- Algorithmic and Mathematical Cryptology
- EC | H2020 | ERC | ERC-ADG
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- UJF, UPMC - Paris 6, SU, UGA
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Chabaud, Ulysse; Diamanti, Eleni; Markham, Damian; Kashefi, Elham; Joux, Antoine (2018)
Projects: EC | AlmaCrypt (669891)The swap test is a central primitive in quantum information, providing an efficient way of comparing two unknown quantum states. In this work, we generalise this test for the case where one has access to multiple copies of a reference state, but to only one copy of the tested state. We present a circuit implementing this test and propose a simple linear optical implementation using the Hadamard interferometer. We show that both the circuit and the interferometer can be used as programmable pr...Gélin , Alexandre; Kleinjung , Thorsten; Lenstra , Arjen K. (2017)
Projects: EC | AlmaCrypt (669891)International audience; We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factoriza-tion method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.Joux , Antoine; Pierrot , Cécile (2016)
Projects: EC | AlmaCrypt (669891)International audience; In this article, we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense columns with possibly large coefficients. We modify Block Wiedemann algorithm and show that the contribution of these heavy columns can be made negligible compared to the one of the sparse part of the matrix. In particular, this eases the computation of discrete logari...Gélin , Alexandre; Wesolowski , Benjamin (2017)
Projects: NWO | Netherlands Streaming (NEST) (2300152619), EC | AlmaCrypt (669891)International audience; Cryptographic schemes based on supersingular isogenies have become an active area of research in the field of post-quantum cryptography. We investigate the resistance of these cryptosystems to fault injection attacks. It appears that the iterative structure of the secret isogeny computation renders these schemes vulnerable to loop-abort attacks. Loop-abort faults allow to perform a full key recovery, bypassing all the previously introduced validation methods. Therefore...Narayanan, Anand Kumar; Weidner, Matthew (2017)
Projects: EC | AlmaCrypt (669891), NSF | AF: Small: Algorithms for Matrix Multiplication, Polynomial Factorization and Generalized Fourier Transform (1423544)We construct explicit algebraic geometry codes built from the Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for alphabet sizes at least 192. Messages are identied with functions in certain Riemann-Roch spaces associated with divisors supported on multiple places. Encoding amounts to evaluating these functions at degree one places. By exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we devise an intricate deterministic \omega/2 < 1.19 ru...
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