Fast exhaustive search for polynomial systems in

C Bouillaguet, HC Chen, CM Cheng, T Chou… - … and Embedded Systems, 2010 - Springer
We analyze how fast we can solve general systems of multivariate equations of various low
degrees over F_2; this is a well known hard problem which is important both in itself and as …

Algebraic Cryptanalysis with MRHS Equations

P Zajac - Cryptography, 2023 - mdpi.com
In this work, we survey the existing research in the area of algebraic cryptanalysis based on
Multiple Right-Hand Sides (MRHS) equations (MRHS cryptanalysis). MRHS equation is a …

Obtaining and solving systems of equations in key variables only for the small variants of AES

S Bulygin, M Brickenstein - Mathematics in Computer Science, 2010 - Springer
This work is devoted to attacking the small scale variants of the Advanced Encryption
Standard (AES) via systems that contain only the initial key variables. To this end, we …

Upper bounds on the complexity of algebraic cryptanalysis of ciphers with a low multiplicative complexity

P Zajac - Designs, Codes and Cryptography, 2017 - Springer
Lightweight cipher designs try to minimize the implementation complexity of the cipher while
maintaining some specified security level. Using only a small number of AND gates lowers …

A new method to solve MRHS equation systems and its connection to group factorization

P Zajac - Journal of Mathematical Cryptology, 2013 - degruyter.com
Multiple right-hand side (MRHS) equations over finite fields are a relatively new tool useful
for algebraic cryptanalysis. The main advantage is in an efficient representation of the …

Solving compressed right hand side equation systems with linear absorption

TE Schilling, H Raddum - Sequences and Their Applications–SETA 2012 …, 2012 - Springer
In this paper we describe an approach for solving complex multivariate equation systems
related to algebraic cryptanalysis. The work uses the newly introduced Compressed Right …

Analysis of trivium using compressed right hand side equations

TE Schilling, H Raddum - Information Security and Cryptology-ICISC 2011 …, 2012 - Springer
We study a new representation of non-linear multivariate equations for algebraic
cryptanalysis. Using a combination of multiple right hand side equations and binary decision …

[PDF][PDF] Methods to solve algebraic equations in cryptanalysis

I Semaev, M Mikuš - Tatra Mountains Mathematical Publications, 2010 - sciendo.com
The goal of the present paper is a survey of methods to solve equation systems common in
cryptanalysis. The methods depend on the equation representation and fall into three …

Local reduction and the algebraic cryptanalysis of the block cipher GOST

P Zajac, R Čagala - Periodica Mathematica Hungarica, 2012 - Springer
In our constribution we explore a combination of local reduction with the method of
syllogisms and the applications of generic guessing strategies in the cryptanalysis of the …

Solving equation systems by agreeing and learning

TE Schilling, H Raddum - Arithmetic of Finite Fields: Third International …, 2010 - Springer
We study sparse non-linear equation systems defined over a finite field. Representing the
equations as symbols and using the Agreeing algorithm we show how to learn and store …