Description
An elliptic curve addition law is said to be complete if it correctly computes the sum of any two points in the elliptic curve group. One of the main reasons for the increased popularity of Edwards curves in the ECC community is that they can allow a complete group law that is also relatively efficient (e.g., when compared to all known addition laws on Edwards curves). Such complete addition formulas can simplify the task of an ECC implementer and, at the same time, can greatly reduce the potential vulnerabilities of a cryptosystem. Unfortunately, until now, complete addition laws that are relatively efficient have only been proposed on curves of composite order and have thus been incompatible with all of the currently standardized prime order curves.<br/> In this paper we present optimized addition formulas that are complete on every prime order short Weierstrass curve defined over a field k with char(k) not 2 or 3. Compared to their incomplete counterparts, these formulas require a larger number of field additions, but interestingly require fewer field multiplications. We discuss how these formulas can be used to achieve secure, exception-free implementations on all of the prime order curves in the NIST (and many other) standards.
Next sessions
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Dissecting CRAFT, a full-round attack
Speaker : Eran Lambooij - Inria
I will present the first full-round key recovery attack on CRAFT, a block cipher introduced at ToSC 2019. The attack builds on the previous observation (ToSC 2026) that the state of CRAFT can be decomposed into two parts that barely exchange information. We transform this property into a dissection attack on the full-round cipher. This shows that in some cases we can elevate the dissection attack[…]-
Cryptography
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Key Attack on the ACDGV Matrix Encryption Scheme
Speaker : Anmoal Porwal - Technical University of Munich
I will present our key-recovery attack on the ACDGV public-key encryption scheme proposed at ASIACRYPT 2024 by Aragon, Couvreur, Dyseryn, Gaborit, and Vinçotte. The secret key is a Gabidulin code hidden by appending random rows and columns and by left- and right-multiplication with invertible matrices. Our attack exploits the resulting algebraic structure to recover an equivalent secret key. It[…]-
Cryptography
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Asymmetric primitive
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Module Learning With Errors and Structured Extrapolated Dihedral Cosets
Speaker : Jinwei Zheng - Télécom Paris
The Module Learning With Errors (MLWE) problem is the fundamental hardness assumption underlying the key encapsulation and signature schemes ML-KEM and ML-DSA, which have been selected by NIST for post-quantum cryptography standardization. Understanding its quantum hardness is crucial for assessing the security of these standardized schemes. Inspired by the equivalence between LWE and[…]-
Cryptography
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