Description
Division polynomials express multiples of *affine* points on Weierstrass elliptic curves over fields. The restriction to affine points becomes an issue with elliptic curves over arbitrary rings, where it may happen that there are multiple 'points at infinity'. We will explain how a modification of the classical division polynomials describes multiplication on all points of Weierstrass elliptic curves over arbitrary rings.
Prochains exposés
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CryptoVerif: a computationally-sound security protocol verifier
Orateur : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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Structured-Seed Local Pseudorandom Generators and their Applications
Orateur : Nikolas Melissaris - IRIF
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]-
Cryptography
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Post-Quantum Public-Key Pseudorandom Correlation Functions for OT
Orateur : 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
Orateur : 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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