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).