A computer implemented method, wherein the computer comprises a processor with AESDECLAST, AESENC and PSHUFB instructions, wherein: the AESDECLAST instruction performing the sequence of Advanced Encryption Standard, AES, transformations inverse ShiftRows, inverse SubstituteBytes, AddRoundKey; the AESENC instruction performing the sequence of AES transformations ShiftRows, SubstituteBytes, MixColumns, AddRoundKey; and the PSHUFB instruction shuffling and zeroing bytes based on a mask, the method comprising: performing a Galois Field multiplication operation in parallel on each of the four bytes (d, c, b, a) of a block of bytes by: performing a PSHUFB instruction to set the odd bytes positions of the block of bytes to provide a preliminary first result; performing a first AES MixColumns transformation on the the preliminary first result to provide an intermediate first result; performing a PSHUFB instruction to set the odd bytes positions of the intermediate first result to zero to produce an updated first result; performing a PSHUFB instruction to set the even bytes positions of the block of bytes to provide a preliminary second result; performing a second AES MixColumns transformation on the preliminary second result to provide an intermediate second result; performing a PSHUFB instruction to set the even bytes positions of the intermediate second result to zero to produce an updated second result; and combining the updated first result and the updated second result to provide the result of the Galois Field multiplication operation, wherein each of first and second AES MixColumns transformation is performed by: executing an AESDECLAST round instruction followed by an AESENC round instruction; and wherein the Galois Field is GF(2 8) defined via the reduction polynomial x 8 + x 4 + x 3 + x + 1, and wherein the Galois Field multiplication operation is a multiplication by 2. the AESDECLAST instruction performing the sequence of Advanced Encryption Standard, AES, transformations inverse ShiftRows, inverse SubstituteBytes, AddRoundKey; the AESENC instruction performing the sequence of AES transformations ShiftRows, SubstituteBytes, MixColumns, AddRoundKey; and the PSHUFB instruction shuffling and zeroing bytes based on a mask, performing a Galois Field multiplication operation in parallel on each of the four bytes (d, c, b, a) of a block of bytes by: performing a PSHUFB instruction to set the odd bytes positions of the block of bytes to provide a preliminary first result; performing a first AES MixColumns transformation on the the preliminary first result to provide an intermediate first result; performing a PSHUFB instruction to set the odd bytes positions of the intermediate first result to zero to produce an updated first result; performing a PSHUFB instruction to set the even bytes positions of the block of bytes to provide a preliminary second result; performing a second AES MixColumns transformation on the preliminary second result to provide an intermediate second result; performing a PSHUFB instruction to set the even bytes positions of the intermediate second result to zero to produce an updated second result; and combining the updated first result and the updated second result to provide the result of the Galois Field multiplication operation, wherein each of first and second AES MixColumns transformation is performed by: executing an AESDECLAST round instruction followed by an AESENC round instruction; and wherein the Galois Field is GF(2 8) defined via the reduction polynomial x 8 + x 4 + x 3 + x + 1, and wherein the Galois Field multiplication operation is a multiplication by 2. executing an AESDECLAST round instruction followed by an AESENC round instruction; and wherein the Galois Field is GF(2 8) defined via the reduction polynomial x 8 + x 4 + x 3 + x + 1, and wherein the Galois Field multiplication operation is a multiplication by 2.