encryption and decryption is safe, versatility is stronger, does not have to operation platform hardware There is any specific demand.
Description of the drawings
The schematic flow sheet that Fig. 1 is signed for client.
Specific embodiment
The present invention design concept be：It is directed in untrusted environment that key operation is dangerous, malicious attacker can pass through White-box attack means obtain the problem of system key and launch research, the fractionation of big number are realized by using residue number system, so as to drop The size of low key list；Being obscured by using scramble guarantees that intermediate result is invisible to attacker；By using the random of high in the clouds The factor guarantees the non-intellectual of terminal key operation relation, realizes the signature private key safety in terminal signature calculating process, while Can be verified using the SM2 sign test algorithms of standard.
The present invention is built based on national commercial cipher algorithm SM2 Digital Signature Algorithms, and SM2 Digital Signature Algorithms please join Plus the administrative standard that national commercial cipher management board issues, while invention also uses a typical mathematical tool --- it is remaining Number system, is described in detail as follows：
The definition of residue number system can be described as：It is now assumed that there is a residue number system, it is by one group of prime number each other Remainder base β=(m1, m2..., mkCome what is determined, M=m1m2…mkFor the dynamic range of this group of base.For arbitrary integer x≤M, (x can be uniquely expressed as under this group of base of β1, x2..., xk), wherein xiIt is x to miModulus result, be designated as For residue number system, only when the expression of integer x ability existence anduniquess within dynamic range.
Assume that integer x, y are expressed as x=(x under base β1, x2..., xk) and y=(y1, y2..., yk), then：
Wherein " ο " for+,-, × computing.
Residue number system for x represents (x1, x2..., xk), by Chinese remainder theorem：
Wherein α ＜ k, Mi=M/mi,For MiIn mould miUnder it is inverse.α can be by selecting a suitable submodule mrTo recover, wherein mr>=k+1 and gcd (M, mr)=1.If xrIt is x to mrModulus result, i.e.,：
Then：
Because α is ＜ k ＜ mr, soFor arbitrary integer x, can be in extension base Under be expressed as (x1, x2..., xk|xr), referred to as extend RNS and represent.
The applicable system of the method for the invention includes client and server.Client namely performs digital signature calculation The user of method, its running environment is incredible, and server is collaboration signer, and it belongs to a portion of KMC Part, it is mainly client and provides a random factor.
It is assumed that the system modulus of the system is n, submodule is mr, the basic point of selected elliptic curve is G, and signature disappears Cease for M, ZAFor the identity of client, HvIt is the abstract function (can practical commercial cipher standard SM3 algorithm) for using.We Method includes altogether 4 parts：(1) parameter is chosen and key is generated；(2) generation of private key table；(3) signature calculation；(4) sign test meter Calculate.Wherein (1) and (4) performs with reference to national commercialization SM2 Digital Signature Algorithms standard.
The concrete steps of the present invention are described as follows：
Step one：Client chooses public key d, private key P.A residue number system is selected, prime number base is β=(p1, p2..., pt), the dynamic range of base β meets ω=p1p2p3…pt≥2768。
Step 2：Client generates the first private key look-up table, the second private key look-up table.Concrete grammar is：
Step 2.1：It (is consistent with the S boxes used in symmetric cryptographic algorithm to randomly select two non-linear replacement of keys tables ), Sbox1, Sbox2 are designated as respectively, and oneself client id and Sbox1 are sent to by server by the public key of server Preserved.
Step 2.2：Public key P is converted into into P using residue number systemi, wherein i=1 ..., t, r, and generate the first private key and look into Look for table Table1, i(i=1 ..., t, r), generation method is：Random ergodic produces two random number Ns1And N2, wherein N2, N1∈ [1, n-1], by residue number system N is separately converted to1iAnd N2i, calculate ui=sbox2 (N1, i×sbox1-1(sbox1 (N2, i))modpi), all u that traversal is producediAs table Table1, iThe element of (i=1 ..., t, r).
