Towards a Unifying View of Block Cipher Cryptanalysis

We introduce commutative diagram cryptanalysis, a framework for expressing certain kinds of attacks on product ciphers. We show that many familiar attacks, including linear cryptanalysis, differential cryptanalysis, differential-linear cryptanalysis, mod n attacks, truncated differential cryptanalysis, impossible differential cryptanalysis, higherorder differential cryptanalysis, and interpolation attacks can be expressed within this framework. Thus, we show that commutative diagram attacks provide a unifying view into the field of block cipher cryptanalysis. Then, we use the language of commutative diagram cryptanalysis to compare the power of many previously known attacks. Finally, we introduce two new attacks, generalized truncated differential cryptanalysis and bivariate interpolation, and we show how these new techniques generalize and unify many previous attack methods.