A Security Verification Method of SM2 Signature Algorithm Based on Unknown Random Number

Abstract

The invention discloses an SM2 signature algorithm security verification method based on an random number unknown. The method comprises the following steps: (1) signing N+1 messages M respectively by adopting an SM2 signature algorithm, and injecting an error into every SM2 signing in order that identical errors occur in signing results s of identical set bit parts of a random number k used in every signing; (2) subtracting error signing results s in other N signing respectively from the error signing result of first signing with reference to an equation of the error signing result s of first signing to obtain an equation set, namely, a lattice attack model; and (3) solving the lattice attack model, recovering all bits of the random number k used in every signing, substituting the recovered bits into an equation for calculating corresponding signing results s to obtain a private key dA, and judging that the SM2 signature algorithm is unsafe if the private key dA is a correct private key. Through adoption of the method, the security capability of the SM2 signature algorithm in attack resistance can be analyzed more effectively and comprehensively.

Description

Technical field [0001] The invention specifically relates to a method for verifying the security of an SM2 signature algorithm based on an unknown random number, which belongs to the technical field of information security. Background technique [0002] Since Miller and Koblitz introduced elliptic curves into cryptography in the 1980s, and Lenstra proposed the use of elliptic curves for factorization algorithms, elliptic curves have played an increasingly important role in cryptography. ECC is based on the finite field elliptic curve discrete logarithm problem (ECDLP): in a cyclic additive group, G is the generator, and the order of G is n, knowing Q=kG and G, find the value of k, where Q= kG is a scalar multiplication operation on a finite field, specifically an algebraic operation on a finite field. [0003] If F is a finite field, it contains at least two elements, and there is an addition + and a multiplication·operation, and the following conditions are met: [0004] 1) (F, +)...

AI Technical Summary

Problems solved by technology

At present, the error injection method of the lattice-based error attack method of the signature algorithm is mainly to ignore some point multiplication and point addition operations in the scalar multiplication operation. This error injection method is easy to be protected by algorithm-level signature verification. Therefore, it is urgently needed Some error attack methods based on lattice attacks that cannot be defended or defended against are difficult to reevaluate and define the security of the algorithm

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