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Large Multiplication

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Victor Shoup , Alexander Yee , Basecase Karatsuba , Emma Haruka Iwao , Shigeru Kondo , Peter Trueb , Timothy Mullican , Swap Mode , Small Primes , Fused Multiply Add , Theoretic Transform , Number Theoretic Transform , Chinese Remainder , Scalable Transform , Sandy Bridge , Cannon Lake , Digit Viewer , Region Far , Radix Reductions , Pass Merging , Binary Splitting ,

Jane Street Tech Blog - Accelerating zk-SNARKs - MSM and NTT algorithms on FPGAs with Hardcaml

In 2022 a consortium of companies ran an international competition,called the ZPrize, to advance the state ofthe art in “zero-knowledge” cryptography. We dec. ....

Hardcaml Zprize , Multi Scalar Multiplication , Number Theoretic Transform , Jane Street , Succinct Non Interactive Arguments , Fast Fourier Transform ,

"Tight bound on NewHope failure probability" by Thomas Plantard, Arnaud Sipasseuth et al.

NewHope Key Encapsulation Mechanism (KEM) has been presented at USENIX 2016 by Alkim et al. and was one of the lattice-based candidates to the post-quantum standardization initiated by the NIST. However, despite the relative simplicity of the protocol, the bound on the decapsulation failure probability resulting from the original analysis is not tight. In this work we refine this analysis to get a tight upper-bound on this probability which happens to be much lower than what was originally evaluated. As a consequence, we propose a set of alternative parameters, increasing the security and the compactness of the scheme. However using a smaller modulus prevent the use of a full NTT algorithm to perform multiplications of elements in dimension 512 or 1024. Nonetheless, similarly to previous works, we combine different multiplication algorithms and show that our new parameters are competitive on a constant time vectorized implementation. Our most compact parameters bring a speed-up of 17% ....

Hope Key Encapsulation Mechanism , Vx Implementation , Lattice Based Cryptography , Number Theoretic Transform , Post Quantum Cryptography , Ing Lwe ,