CN114065247B - Quantum digital mixing signcryption method - Google Patents
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Abstract
The invention provides a quantum digital mixed signcryption method, which comprises the steps that a signcryption party performs key negotiation with a receiver and a signcryption checking party, the signcryption operation is executed, and the receiver and the signcryption checking party verify mixed signatures. The method of the invention realizes the encryption effect of the plaintext message by mixing the plaintext message, the plaintext abstract and the character string formed by the coefficients of each item except the highest item, the proposal does not need to encrypt the plaintext message by using an extra key, thereby effectively saving key resources and achieving the effect that the plaintext message does not directly appear in the transmission process, and improving the hash function used in the signcryption process, so that the receiver and the signcryption party cannot obtain the irreducible polynomial generating the hash function in advance before verification, and further ensuring the security of the whole signcryption process.
Description
Technical Field
The invention relates to the technical field of quantum security, in particular to a quantum digital mixing signcryption method.
Background
Encryption and digital signature are two basic encryption tools that guarantee confidentiality, integrity, authenticity, and non-repudiation. Until 1997, they were still considered as important but completely different components of various cryptosystems. In an asymmetric key system, a traditional method is to digitally sign a message and then encrypt an output, and the superposition scheme has low efficiency and high cost, and any scheme cannot guarantee the security.
Signcryption is a relatively new cryptographic technique, and Yuliang Zheng proposed the first signcryption scheme in 1997. Zheng also proposes an elliptic curve-based signature encryption scheme that can save 58% of calculation amount and 40% of communication cost compared with a conventional elliptic curve-based signature re-encryption scheme. Compared with the traditional sign-then-encryption scheme, the signcryption can complete the functions of digital signature and encryption in one logic step, effectively reduces the computational power consumption and communication loss, and simultaneously provides the characteristics of the digital signature and encryption scheme in a more efficient manner.
The current general digital signcryption scheme is mostly based on an asymmetric key system, the security of the digital signcryption scheme is based on an unproven mathematical calculation difficult problem, along with the rapid improvement of classical calculation power and the explosive development of quantum algorithms, the violent cracking of various signcryption algorithms by an attacker is possible in the near future, and the security of the current digital signcryption scheme can not meet the requirements of the current rapid development digital society for guaranteeing the security of messages while verifying the authenticity of the messages.
In summary, the security of the existing classical digital signcryption scheme cannot meet the current requirements of the rapidly developed digital society, in addition, when a long message is signed, the existing scheme also has the defects of overlong key length, too much, too low resource utilization rate, poor system compatibility, rapid rise of computation complexity and the like, and under the condition, it is particularly important and urgent to find an efficient and unconditionally safe quantum digital signcryption scheme.
Disclosure of Invention
1. Technical problem to be solved
The security of the classical digital signcryption protocol in the present stage is greatly threatened, a plurality of early hash functions and public key algorithms are already broken, the security is no longer ensured, and especially the appearance of a future quantum computer also forms a fatal threat to the algorithm security of the current digital signcryption protocol. Meanwhile, in the conventional signcryption scheme, a plaintext message to be transmitted needs to be encrypted, which consumes an additional encryption key and occupies additional communication resources. In order to solve the problems, the invention provides a quantum digital mixed signcryption method.
2. Technical proposal
The invention provides a quantum digital mixed signcryption method, which comprises the following steps:
The signer and the receiver conduct key negotiation, respectively obtain a first hash function key and a first key, respectively, and conduct key negotiation, respectively obtain a second hash function key and a second key;
The signer performs mixed signer operation on the message plaintext by using the negotiated secret key, and sends the obtained mixed signature to the receiver;
the receiver sends the received mixed signature and two groups of keys negotiated with the signer to the signer;
The signer sends two groups of keys negotiated with the signer to the receiver;
and the receiver and the signer respectively carry out signcryption verification on the mixed signature, when the two sides pass the signcryption verification, the signcryption is successful, otherwise, the signcryption process is re-executed.
