xgcl/sm/sm4/experiment/README.md

sage: G. = GF(28, name='b', modulus=x^8+x^7+x^6+x^5+x^4+x^2+1) sage: K. = GF(28, name='b', modulus=x^8+x^4+x^3+x+1) sage: B = GF(2) sage: R. = PolynomialRing(B) sage: G. = GF(2**8, name='a', modulus=x^8+x^7+x^6+x^5+x^4+x^2+1) sage: from sage.rings.finite_rings.hom_finite_field import FiniteFieldHomomorphism_generic sage: F = FiniteFieldHomomorphism_generic(Hom(G, K)) sage: F Ring morphism: From: Finite Field in a of size 2^8 To: Finite Field in b of size 2^8 Defn: a |--> b^5 + b + 1 sage:F.inverse()

rho = MS.matrix( [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1], )

B = MS.matrix( [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1], )

SM4-S(x) = A2(AES-S(A1(x)) A1(x) = M1x + C1 A2(x) = M2x + C2

M1 = rho * B = [0 0 1 1 0 0 1 0] [0 0 0 1 0 1 0 0] [1 0 1 1 1 1 1 0] [1 0 0 1 1 1 0 1] [0 1 0 1 1 0 0 0] [0 1 0 0 0 1 0 0] [0 0 0 0 1 0 1 0] [1 0 1 1 1 0 1 0]

C1 = rho(D) = [0 1 1 1 1 1 0 0]

A = MS.matrix( [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1], )

M2 = B * rho^{-1} * A^{-1} = [0 0 0 1 0 0 1 0] [0 1 1 1 0 0 0 0] [0 0 1 1 0 0 1 0] [1 1 1 0 0 0 1 0] [1 0 1 0 0 1 1 0] [1 0 1 1 1 0 0 0] [0 1 0 1 1 1 0 1] [1 1 0 0 1 0 1 1]

C2 = B * A^{-1} * rho^{-1} C + D = [0 1 1 0 1 1 0 1]