Step 2.3：The second private key look-up table Table is generated using private key d and residue number system2, i(i=1 ..., t, r), it is raw It is into method：Random ergodic produces two random number L1And L2, wherein L2, L1∈ [1, n-1], is distinguished by residue number system It is converted into L1iAnd L2i, while private key d is converted to into di, calculate si=di×(sbox2-1(L1i)-L2i×di)mod pi, will travel through The all s for producingiAs table Table2, iThe element of (i=1 ..., t, r)；
Step 3：Client is signed, and concrete grammar is：
Step 3.1：Client calculates M '=M | | ZA；Wherein, M is signature information, ZAFor the identity of client.
Step 3.2：Client calculates eap-message digest e=H with hash functionv(M’)。
Step 3.3:Client produces the first random number k with randomizer1∈ [1, n-1]；
Step 3.4：Client calculates elliptic curve point Q1=[k1] * G, and by e and Q1It is sent to server；Wherein,
Step 3.5:Server produces the second random number k with randomizer2∈ [1, n-1]；
Step 3.6:Server calculates elliptic curve point (x1, y1)=[k2]*Q1；
Step 3.7：Server calculates Part I signature r=(x1+ e) mod n, by the second random number k2Based on base β | prK is expressed as with residue number system2=(k2,1..., k2, t|k2, r), obscured by Sbox1, then by r and Sbox1 (k2) =[sbox1 (k2,1), sbox1 (k2,2) ..., sbox1 (k2, t)|sbox1(k2, r)] it is sent to client.
Step 3.8：Client is by the first random number k1With r based on base β | prK is expressed as with residue number system1=(k1,1, k1,2..., k1, t|k1, r) and r=(r1, r2..., rt|rr)；
Step 3.9：Client uses the first private key look-up table Table1, i(i=1 ..., t, r) calculates intermediate value ui= sbox2(k1, i×sbox1-1(sbox1(k2, i))modpi)。
Step 4.0:Client uses the second private key look-up table Table2, i(i=1 ..., t, r) calculates si=di× (sbox2-1(ui)-ri×dA, i)mod pi, wherein private key dAIt is hidden in the second private key look-up table Table2, iIn.
Step 4.1：Client recovers s using Chinese remainder theorem.
Step 4.3：Client calculates s '=s mod n, and s ' is Part II signature value.
Step 5：Output message M and signature.
Further, each random number is produced using randomizer.

Claims (2)

1. a kind of SM2 whitepack digital signature implementation methods based on residue number system, the applicable system of methods described includes client And server, the system modulus of the system is n, and submodule is mr, the basic point of selected elliptic curve is G, signature information For M, it is characterised in that comprise the steps：
Step one：Client chooses public key d, private key P；A residue number system is selected, prime number base is β=(p1, p2..., pt), base The dynamic range of β meets ω=p1p2p3…pt≥2768；
Step 2：Client generates the first private key look-up table, the second private key look-up table；Concrete grammar is：
Step 2.1：Two non-linear replacement of keys tables are randomly selected, Sbox1, Sbox2, and the public affairs for passing through server are designated as respectively Oneself client id and Sbox1 are sent to server and are preserved by key；
Step 2.2：Public key P is converted into into P using residue number systemi, wherein i=1 ..., t, r, and generate the first private key look-up table Table1, i(i=1 ..., t, r), generation method is：Random ergodic produces two random number Ns1And N2, wherein N2, N1∈ [1, n- 1], N is separately converted to by residue number system1iAnd N2i, calculate ui=sbox2 (N1, i×sbox1-1(sbox1(N2, i)) modpi), all u that traversal is producediAs table Table1, iThe element of (i=1 ..., t, r)；
