International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Linear Sequential Circuit Approximation of Grain and Trivium Stream Ciphers

Shahram Khazaei
Mahdi M. Hasanzadeh
Mohammad S. Kiaei
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Abstract: Grain and Trivium are two hardware oriented synchronous stream ciphers proposed as the simplest candidates to the ECRYPT Stream Cipher Project, both dealing with 80-bit secret keys. In this paper we apply the linear sequential circuit approximation method to evaluate the strength of these stream ciphers against distinguishing attack. In this approximation method which was initially introduced by Golic in 1994, linear models are effectively determined for autonomous finite-state machines. We derive linear functions of consecutive key-stream bits which are held with correlation coefficient of about 2^-63.7 and 2^-126 for Grain and Trivium ciphers, respectively. Then using the concept of so-called generating function, we turn them into linear functions with correlation coefficient of 2^-29 for Grain and 2^-72 for Trivium. It shows that the Grain output sequence can be distinguished from a purely random sequence, using about 2^58 bits of the output sequence with the same time complexity. However, our attempt fails to find a successful distinguisher for Trivium.
  title={Linear Sequential Circuit Approximation of Grain and Trivium Stream Ciphers},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Stream Cipher, Distinguishing Attack, Linear Sequential Circuit Approximation, Grain, Trivium, ECRYPT, Security Evaluation.},
  note={ 13249 received 11 Apr 2006},
  author={Shahram Khazaei and Mahdi M. Hasanzadeh and Mohammad S. Kiaei},