The Density of Different Dimensional Cubes in Cryptographic Primitives

What is it about?

We give algorithms to evaluate the structure of monomials in cryptologic primitives. In this way, we give a theoretical evaluation to the primitives against cube testers, especially the balance testers. The correctness of our theory has been verified by the famous stream ciphers Trivium, Grain-128, Grain-128a and Grain-v1.

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Why is it important?

All existing cube tester results are acquired by practical experiments. There is a lack of theoretical evaluation to the resistance of primitives against cube testers because the structure of different dimensional cubes is hard to evaluate. This work solves this problem to some extent.