Patent ID: 8074076

Claim:
A method to protect an assembly having a processor and a memory, the method comprising: operating the processor of the assembly according to instructions stored in the memory to cause the processor to perform the steps: performing a cryptographic calculation process that uses a homographic function f of the type: f ( z )=( az+b )/( cz+d ) when ( cz+d ) is not equal to 0 and f (âˆ’ d/c )= a/c by operating on masked variables, wherein, for any k, if x is an input and y=f(x+k) is an output of the function f, to pass directly from a masked value x+m_i (additive masking of type XOR) to a masked value y+m_j using a composition of: several transformations F_i and G_j wherein iâ‰§1 and j>1, each transformation F_i and G_j operating on the set Kâ€² wherein Kâ€²=K U oo, and wherein K=GF(2^k), each transformation F_i(z) and G_j(z) are defined as (az+b)/(cz+d) when (cz+d) is not equal to 0, F_i(âˆ’d/c) and G_j(âˆ’d/c)=oo, and F_j(oo) and G_j(oo)=a/c; and the exchange of two points.