Further, the hybrid signcryption operation includes the steps of:
(1) The signcryption party obtains a group of random numbers from the local place to generate an irreducible polynomial;
(2) The signer obtains a third hash function key of the signer for generating a hash function by using the first hash function key and the second hash function key which are negotiated with the receiver and the signer;
(3) The signcryption party selects an irreducible polynomial and a third hash function key to generate a hash function based on a linear shift register;
(4) The signcryption party uses the hash function to carry out hash operation on the plaintext message to obtain a plaintext abstract;
(5) The signcryption party mixes the plaintext message, the plaintext abstract and the character string formed by the coefficients of each item except the highest item in the irreducible polynomial according to a preset rule to obtain a mixed abstract;
(6) The signer obtains a third key for encryption of the signer by using the first key and the second key negotiated with the receiver and the signer;
(7) And the signer uses a third key to perform unconditional secure encryption on the mixed digest to obtain a mixed signature.
Further, the generating process of the irreducible polynomial is as follows:
1) Firstly, sequentially using coefficients of each item except the highest item in each bit of corresponding polynomial of the random number to generate a polynomial in GF (2) domain, wherein the coefficient of the highest item is 1;
2) Then, verifying whether the polynomial is an irreducible polynomial, if the verification result is no, re-acquiring another group of random numbers from the local of the signcryption party, returning to the step 1) as new random numbers, regenerating the polynomial and verifying; if the verification result is yes, stopping verification to obtain an irreducible polynomial.
Further, the method for verifying whether the polynomial is an irreducible polynomial comprises the following steps:
Sequential verification Whether or not it is true, whereinRepresentation pairRounding, if all i are verified to pass, p (x) is an irreducible polynomial of order n over GF (2); wherein gcd (f (x), g (x)) represents the maximum common factor of f (x) and g (x) over GF (2), f (x) and g (x) referring to two arbitrary polynomials.
Further, the method for verifying whether the polynomial is an irreducible polynomial comprises the following steps:
Verification condition (1) (2)Whether or not to do so simultaneously, whereinRepresentation ofWhere d is an arbitrary element of n, gcd (f (x), g (x)) represents the maximum factors of f (x) and g (x) over GF (2), f (x) and g (x) refer to two arbitrary polynomials, and when both validation conditions are satisfied, p (x) is an irreducible polynomial of order n over GF (2).
Further, before the step 1), if the last bit of the random number is 0, the last bit of the random number is 1; or if the last bit of the n-bit random number is 0, regenerating the random number until the last bit of the generated random number is 1.
Further, the hash function is a toeplitz matrix hash function based on a linear shift register.
Further, the signcryption verification includes the following steps:
(1) The receiver and the signer obtain a fourth hash function key according to the first hash function key and the second hash function key which are owned by the receiver and the signer respectively, and obtain a fourth key according to the first key and the second key;
(2) The receiver and the signature verification party decrypt the mixed signature by using the fourth secret key obtained by each receiver and the signature verification party to obtain a mixed abstract;
(3) Separating the mixed abstract according to a preset rule to obtain a character string composed of the plaintext message, the inverse plaintext abstract and the coefficients of each item except the highest item in the irreducible polynomial;
(4) Generating an irreducible polynomial with the highest term coefficient of 1 by corresponding each bit of the character string to the coefficient of each term except the highest term in the polynomials;
(5) Obtaining a hash function based on a linear shift register by using the irreducible polynomial and a third hash function key;
(6) Carrying out hash operation on the plaintext message by utilizing the hash function to obtain a plaintext abstract;
(7) And judging whether the forward plaintext abstract is equal to the reverse plaintext abstract, if so, accepting the signature, otherwise, refusing the signature.
Further, in the present invention, the length of the plaintext message is m, the lengths of the first hash function key and the second hash function key are n, and the lengths of the first key and the second key are 2n+m.
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
(1) According to the quantum digital mixed signcryption method provided by the invention, the effect of encrypting the plaintext message to be transmitted is achieved in a mixed mode, an encryption key is not required to be additionally consumed, key resources are greatly saved, and the operation complexity of a three-party processing process is reduced;
(2) The invention provides a quantum digital mixed signcryption method, and unconditional security of the method is a one-time hash technical guarantee based on a non-fixed irreducible polynomial and one-time secret proved by an informatics theory. The security of the hash function used for executing the signcryption process is ensured by the irreducible polynomial and the hash function key together, the irreducible polynomial depends on the random number of the local signcryption party, the random number is not known in advance by the receiver and the signcryption party before the signcryption process, and the security of the whole signcryption process is ensured;
(3) By adopting the signcryption method, the messages with any length can be signed, and the efficiency and the safety are higher.
