We design and implement a novel post-quantum signature scheme based on the Legendre
PRF, named Loquat. Prior to this work, efficient approaches for constructing post-quantum …

Sequences of consecutive Legendre and Jacobi symbols as pseudorandom bit generators
were proposed for cryptographic use in 1988. Major interest has been shown towards …

Ring signatures allow a signer to anonymously sign a message on behalf of a
spontaneously formed group. It not only ensures the authenticity of the message but also …

In this paper, we study the security of the Legendre PRF against quantum attackers, given
classical queries only, and without quantum random-access memories. We give two …

Due to its amazing speed and multiplicative properties the Legendre PRF recently finds
widespread applications eg in Ethereum 2.0, multiparty computation and in the quantum …

One of the most celebrated and useful cryptanalytic algorithms is Hellman's time/memory
tradeoff (and its Rainbow Table variant), which can be used to invert random-looking …

Linear Legendre pseudorandom functions were introduced in 1988 by Damgård, and higher
degree generalisations were introduced by Russell and Shparlinski in 2004. We present …

The field of post-quantum cryptography studies cryptographic systems that are secure
against an adversary in possession of a quantum computer. In 2017, the National Institute of …

Abstract An Oblivious Pseudo-Random Function (OPRF) is a two-party protocol for jointly
evaluating a Pseudo-Random Function (PRF), where a user has an input x and a server has …

For modern cryptography, the security of a system is defined as the sum of the resources
required to break it. With the advent of efficient quantum computers and the new algorithmic …