Step 2.3：The second private key look-up table Table is generated using private key d and residue number system2, i(i=1 ..., t, r), generation side Method is：Random ergodic produces two random number L1And L2, wherein L2, L1∈ [1, n-1], is respectively converted it by residue number system For L1iAnd L2i, while private key d is converted to into di, calculate si=di×(sbox2-1(L1i)-L2i×di)mod pi, traversal is produced All siAs table Table2, iThe element of (i=1 ..., t, r)；
Step 3：Client is signed, and concrete grammar is：
Step 3.1：Client calculates M '=M | | ZA；Wherein, M is signature information, ZAFor the identity of client；
Step 3.2：Client calculates eap-message digest e=H with hash functionv(M’)；
Step 3.3:Client produces the first random number k1∈ [1, n-1]；
Step 3.4：Client calculates elliptic curve point Q1=[k1] * G, and by e and Q1It is sent to server；Wherein,
Step 3.5:Server produces the second random number k2∈ [1, n-1]；
Step 3.6:Server calculates elliptic curve point (x1, y1)=[k2]*Q1；
Step 3.7：Server calculates Part I signature r=(x1+ e) mod n, by the second random number k2Based on base β | prUse Residue number system is expressed as k2=(k2,1..., k2, t|k2, r), obscured by Sbox1, then by r and
Sbox1(k2)=[sbox1 (k2,1), sbox1 (k2,2) ..., sbox1 (k2, t)|sbox1(k2, r)] it is sent to client；
Step 3.8：Client is by the first random number K1With r based on base β | prK is expressed as with residue number system1=(k1,1, k1,2..., k1, t|k1, r) and r=(r1, r2..., rt|rr)；
Step 3.9：Client uses the first private key look-up table Table1, i(i=1 ..., t, r) calculates intermediate value ui=sbox2 (k1, i×sbox1-1(sbox1(k2, i))modpi)；
Step 4.0:Client uses the second private key look-up table Table2, i(i=1 ..., t, r) calculates si=di×(sbox2-1 (ui)-ri×dA, i)modpi, wherein private key dAIt is hidden in the second private key look-up table Table2, iIn；
Step 4.1：Client recovers s using Chinese remainder theorem；
Step 4.3：Client calculates s '=s mod n, and s ' is Part II signature value；
Step 5：Output message M and signature.
2. the SM2 whitepack digital signature implementation methods of residue number system are based on as claimed in claim 1, and each random number is to utilize Randomizer is produced.
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CN107465508A (en) * 2017-08-07 2017-12-12 收付宝科技有限公司 A kind of method, system and the equipment of software and hardware combining construction true random number
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CN108134673A (en) * 2017-12-29 2018-06-08 北京梆梆安全科技有限公司 A kind of method and device for generating whitepack library file
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CN108040077A (en) * 2018-02-09 2018-05-15 成都康赛信息技术有限公司 The mixed scrambling Encryption Algorithm for preventing network system data from revealing
CN108737103A (en) * 2018-03-27 2018-11-02 中国科学院数据与通信保护研究教育中心 A kind of SM2 algorithm endorsement methods applied to CS frameworks
CN108737103B (en) * 2018-03-27 2021-06-29 中国科学院数据与通信保护研究教育中心 SM2 algorithm signature method applied to CS framework
CN108667619B (en) * 2018-05-10 2020-11-24 武汉大学 White box implementation method and device for SM9 digital signature
CN108667619A (en) * 2018-05-10 2018-10-16 武汉大学 A kind of the whitepack implementation method and device of SM9 digital signature
CN109412813B (en) * 2018-09-14 2019-08-09 北京海泰方圆科技股份有限公司 The endorsement method of elliptic curve, sign test method and apparatus
CN109412813A (en) * 2018-09-14 2019-03-01 北京海泰方圆科技股份有限公司 The endorsement method of elliptic curve, sign test method and apparatus
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CN110971409A (en) * 2019-12-03 2020-04-07 成都卫士通信息产业股份有限公司 White box implementation method, device, equipment and medium for point doubling operation on elliptic curve
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