Drawings
Fig. 1 is a schematic flow chart of the hybrid signcryption.
Detailed Description
According to the cryptographic consensus, the quantum digital mixed signcryption scheme provided by the invention has three participants: the signer Alice, the receiver Bob and the signer Charlie are respectively marked as A, B, C, the plaintext message to be transmitted is M, and the length is M.
The invention will now be described in detail with reference to the drawings and the accompanying specific examples.
The invention provides a specific process of a quantum digital mixed signcryption method, which is shown in figure 1, and comprises the following steps:
1. The signer A and the receiver B carry out key negotiation, respectively obtain a first hash function key L ab and a first key R ab, respectively, and carry out key negotiation with the signer C, respectively obtain a second hash function key L ac and a second key R ac; wherein the first hash function key L ab and the second hash function key L ac have a length n and the first key R ab and the second key R ac have a length 2n+m; in practical use, a length of n of 128 is sufficient to ensure the security of the whole signcryption process.
2. The signcryption party A carries out mixed signcryption operation on the message plaintext by utilizing the negotiated secret key, and the method is concretely as follows:
(1) The signcryption party A obtains a group of random numbers k with the length of n from the local place and is used for generating an irreducible polynomial p (x), specifically:
firstly, sequentially using coefficients of each item except the highest item in each corresponding polynomial of n-bit random number k to generate an n-order polynomial in GF (2) domain, wherein the coefficient of the highest item is 1; for example, the random number k= (a n-1,an-2,...,a1,a0), then the generated polynomial is p (x) =x n+an-1xn-1+…+a1x+a0; preferably, only when a 0 =1, the generated polynomial is likely to be an irreducible polynomial, so, to reduce the calculation amount in the later verification of the irreducible polynomial, the n-bit random number k can be judged first: if a 0 =0, let a 0 =1, regenerate an irreducible polynomial of order n in GF (2) domain; or if a 0 =0, regenerating an n-bit random number until the last bit of the generated random number is 1, and then generating an n-order irreducible polynomial in the GF (2) domain by using the newly generated random number; this reduces the amount of computation in the case of a late verification irreducible polynomial, and finally results in a 0 =1, the resulting polynomial being p (x) =x n+an-1xn-1+…+a1 x+1;
then, verifying whether the polynomial is an irreducible polynomial, if the verification result is no, directly generating another group of n-bit random numbers from a random number generator of the transmitting end, returning the random numbers as new n-bit random numbers to the previous steps to regenerate the polynomial and verify; if the verification result is "yes", stopping verification to obtain an irreducible polynomial p (x).
There are several ways to verify the irreducible polynomials here, preferably the two ways we mention in this invention:
The method comprises the following steps: sequential verification Whether or not it is true, whereinRepresentation pairRounding, if all i are verified to pass, p (x) is an irreducible polynomial of order n over GF (2); wherein gcd (f (x), g (x)) represents the maximum common factor of f (x) and g (x) over GF (2), f (x) and g (x) referring to two arbitrary polynomials.
The second method is as follows: verification condition (1)(2)Whether or not to do so simultaneously, whereinRepresentation ofWhere d is an arbitrary prime factor of n, gcd (f (x), g (x)) represents the maximum factors of f (x) and g (x) over GF (2), f (x) and g (x) refer to two arbitrary polynomials, and when both validation conditions are satisfied, p 1 (x) is an irreducible polynomial of order n over GF (2).
In general, n=2 k is taken, so only d=2 needs to be taken in condition (2). Alternatively, n=2 7 =128 is taken. Since this method only needs to verify these two conditions, we use Fast modular composition algorithm to get quicklyAndBy usingReplacement of condition (2)And (3) performing calculation, and obtaining a calculation result faster by a method of reducing the order.
