Section: New Results

Homomorphic coding for soft error resilience

We extended our results for fault-tolerant modular computations in two directions. To improve the correction rate of Reed-Solomon codes, power-decoding techniques consist in augmenting the number of syndrom equations by raising the received word to successive powers. The correction is done by a generalization of Berlekamp-Massey algorithm acting on multiple sequences. This method is, if not equivalent, at least very close to the list-decoding proposed by Sudan in its first version, in particular, error correction rates are identical. We improve the power-decoding method by reformulation into a vector rational function reconstruction, with benefit from fast polynomial matrix arithmetic. Besides, for basic exact linear algebra computations (eg dense linear system), we designed interactive protocols between a trusted platform and a non trusted one for resilience to soft-errors.