Cryptology ePrint Archive: Report 2014/211

Some Randomness Experiments on TRIVIUM

Subhabrata Samajder and Palash Sarkar

Abstract: The first output bit of TRIVIUM can be considered to be a boolean function of 80 key and 80 IV variables. Choose $n$ ($n\leq 30$) of the key variables and set the other variables to constant values. This gives an $n$-variable boolean function. In this work, we experimentally find examples of such boolean functions which deviate from a uniform random $n$-variable boolean function in a statistically significant manner. This improves upon the previously reported experimental `non-randomness' result using the cube testing methodology by Aumasson et al in 2009 for TRIVIUM restricted to 885 rounds. In contrast, we work with full TRIVIUM and instead of using the cube methodology we directly find the algebraic normal form of the restricted version of the first output bit of TRIVIUM. We note, however, that our work does not indicate any weakness of TRIVIUM. On the other hand, the kind of experiments that we conduct for TRIVIUM can also be conducted for other ciphers.

Category / Keywords: Multivariate Polynomial Multiplication, Boolean Functions, Algebraic Normal Form (ANF), Stream Ciphers, TRIVIUM

Date: received 22 Mar 2014, last revised 22 Jul 2014

Contact author: subhabrata samajder at gmail com

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Version: 20140722:133104 (All versions of this report)

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