Improved lattice-based key exchange protocol algorithm

Abstract

The invention relates to a protocol algorithm, specifically a lattice-based key exchange protocol algorithm improved through utilization of random Gaussian noises. The method comprises the steps that1, it is assumed that a constant m is greater than or equal to 2, lambda is equal to O(n), beta is equal to (square root of n)sigma, and q is equal to O(2<lambda>mn[beta]<2>, wherein the sigma is a security parameter in M-DLWE definition, it is assumed that X is equal to {z which is an element of a set R<m>:||z||<=the beta, wherein the i is the element of the set [m]}, wherein the z is the element of the set R, and the||z|| is a norm z of a coefficient vector, hereinafter, an absolute minimum residual system is employed for R<q>, namely, each coefficient a satisfies |a|<q/2,wherein the a is the element of the set R<q>; S2, an m-order random matrix A is selected, wherein the A is the element of the set R<q><m _ x _ m>, and the A is accepted by a first communication partyand a second communication party, wherein; S3, information is issued, specifically, (1), the first communication party selects x,e<1><- D<R<m,sigma>>, computes a=(Ax+e<1>)mod q, and sends the a to thesecond communication party, and (2), the second communication party selects y,e<2><- D<R<m,sigma>>, computes b<T>=(y<T>A+e<2><T>)mod q and sends the b to the first communication party; and S4, sharedkeys are generated, specifically, (1), the first communication party generates the shared key k<1>=MSB(b<T>x mod q); and (2), the second communication party generates the shared key k2=MSB(y<T>a modq).

Description

technical field [0001] The invention relates to a protocol algorithm, in particular to an improved lattice-based key exchange protocol algorithm. Background technique [0002] The Key Exchange (KE: Key Exchange) protocol is a basic cryptographic primitive that plays an important role in building secure communication protocols, for example, providing secure mobile payment, Internet of Vehicles data communication, etc. The KE protocol allows all parties to generate a shareable security key through an insecure network to achieve secure communication in an insecure channel. [0003] The definition of the KE protocol was first formally proposed by Diffie and Hellman in 1996. The security of the KE protocol designed since then is based on solving classical number theory problems. However, these schemes are not safe in the quantum era. The quantum polynomial time algorithm proposed by Shor can solve integer decomposition problems, discrete logarithm problems and discrete logarithm...

AI Technical Summary

Problems solved by technology

But how to design a quantum-resistant key exchange protocol has always been an important challenge

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