Using Local Reduction for the Experimental Evaluation of the Cipher Security

keywords: Algebraic cryptanalysis, local reduction, method of syllogisms, SAT solvers
Evaluating the strength of block ciphers against algebraic attacks can be difficult. The attack methods often use different metrics, and experiments do not scale well in practice. We propose a methodology that splits the algebraic attack into a polynomial part (local reduction), and an exponential part (guessing), respectively. The evaluator uses instances with known solutions to estimate the complexity of the attacks, and the response to changing parameters of the problem (e.g. the number of rounds). Although the methodology does not provide a positive answer (``the cipher is secure''), it can be used to construct a negative test (reject weak ciphers), or as a tool of qualitative comparison of cipher designs. Potential applications in other areas of computer science are discussed in the concluding parts of the article.
mathematics subject classification 2000: 94A60, 14G50
reference: Vol. 37, 2018, No. 2, pp. 349–366