Proxy signature method and system based on lattice

Abstract

The invention provides a proxy signature method and system based on a lattice. The proxy signature method includes the steps of secret key generation, proxy signature secret key generation, proxy verification, proxy signature, verification and the like. The proxy signature method and system based on the lattice have the advantages that the proxy signature method based on a small integer problem on the lattice is disclosed, and the size of a proxy signature private key is reduced by reducing the dimension of the proxy signature private key. Besides, matrix multiplication is mainly used in the aspect of calculation. Compared with the methods of discrete logarithm and big integer problem factorization, modular exponentiation and match operation are not used, and accordingly computation complexity is lower.

Description

technical field [0001] The invention relates to the technical fields of information security and encryption, in particular to a lattice-based proxy signature method and system. Background technique [0002] In 1996, Mambo et al. [1] proposed the concept of proxy signature. In the proxy signature method, the original signer entrusts his signature rights to the proxy signer, and the proxy signer completes the signature instead. The verifier can distinguish that the signature is a proxy signature It is still the original signature, which guarantees the rights of the original signer, that is, the proxy signer cannot forge the signature of the original signer. With the in-depth research on quantum computers and quantum algorithms, researchers have found that quantum computers and quantum algorithms can be used in polynomial time To solve the problem of large integer decomposition and discrete logarithm [2], the method based on these two assumptions will be broken in the quantum e...

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Problems solved by technology

[0002] In 1996, Mambo et al. [1] proposed the concept of proxy signature. In the proxy signature method, the original signer entrusts his signature rights to the proxy signer, and the proxy signer completes the signature instead. The verifier can distinguish that the signature is a proxy signature It is still the original signature, which guarantees the rights of the original signer, that is, the proxy signer cannot forge the signature of the original signer. With the in-depth research on quantum computers and quantum algorithms, researchers have found that quantum computers and quantum algorithms can be used in polynomial time To solve the problem of large integer decomposition and discrete logarithm [2], the method based on these two assumptions will be broken in the quantum environment. Therefore, it is very meaningful to construct a secure proxy signature method in the quantum environment. Lattice public key cryptography as One of the fastest-growing and most concerned post-quantum ciphers in recent years, it has good cryptographic properties. First, it is a linear cipher, and most of its operations are matrix-vector product operations; second, it It is currently the only public key cryptography that can guarantee that the difficulty of the worst case is equivalent to that of the average case. Third, there is no quantum algorithm better than the traditional algorithm to solve the problem of lattice difficulty, so we can say that the lattice public key Ciphers are safe in the quantum environment. After the identity-based encryption and secure lattice signatures on the first lattice were proposed, lattice ciphers have achieved a lot of excellent results[3-7]

[0003] At present, many scholars have conducted research on lattice-based proxy signatures and obtained some results. Jiang et al. [8] constructed a lattice-based proxy signature method using the bonsai tree principle of literature [4]. The proxy signature private key of this method The dimension of is twice the dimension of the original signature private key, and the proxy is unprotected, that is, the original signer can forge the signature of the proxy signer. Xia Feng et al. [9] and Wang et al. [10] respectively use Bonsai Based on the tree principle, a lattice-based proxy signature method was constructed; Kim[11], Biswas[12] and Swapna[13] constructed an identity-based proxy signature method using the fixed-dimensional lattice-based delegation technology of literature [6]. Fixed Dimensional grid-based delegation technology does not increase the dimension of the proxy signature private key, but it significantly increases the norm of the private key

[0004] In the existing lattice proxy signature method, the size of the proxy signature private key is much larger than the private key size of the original signer, making the public and private key sizes too large is a bottleneck in the development of lattice cryptography at present.

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