Generating and Exploring S-Box Multivariate Quadratic Equation Systems with SageMath
A.-M. Leventi-Peetz, J.-V. Peetz
TL;DR
This paper introduces a novel method using SageMath to generate and analyze multivariate quadratic equations from cryptographic S-boxes, addressing limitations of existing MQ metrics in assessing resistance to algebraic attacks.
Contribution
It presents a new approach to derive MQ systems from S-box algebraic expressions and improves the evaluation of their cryptographic strength.
Findings
New method for deriving MQ systems using SageMath
Identifies deficiencies in existing MQ metrics
Provides better tools for assessing S-box resistance
Abstract
A new method to derive Multivariate Quadratic equation systems (MQ) for the input and output bit variables of a cryptographic S-box from its algebraic expressions with the aid of the computer mathematics software system SageMath is presented. We consolidate the deficiency of previously presented MQ metrics, supposed to quantify the resistance of S-boxes against algebraic attacks.
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