Verfahren zur Sicherung Multivariater Kryptosysteme zur Verschlüsselung

Details

Veröffentlichungs-Nr.

EP4727057

Anmeldetag

10. Oktober 2024

Veröffentlichung

15. April 2026

Rechtsraum

EP

IPC

H04L9/30

Abstract

The present invention relates to a cryptographic method for reinforcing security of an initial encryption multivariate public key cryptosystem to generate a modified encryption multivariate public key cryptosystem, wherein said initial encryption multivariate public key cryptosystem comprises :• a secret transformation which transforms a first input value A represented by a first input vector of n variables a₁, ..., a_n in K, into a first output value B represented by a first output vector of m variables b₁, ..., b_m in K through a set of m secret multivariate polynomials of degree t (A₁(a₁, ... ,a_n), ..., A_m(a₁, ..., a_n)) over said finite field or ring K, and which is defined as (A₁(a₁, ...,a_n), ..., A_m(a₁, ..., an)) = (b₁, ..., b_m) corresponding to a secret system of m polynomial equations A_j(a₁,...,a_n) = b_j for j an integer in {1 ,... ,m},• a public transformation which transforms a second input value X represented by a second input vector of n variables x₁, ..., x_n in K, into a second output value Y represented by a second output vector of m variables y₁, ..., y_m in K through a set of m multivariate polynomials of degree t (P₁(x₁, ... ,x_n), ..., P_m(x₁, ..., x_n)) over K, with n and m integers, and which is defined as (P₁(x₁, ... ,x_n), ..., P_m(x₁, ..., x_n)) = (y₁, ..., y_m) corresponding to a public system of m polynomial equations P_j(x₁,...,x_n) = y_j for j an integer in {1,... ,m},• secret linear transformations S and T which verify X = S.A and Y = T.B and which are to be used to decrypt any ciphertext encrypted using said public transformation,wherein said modified encryption multivariate public key cryptosystem is generated by adding to said initial encryption multivariate public key cryptosystem an internal or external perturbation, wherein adding an internal, respectively external, perturbation comprises: determining (E1) t*r secret linear forms L₁, ..., L_r, L'₁, ..., L'_r in said first input vector, and for j in {1,... ,m}, adding (E2) to equation j of said secret, respectively public, system of polynomial equations a linear combination of r products of t of said determined secret linear forms such that b_j = A'_j(a1,. . ,a_n) with A'_j = A_j+∑i=1rαi,j∏k=1tLik or yj=P′jx1,…,xn with P′j=Pj+∑i=1rαi,j∏k=1tLik.

Anmelder

Firma

THALES DIS FRANCE SAS

Land

🇫🇷 Frankreich