(2) The signer a obtains a third hash function key L a of the signer for generating a hash function by using the first hash function key L ab and the second hash function key L ac negotiated with the receiver B and the signer C, and in this embodiment, a one-time-pad exclusive-or operation is preferred, that is
(3) Signcryption party a selects the irreducible polynomial p (x) and the third hash function key L a to generate a linear shift register based hash functionPreferably, the present embodiment selects a linear shift register based Toeplitz matrix (LFSR-Toeplitz) hash function
(4) Signcryption party a uses the hash functionCarrying out hash operation on the plaintext message M to obtain a plaintext abstract digest;
(5) The signcryption party A mixes a character string str1 formed by the plaintext message M, the plaintext abstract digest and the coefficients of each term except the highest term in the irreducible polynomial according to a preset rule to obtain a mixed abstract Mdigest, wherein Mdigest = (M, digest, str 1), and the preset rule can be agreed in advance by the signcryption party A, the receiver B and the signcryption party C;
(6) The signer A obtains a third key R a for encryption by using a first key R ab and a second key R a C negotiated with the receiver B and the signer C, and the length of the third key R a is m+2n;
(7) The signcryption party a uses the third key R a to perform unconditionally secure encryption on the hybrid digest Mdigest, and uses an exclusive-or operation to obtain a hybrid signature sig, namely
3. The signer A sends the obtained mixed signature sig to the receiver B;
4. After receiving the mixed signature sig, the receiver B sends the received mixed signature sig and a first hash function key L ab and a first key R ab which are negotiated with the signer A to the signer C;
5. After receiving the information sent by the receiver B, the signer C sends a second hash function key L ac and a second key R ac negotiated by the signer C and the signer A to the receiver B;
The information sent by the receiver B and the signer C is an authenticated classical channel which passes through, so that the receiver B and the signer C are prevented from being tampered with.
6. The receiver B and the signer C respectively perform signer verification on the mixed signature, and the verification processes of the two parties are the same, so in this embodiment, the verification process of the receiver B is taken as an example, and the signer verification process is specifically described. The method comprises the following steps:
(1) After the foregoing steps 4 and 5, the receiver B has a first hash function key L ab, a first key R ab and a second hash function key L ac and a second key R ac which are sent by the signer C and are negotiated with the signer a, and obtains a fourth hash function key L a 'for generating a hash function by using the first hash function key L ab and the second hash function key L ac and obtains a fourth key R a' for decrypting by using the first key R ab and the second key R ac by adopting the same processing method as the signer a;
(2) The receiver B decrypts the received mixed signature sig by using a fourth key R a' to obtain a mixed digest Mdigest;
(3) Separating the mixed abstract Mdigest according to a preset rule to obtain a character string str1 composed of a plaintext message M, an inverse plaintext abstract digest b′ and coefficients of each item except the highest item in the irreducible polynomial;
(4) Generating an irreducible polynomial p (x)', the highest term coefficient of which is 1, by using the coefficients of each term except the highest term in each bit of the corresponding polynomial of the character string str 1;
(5) Obtaining a linear shift register based hash function using an irreducible polynomial p (x)' and a fourth hash function key L a
(6) Using hash functionsCarrying out hash operation on the plaintext message M to obtain a plaintext abstract digest b;
(7) And judging whether the direct plaintext abstract digest b is equal to the inverse plaintext abstract digest b′, if so, receiving the signature by the receiver B, otherwise, refusing the signature.
The signer C performs the verification of the signer secret by the same method as the receiver B, and can be regarded as the success of the whole signer secret process only when the receiver B and the signer C pass the verification and accept the signature, otherwise, the signer secret process fails as long as the B party does not accept, and the signer secret process needs to be carried out again.
After the above process, the receiver B can obtain the plaintext information M to be sent by the signcryption party, and in the whole transmission process, no extra key is needed to encrypt the plaintext, and the plaintext does not appear alone in the whole information transmission process, so that the key resource is greatly saved by using the method of mixing signcryption, the processes of encrypting by the signcryption party and decrypting by the receiver are reduced, and the operation complexity of the processing process is reduced.
The hash function based on the linear shift register adopted in the scheme of the invention can sign and secret information with any length, thereby realizing the sign and secret information of long information and having higher efficiency and safety.
