Description
In this talk, I'll prove some divisibility properties of the cardinality of elliptic curve groups modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas behind the proofs can be used to find new infinite families of elliptic curves with good division properties increasing the success probability of ECM This is a joint work with Razvan Barbulescu, Joppe W. Bos, Thorsten Kleinjung and Peter L. Montgomery.
Next sessions
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Post-Quantum Public-Key Pseudorandom Correlation Functions for OT
Speaker : Mahshid Riahinia - ENS, CNRS
Public-Key Pseudorandom Correlation Functions (PK-PCF) are an exciting recent primitive introduced to enable fast secure computation. Despite significant advances in the group-based setting, success in the post-quantum regime has been much more limited. In this talk, I will introduce an efficient lattice-based PK-PCF for the string OT correlation. At the heart of our result lie several technical[…] -
Predicting Module-Lattice Reduction
Speaker : Paola de Perthuis - CWI
Is module-lattice reduction better than unstructured lattice reduction? This question was highlighted as `Q8' in the Kyber NIST standardization submission (Avanzi et al., 2021), as potentially affecting the concrete security of Kyber and other module-lattice-based schemes. Foundational works on module-lattice reduction (Lee, Pellet-Mary, Stehlé, and Wallet, ASIACRYPT 2019; Mukherjee and Stephens[…]-
Cryptography
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