1. A method, comprising: protecting data stored in a hardware data media from attack using Advanced Encryption Standard (AES) cyphering circuitry, the protecting including: mapping polynomial representations in an AES finite field of bytes of a state matrix into respective fields of polynomials computed with respect to one of a plurality of irreducible polynomials, generating moved polynomials; applying Chinese-Remainder-Theorem (CRT) based mapping to the generated moved polynomials, generating a polynomial representing the state matrix in a polynomial ring; applying an AES process to the polynomial representing the state matrix in the polynomial ring, generating an AES-processed polynomial; and converting the AES-processed polynomial into the AES finite field, generating an AES-processed state matrix, wherein the method includes: obtaining the polynomial representation (b i (x)) in the AES finite field ( Z 2 ⁡ [ x ] ( r ⁡ ( x ) ) ) of the input bytes (b i ) of said state matrix (B); providing the plurality of irreducible polynomials (f i (y)) and mapping, using a moving map (ψ i ), each polynomial (b i (x)) of said polynomial representation into the respective field of polynomials ( Z 2 ⁡ [ y ] ( f i ⁡ ( y ) ) ) computed with respect to one of said irreducible polynomials (f i (y)), to obtain the respective moved polynomials (α y (y)); mapping said moved polynomials (α i (y)) into a polynomial (a(z)) of the polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) , obtained by applying an isomorphism (ω) between the direct product of said fields of polynomials ( Z 2 ⁡ [ y ] ( f i ⁡ ( y ) ) ) and said polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) based upon the Chinese remainder theorem (CRT), said polynomial (a(z)) representing the state matrix (B) in said polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) ; applying the AES process to said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) ; and reconverting said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) into the AES finite field ( Z 2 ⁡ [ x ] ( r ⁡ ( x ) ) ) to obtain an encrypted state matrix (CB).