The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

The Rank metric decoding problem is the main problem considered in cryptography based
on codes in the rank metric. Very efficient schemes based on this problem or quasi-cyclic …

Multivariate public‐key cryptography (MPKC) is considered a leading candidate for post‐
quantum cryptography (PQC). It is based on the hardness of the multivariate quadratic …

The HFE cryptosystem is one of the most popular multi-variate schemes. Especially in the
area of digital signatures, the HFEv-variant offers short signatures and high performance …

We investigate in this paper the security of HFE and Multi-HFE schemes as well as their
minus and embedding variants. Multi-HFE is a generalization of the well-known HFE …

There are several attempts to build asymmetric pubic key encryption schemes based on
multivariate polynomials of degree two over a finite field. However, most of them are …

The Minrank (MR) problem is a computational problem closely related to attacks on code-
and multivariate-based schemes. In this paper we revisit the so-called Kipnis-Shamir (KS) …

In the last two decades, many computational problems arising in cryptography have been
successfully reduced to various systems of polynomial equations. In this paper, we revisit a …

In this paper, we first prove an explicit formula which bounds the degree of regularity of the
family of HFEv (“HFE with vinegar”) and HFEv-(“HFE with vinegar and minus”) multivariate …

The HFEv-signature scheme is a twenty year old multivariate public key signature scheme. It
uses the Minus and the Vinegar modifier on the original HFE scheme. An instance of the …