Method for synchronized signature with additive rsa key splitting using a sliding window

Abstract

The present invention relates to a method of secure generation by a client device and a server device of an RSA signature of a message to be signed with a private exponent component d of an RSA key (p, q, N, d, e), wherein said client device stores a client device private exponent component dA, a client value, and a client dynamic offset, and said server device stores a server device private exponent component dB, where dB=d−dA modulo phi(N), a server value, a server dynamic offset and a failure counter, comprising: a. receiving from the client device a client part of said RSA signature (HS) of said message to be signed, after incrementing its client value (pvA) by a first predetermined step E, from the client device private exponent component and from an updated client dynamic offset function of said client dynamic offset and of said client value, b. setting said failure counter to a first default value, c. incrementing said server value (pvB) by a second predetermined step (E'), d. generating a server part of said RSA signature (HS) of said message to be signed, from the server device private exponent component and from an updated server dynamic offset function of said server dynamic offset and of said server value, e. generating said RSA signature by combining said client part of said RSA signature (HS) and said server part of said RSA signature (HS), f. checking if the generation of the RSA signature was a failure and when it was a failure, incrementing said failure counter and g\ iteratively repeating above steps c\ to f\, until said RSA signature is successfully generated or said failure counter reaches a first predetermined threshold S.