Method and system for protecting cryptographic operations against side-channel attacks

A cryptographic system comprising:

• a plurality of processing units configured to execute operations of a cryptographic scheme, said cryptographic system incorporating secret data, said operations being applied to a data block u to generate a protected data block X,
• wherein said processing units comprise a first sharing processing unit configured to execute an arithmetic sharing function applied to said data block u using at least one secret key, and providing as an output a first arithmetic share component A and a second arithmetic share component M,
• wherein the processing units further comprise a second sharing processing unit and a computation processing unit, said second sharing processing unit being configured to determine a random component A(0), said second sharing processing unit being further configured to execute a Boolean sharing function applied to said first arithmetic share component A and to said random component A(0) and providing as an output an intermediate Boolean share component A(1), said computation processing unit being configured to execute a recursive carry computation function configured to compute a first Boolean share component X(0), a second Boolean share component X(1) and a third Boolean share component X(2) from said second arithmetic share component M, said random component A(0) and said intermediate Boolean share component A(1), and
• wherein said protected data block X being generated from said first Boolean share component X(0), said second Boolean share component X(1) and said third Boolean share component X(2),
• the system generating encrypted data corresponding to said protected data block, and
• said encrypted data being protected against side channels attacks and fault attacks.