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Method to protect a cryptographic assembly by homographic masking

  • US 8,074,076 B2
  • Filed: 05/11/2005
  • Issued: 12/06/2011
  • Est. Priority Date: 05/11/2004
  • Status: Expired due to Fees
First Claim
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1. 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(−

    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 i≧

    1 and j>

    1, each transformation F_i and G_j operating on the set K′

    wherein K′

    =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(−

    d/c) and G_j(−

    d/c)=oo, and F_j(oo) and G_j(oo)=a/c; and

    the exchange of two points.

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