CN113904777A - Signcryption method based on SM2 digital signature algorithm - Google Patents

Signcryption method based on SM2 digital signature algorithm Download PDF

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CN113904777A
CN113904777A CN202111110965.2A CN202111110965A CN113904777A CN 113904777 A CN113904777 A CN 113904777A CN 202111110965 A CN202111110965 A CN 202111110965A CN 113904777 A CN113904777 A CN 113904777A
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CN113904777B (en
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何德彪
陈鑫
罗敏
刘丽群
崔晓晖
黄欣沂
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Wuhan University WHU
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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
    • H04L9/3252—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 DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr schemes
    • 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
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H04L9/0825—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/72—Signcrypting, i.e. digital signing and encrypting simultaneously

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  • Computer Networks & Wireless Communication (AREA)
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Abstract

The invention relates to a signing and encrypting method based on SM2 digital signature algorithm, which is based on domestic commercial cipher algorithm and comprises four algorithms of initialization algorithm, secret key generation algorithm, signing and encrypting algorithm and signing and decrypting algorithm, thereby realizing autonomous control of data storage and sharing, promoting the application of domestic commercial cipher algorithm, realizing data storage and sharing which can prove safe in the environments of cloud computing, Internet of things, block chain and the like, meeting the safety requirements of confidentiality, authentication, integrity, unforgeability and the like of transmitted information, and simultaneously meeting the compliance requirement of domestic commercial cipher application.

