Related papers: Public-Key Encryption from the MinRank Problem
We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…
MinRank is an NP-complete problem in linear algebra whose characteristics make it attractive to build post-quantum cryptographic primitives. Several MinRank-based digital signature schemes have been proposed. In particular, two of them,…
The rank decoding problem has been the subject of much attention in this last decade. This problem, which is at the base of the security of public-key cryptosystems based on rank metric codes, is traditionally studied over finite fields.…
A Sidon space is a subspace of an extension field over a base field in which the product of any two elements can be factored uniquely, up to constants. This paper proposes a new public-key cryptosystem of the multivariate type which is…
We present a rank metric code-based encryption scheme with key and ciphertext sizes comparable to that of isogeny-based cryptography for an equivalent security level. The system also benefits from efficient encryption and decryption…
We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…
The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a…
In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with that of the actual secret message.…
In this paper, we suggest a code-based public key encryption scheme, called McNie. McNie is a hybrid version of the McEliece and Niederreiter cryptosystems and its security is reduced to the hard problem of syndrome decoding. The public key…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure…
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
We consider a coded cooperative data exchange problem with the goal of generating a secret key. Specifically, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one,…
In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
Traditional methods in public key cryptography are based on number theory, and suffer from problems such as dealing with very large numbers, making key creation cumbersome. Here, we propose a new public key cryptosystem based on strings…