Mathematics and Computers in Simulation 68 (2005) 1–7 The strict avalanche criterion randomness test Julio Cesar Hernandez Castro a,∗ , Jos´ e Mar´ ıa Sierra b , Andre Seznec a , Antonio Izquierdo a , Arturo Ribagorda a a INRIA-IRISA, CAPS TEAM, Campus de Beaulieu, 35042 Rennes, France b Carlos III University 28911 Legan´ es, Madrid, Spain Received 29 April 2004; received in revised form 4 September 2004; accepted 8 September 2004 Available online 19 November 2004 Abstract A new statistical test for randomness, the strict avalanche criterion (SAC) test, is presented, together with its results over some well-known generators in the literature. These results are analyzed and some possible applications of the test, as for measuring the strength of cryptographic primitives including block ciphers, stream ciphers and pseudorandom number generators, especially during the design and analysis phase, are detailed. Finally, the source code for a basic version of the SAC test is provided, which proves some of its other advantages: it is easy to implement, and very fast so well-suited for practical applications. © 2004 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Pseudo randomness test; Pseudorandom number generators; Avalanche effect; Strict avalanche effect; Chi-square test 1. Introduction The problem of randomness testing or, alternatively, of assessing the quality of different pseudoran- dom number generators (PRNG) is becoming increasingly crucial, specially for assuring the safety of communications [1], due to the nowadays wide use of public key cryptography, key management and digital signatures that all rely in the existence of secure methods for generating random numbers and ∗ Corresponding author. Tel.: +34 9 1624 9422; fax: +34 9 1624 9129. E-mail addresses: jcesar@irisa.fr, jcesar@inf.uc3m.es (J.C.H. Castro), sierra@inf.uc3m.es (J.M. Sierra), seznec@irisa.fr (A. Seznec), aizquierdo@inf.uc3m.es (A. Izquierdo), arturo@inf.uc3m.es (A. Ribagorda). URL: http://www.irisa.fr/caps. 0378-4754/$30.00 © 2004 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2004.09.001