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The calculation of the Tate pairing on ordinary curves involves two major steps: the Miller Loop (ML) followed by the Final Exponentiation (FE). The rst step for achieving a full pairing inversion would be to invert this FE, which in itself is a mathematically di-cult problem. To our best knowledge, most fault attack schemes proposed against pairing(More)
The latest implementations of pairings allow efficient schemes for Pairing Based Cryptography. These make the use of pairings suitable for small and constrained devices (smart phones, smart cards…) in addition to more powerful platforms. As for any cryptographic algorithm which may be deployed in insecure locations, these implementations must be secure(More)
The arithmetic in a finite field constitutes the core of Public Key Cryptography like RSA, ECC or pairing-based cryptography. This paper discusses an efficient hardware implementation of the Coarsely Integrated Operand Scanning method (CIOS) of Montgomery modular multiplication combined with an effective systolic architecture designed with a Two-dimensional(More)
The security of cryptographic algorithms can be considered in two contexts. On the one hand, these algorithms can be proven secure mathematically. On the other hand, physical attacks can weaken the implementation of an algorithm yet proven secure. Under the common name of physical attacks, different attacks are regrouped: side channel attacks and fault(More)