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AlmaCrypt

Title
Algorithmic and Mathematical Cryptology
Funding
EC | H2020 | ERC | ERC-ADG
Call
ERC-2014-ADG
Contract (GA) number
669891
Start Date
2016/01/01
End Date
2020/12/31
Open Access mandate
yes
Data Pilot
no
Organizations
UPMC - Paris 6, UPMC - Paris 6, UGA, UJF
More information
Detailed project information (CORDIS)

 

  • Parametrizations for Families of ECM-Friendly Curves

    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.

    Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations

    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...

    Loop-Abort Faults on Supersingular Isogeny Cryptosystems

    Gélin , Alexandre; Wesolowski , Benjamin (2017)
    Projects: EC | AlmaCrypt (669891), NWO | Netherlands Streaming (NEST) (2300152619)
    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...

    Nearly linear time encodable codes beating the Gilbert-Varshamov bound

    We construct explicit nearly linear time encodable error-correcting codes beating the Gilbert-Varshamov bound. Our codes are algebraic geometry codes built from the Garcia-Stichtenoth function field tower and beat the Gilbert-Varshamov bound for alphabet sizes at least $19^2$. Messages are identified 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 s...
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