Description

Signcryption method based on SM2 digital signature algorithm
Technical Field
The invention relates to the field of computers, in particular to a signcryption method based on an SM2 digital signature algorithm.
Background
The signcryption is an important cryptology primitive, can simultaneously complete two functions of digital signature and encryption in a reasonable logic step, has higher efficiency than a scheme of firstly encrypting and then signing, and can simultaneously realize data confidentiality and integrity protection. The SM2 algorithm is an elliptic curve public key cryptographic algorithm released by the national crypto authority in 2010, and includes a digital signature algorithm, a key exchange protocol and a public key encryption algorithm. The SM2 algorithm has become the standard GM/T0003.2-2012 of the public key algorithm in China, and enters the international standard ISO/IEC 14888-3: 2016, it has important meaning to the information security construction of our country.
With the wide application of technologies such as cloud computing, internet of things, block chaining and the like, security and privacy of data storage and sharing become more and more concerned issues for researchers. Different from the traditional scheme of firstly encrypting and then signing, the signing and encrypting scheme reduces the calculation amount and ciphertext expansion while meeting the security requirements of confidentiality, authentication, unforgeability and the like of data storage and sharing. However, the existing signcryption schemes are designed based on foreign cryptographic algorithms/standards, and the signcryption schemes based on domestic commercial cryptographic algorithms are designed, so that autonomous and controllable data security sharing/transmission is realized.
Disclosure of Invention
The technical problem of the invention is mainly solved by the following technical scheme:
a signcryption method based on SM2 digital signature algorithm is characterized by comprising the following steps:
the method comprises the following steps of initialization, wherein an administrator defines an elliptic curve, a plurality of hash functions and two prime numbers, generates a generation element with an order as one of the prime numbers based on the elliptic curve, and finally outputs a system function with parameters of the generation element, the two prime numbers, the hash functions and the elliptic curve;
a step of generating a secret key, in which a sender generates a random number and a sender public key containing a generator; the receiver generates a random number and a receiver public key containing a generator;
a signing and encrypting step, namely calculating and outputting a signing and encrypting ciphertext containing the elliptic parameter, the plaintext data, the sender private key, the receiver public key and the random number according to the given plaintext data, the sender private key and the random number;
and (3) a decryption step: and the decryption user sends a decryption request, calculates partial parameters in the signcryption text and verifies the partial parameters, and if the partial parameters pass the verification, the clear text data is output, otherwise, the decryption request is rejected.
In the foregoing signcryption method based on the SM2 digital signature algorithm, the initialization step specifically includes:
step 2.1, selecting the length l as large prime numbers p and q;
step 2.2, selecting and defining in a finite field FpUpper elliptic curve E: y2＝x3+a·x+bmodq；
Step 2.3, selecting a generator G with the order q on the elliptic curve E;
step 2.4, select 3 hash functions H0:{0,1}*→{0,1}256，H1:{0,1}*→{0,1}nAnd
Figure BDA0003273981070000021
step 2.5, outputting system parameter params ═ { p, q, a, b, G, H0,H1,H2}；
In the foregoing signcryption method based on the SM2 digital signature algorithm, the key generation step specifically includes:
step 3.1 the sender generates random numbers with a random number generator
Figure BDA0003273981070000022
Step 3.3, sender calculates public key PS＝dS·G；
Step 3.3, the recipient generates random numbers with a random number generator
Figure BDA0003273981070000023
Step 3.4, the receiver calculates the public key PR＝dR·G。
In the foregoing signcryption method based on the SM2 digital signature algorithm, the signcryption step specifically includes:
step 4.1, Generation of random numbers with a random number Generator
Figure BDA0003273981070000031
Step 4.2, calculating elliptic curve point T1＝k·G＝(x1,y1)；
Step 4.3, calculating elliptic curve point T2＝k·PR；
Step 4.4, calculating the hash value ZS＝H0(ENTLS||IDS||a||b||PS)；
Step 4.5, calculating bit string
Figure BDA0003273981070000032
Step 4.6, calculating the hash value e ═ H2(ZS||c)；
Step 4.7, calculate integer r ═ e + x1mod q；
Step 4.8, calculate integer s ═ 1+ dS)-1·(k-r·dS)mod q；
And 4.9, outputting the signed cipher text CT (c, r, s).
In the foregoing signcryption method based on the SM2 digital signature algorithm, the step of unfastening specifically includes:
step 5.1, calculating the hash value ZS＝H0(ENTLS||IDS||a||b||PS)；
Step 5.2, calculating the hash value e ═ H2(ZS||c)；
Step 5.3, calculating an integer t ═ r + smod q;
step 5.4, calculating an elliptic curve point T1＝s·G+t·PS＝(x1,y1)；
Step 5.5, verify the equation r ═ e + x1Whether mod q is true or not, if not, rejecting the message and terminating;
step 5.6, calculating elliptic curve point T2＝dR·T1；
Step 5.7, calculating and outputting plaintext data
Figure BDA0003273981070000033
Compared with the prior art, the invention has the following advantages and beneficial effects: at present, the signcryption scheme is designed by adopting foreign cryptographic algorithms/standards, and domestic commercial cryptographic algorithms are not applied to the design of the signcryption scheme. In the signcryption scheme designed by the invention, based on an SM2 digital signature algorithm, the autonomous and controllable data security storage and sharing under the environments of cloud computing, the Internet of things, a block chain and the like are realized, the security requirements of confidentiality, authentication, integrity, non-forgeability and the like of transmission information are met, and the requirement of the application compliance of domestic commercial passwords is met.
Drawings
FIG. 1 is a flow chart of a method of the present invention.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
Example (b):
first, the symbols and definitions related to the present embodiment will be explained
q: big prime number
Fq: a finite field containing q elements.
a,b：FqThe elements in (1), which define FqAn elliptic curve E above.
E(Fq)：FqThe set of all rational points of the upper elliptic curve E, including the point of infinity O.
#E(Fq)：E(Fq) The number of points, called elliptic curve E (F)q) The order of (a).
O: a particular point on the elliptic curve is called the infinity point or the null point.
Figure BDA0003273981070000041
A cyclic group containing all points of the elliptic curve E and points at infinity.
G: group of
Figure BDA0003273981070000042
The generator of (1).
H (·): a secure cryptographic hash function, such as the SM3 algorithm.
M: a message value.
n: the message length.
L |: and (5) splicing bit strings.
The scheme comprises four algorithms: an initialization algorithm, a key generation algorithm, a signcryption algorithm, and a signcryption algorithm.
Initialization algorithm Setup: the system administrator executes the following algorithm to generate system parameters.
1) Selecting the length l as large prime numbers p and q;
2) selection is defined in a finite field FpUpper elliptic curve E: y2＝x3+a·x+bmodq；
3) Selecting a generator G with the order q on the elliptic curve E;
4) selecting 3 hash functions H0:{0,1}*→{0,1}256，H1:{0,1}*→{0,1}nAnd
Figure BDA0003273981070000051
5) output system parameter params ═ { p, q, a, b, G, H0,H1,H2}；
Key generation algorithm KeyGen: the sender and the receiver respectively execute the algorithm to generate respective public and private keys.
1) Random number generator for generating random number by sender
Figure BDA0003273981070000052
2) Sender calculates public key PS＝dS·G；
3) For the receiverRandom number generator for generating random numbers
Figure BDA0003273981070000053
4) The receiver calculates the public key PR＝dR·G；
Signcrypt algorithm Signcrypt: given plaintext data M e {0,1}nRecipient public key PRAnd sender private key dSExecuting the following operation steps:
1) generating random numbers using a random number generator
Figure BDA0003273981070000054
2) Calculating elliptic curve point T1＝k·G＝(x1,y1)；
3) Calculating elliptic curve point T2＝k·PR；
4) Computing a hash value ZS＝H0(ENTLS||IDS||a||b||PS)；
5) Computing bit strings
Figure BDA0003273981070000055
6) Calculating the hash value e ═ H2(ZS||c)；
7) Calculating the integer r ═ e + x1mod q；
8) Calculating the integer s ═ 1+ dS)-1·(k-r·dS)mod q；
9) Outputting a signcryption ciphertext CT ═ c, r, s;
the Unsigncrypt algorithm Unsigncrypt: in order to decrypt and verify the signed cipher text CT ═ c, r, s, the decryption user performs the following operation steps:
1) computing a hash value ZS＝H0(ENTLS||IDS||a||b||PS)；
2) Calculating the hash value e ═ H2(ZS||c)；
3) Calculating an integer t ═ r + smod q;
4) calculating elliptic curve point T1＝s·G+t·PS＝(x1,y1)；
5) Verify equation r ═ e + x1Whether mod q is true or not, if not, rejecting the message and terminating;
6) calculating elliptic curve point T2＝dR·T1；
7) Calculate and output plaintext data
Figure BDA0003273981070000061
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (5)