Claims (8)
1. A method of quantum digital hybrid signcryption, the method comprising:
The signer and the receiver conduct key negotiation, respectively obtain a first hash function key and a first key, respectively, and conduct key negotiation, respectively obtain a second hash function key and a second key;
The signer performs mixed signer operation on the message plaintext by using the negotiated secret key, and sends the obtained mixed signature to the receiver;
the receiver sends the received mixed signature and two groups of keys negotiated with the signer to the signer;
The signer sends two groups of keys negotiated with the signer to the receiver;
The receiver and the signer respectively carry out signcryption verification on the mixed signature, when both sides pass the verification, the signcryption is successful, otherwise, the signcryption process is re-executed;
Wherein the hybrid signcryption operation includes the steps of:
(1) The signcryption party obtains a group of random numbers from the local place to generate an irreducible polynomial;
(2) The signer obtains a third hash function key of the signer for generating a hash function by using the first hash function key and the second hash function key which are negotiated with the receiver and the signer;
(3) The signcryption party selects an irreducible polynomial and a third hash function key to generate a hash function based on a linear shift register;
(4) The signcryption party uses the hash function to carry out hash operation on the plaintext message to obtain a plaintext abstract;
(5) The signcryption party mixes the plaintext message, the plaintext abstract and the character string formed by the coefficients of each item except the highest item in the irreducible polynomial according to a preset rule to obtain a mixed abstract;
(6) The signer obtains a third key for encryption of the signer by using the first key and the second key negotiated with the receiver and the signer;
(7) And the signer uses a third key to perform unconditional secure encryption on the mixed digest to obtain a mixed signature.
2. The method of claim 1, wherein the generating of the irreducible polynomial is:
1) Firstly, sequentially using coefficients of each item except the highest item in each bit of corresponding polynomial of the random number to generate a polynomial in GF (2) domain, wherein the coefficient of the highest item is 1;
2) Then, verifying whether the polynomial is an irreducible polynomial, if the verification result is no, re-acquiring another group of random numbers from the local of the signcryption party, returning to the step 1) as new random numbers, regenerating the polynomial and verifying; if the verification result is yes, stopping verification to obtain an irreducible polynomial.
3. The method of quantum digital hybrid signcryption according to claim 2, wherein the method of verifying whether the polynomial is an irreducible polynomial is:
Sequentially verifying whether gcd (p (x), x 2i -x) =1 is true, wherein Representation pairRounding, if all i are verified to pass, p (x) is an irreducible polynomial of order n over GF (2); wherein gcd (f (x), g (x)) represents the maximum common factor of f (x) and g (x) over GF (2), f (x) and g (x) referring to two arbitrary polynomials.
4. The method of quantum digital hybrid signcryption according to claim 2, wherein the method of verifying whether the polynomial is an irreducible polynomial is:
Verification condition 1: Condition 2: Whether or not to do so simultaneously, wherein Representation ofD is an arbitrary prime factor of n, gcd (f (x), g (x)) represents the maximum factors of f (x) and g (x) on GF (2), f (x) and g (x) refer to two arbitrary polynomials, and when the two verification conditions are satisfied at the same time, p (x) is an irreducible polynomial of order n on GF (2).
5. The method of claim 2, wherein prior to step 1), if the last bit of the random number is 0, the last bit of the random number is 1; or if the last bit of the n-bit random number is 0, regenerating the random number until the last bit of the generated random number is 1.
6. The quantum digital hybrid signcryption method of claim 1, wherein the hash function is a linear shift register based toeplitz matrix hash function.
7. The method of quantum digital hybrid signcryption as recited in claim 1, wherein the signcryption verification comprises the steps of:
(1) The receiver and the signer obtain a fourth hash function key according to the first hash function key and the second hash function key which are owned by the receiver and the signer respectively, and obtain a fourth key according to the first key and the second key;
(2) The receiver and the signature verification party decrypt the mixed signature by using the fourth secret key obtained by each receiver and the signature verification party to obtain a mixed abstract;
(3) Separating the mixed abstract according to a preset rule to obtain a character string composed of the plaintext message, the inverse plaintext abstract and the coefficients of each item except the highest item in the irreducible polynomial;
(4) Generating an irreducible polynomial with the highest term coefficient of 1 by corresponding each bit of the character string to the coefficient of each term except the highest term in the polynomials;
(5) Obtaining a hash function based on a linear shift register by using the irreducible polynomial and a third hash function key;
(6) Carrying out hash operation on the plaintext message by utilizing the hash function to obtain a plaintext abstract;
(7) And judging whether the forward plaintext abstract is equal to the reverse plaintext abstract, if so, accepting the signature, otherwise, refusing the signature.
8. The method of any one of claims 1-6, wherein the plaintext message has a length m, the first hash function key and the second hash function key have a length n, and the first key and the second key have a length 2n+m.
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