Abstract: High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware ...

Intel:registered: HE Acceleration Library is an open-source library which provides efficient implementations of integer arithmetic on Galois fields. Such arithmetic is prevalent in cryptography, ...

Abstract: Modular inversion, the multiplicative inverse of an integer in the ring of integers modulo a prime number, is widely used in public-key cryptography. However, it is one of the most ...

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ABSTRACT: A cryptosystem based on computation of square roots of complex integers modulo composite n is described in this paper. This paper provides an algorithm extracting a square root of Gaussian ...

The Shor's algorithm can find solutions to the discrete logarithm problem on binary elliptic curves in polynomial time. A major challenge in implementing Shor's algorithm is the overhead of ...

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it.