Method for securing an AES block cipher algorithm against high-order side-channel attacks

A method for securing against high-order side-channel attacks an execution of a SubBytes step of a block cipher algorithm based on Advanced Encryption Standard and operating on an internal state x split into a first set of (n+1) shares (x0, x1, x2 . . . xn) by a (n+1)-additive sharing, with n a non-zero integer,

• said SubBytes step comprising:
• a substep of affine transformation in GF(28) on the state x and a substep of a field inversion in GF(256)*,
• wherein said substep of field inversion is performed by a cryptographic device (101) and comprises:
• computing (S1) a Dirac output value by executing at least one Dirac function on a plurality of shares xi of the internal state x, with i an integer in [0,n], said Dirac function being a function defined in GF(256) such that said Dirac output value is equal to 1 when x equals 0 and is equal to 0 otherwise;
• adding (S2) said Dirac output value to one of said shares of the first set of shares to obtain a second set of shares;
• performing a conversion of the second set of shares (S3) from said (n+1) additive sharing to a (n+1)-multiplicative sharing;
• performing an inversion of each share of the (n+1)-multiplicative sharing (S4);
• performing a conversion of the inverted shares (S5) from said multiplicative sharing to a (n+1)-additive sharing to obtain a third set of shares;
• and
• adding (S6) said Dirac output value to one of said shares of the third set of shares
• and wherein the step of computing the Dirac output value (S1) comprises:
• replacing one of the shares xi by its binary complementary ˜xi with i an integer in {0, 1, . . . n} and ˜ the Boolean negation operation;
• and
• performing a XOR between (n+1) binary values, each of said binary values being computed by performing a Boolean conjunction AND operation & between a plurality of bits of said shares having different indexes in said shares, with XOR the Boolean exclusive disjunction operation.