1. A signcryption method based on SM2 digital signature algorithm is characterized by comprising the following steps:
the method comprises the following steps of initialization, wherein an administrator defines an elliptic curve, a plurality of hash functions and two prime numbers, generates a generation element with an order as one of the prime numbers based on the elliptic curve, and finally outputs a system function with parameters of the generation element, the two prime numbers, the hash functions and the elliptic curve;
a step of generating a secret key, in which a sender generates a random number and a sender public key containing a generator; the receiver generates a random number and a receiver public key containing a generator;
a signing and encrypting step, namely calculating and outputting a signing and encrypting ciphertext containing the elliptic parameter, the plaintext data, the sender private key, the receiver public key and the random number according to the given plaintext data, the sender private key and the random number;
and (3) a decryption step: and the decryption user sends a decryption request, calculates partial parameters in the signcryption text and verifies the partial parameters, and if the partial parameters pass the verification, the clear text data is output, otherwise, the decryption request is rejected.
2. The signcryption method based on the SM2 digital signature algorithm as claimed in claim 1, wherein the initialization step specifically comprises:
step 2.1, selecting the length l as large prime numbers p and q;
step 2.2, selecting and defining in a finite field FpUpper elliptic curve E: y2＝x3+a·x+bmodq；
Step 2.3, selecting a generator G with the order q on the elliptic curve E;
step 2.4, select 3 hash functions H0:{0,1}*→{0,1}256，H1:{0,1}*→{0,1}nAnd
Figure FDA0003273981060000011
step 2.5, outputting system parameter params ═ { p, q, a, b, G, H0,H1,H2}。
3. The signcryption method based on the SM2 digital signature algorithm of claim 1, wherein the key generation step specifically includes:
step 3.1 the sender generates random numbers with a random number generator
Figure FDA0003273981060000021
Step 3.3, sender calculates public key PS＝dS·G；
Step 3.3, the recipient generates random numbers with a random number generator
Figure FDA0003273981060000022
Step 3.4, the receiver calculates the public key PR＝dR·G。
4. The signcryption method based on the SM2 digital signature algorithm of claim 1, wherein the signcryption step specifically includes:
step 4.1, Generation of random numbers with a random number Generator
Figure FDA0003273981060000023
Step 4.2, calculating elliptic curve point T1＝k·G＝(x1,y1)；
Step 4.3, calculating elliptic curve point T2＝k·PR；
Step 4.4, calculating the hash value ZS＝H0(ENTLS||IDS||a||b||PS)；
Step 4.5, calculating bit string
Figure FDA0003273981060000024
Step 4.6, calculating the hash value e ═ H2(ZS||c)；
Step 4.7, calculate integer r ═ e + x1mod q；
Step 4.8, calculate integer s ═ 1+ dS)-1·(k-r·dS)mod q；
And 4.9, outputting the signed cipher text CT (c, r, s).
5. The signcryption method based on the SM2 digital signature algorithm of claim 1, wherein the signcryption step specifically includes:
step 5.1, calculating the hash value ZS＝H0(ENTLS||IDS||a||b||PS)；
Step 5.2, calculating the hash value e ═ H2(ZS||c)；
Step 5.3, calculating an integer t ═ r + smod q;
step 5.4, calculating an elliptic curve point T1＝s·G+t·PS＝(x1,y1)；
Step 5.5, verify the equation r ═ e + x1Whether mod q is true or not, if not, rejecting the message and terminating;
step 5.6, calculating the elliptic curveLine point T2＝dR·T1；
Step 5.7, calculating and outputting plaintext data
Figure FDA0003273981060000031
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