Software Oriented Stream Ciphers Based upon FCSRs in Diversified Mode

Feedback with Carry Shift Registers (FCSRs) are a promising alternative to LFSRs for the design of stream ciphers. Most of the FCSR-based stream ciphers use a Galois representation. In this case, the control of a single bit leads to the control of the feedback values. This particular property was exploited to break most of the existing proposals. Recently, a new representation for FCSR automata was presented. This representation is a generalization of both Galois and Fibonacci representations. In this representation any cell can be used for a feedback for any other cell. With a good choice for the parameters, those new FCSR automatas are resistant to the previous attacks and the internal diffusion is significantly improved. Using this approach, a new hardware oriented version of F-FCSR has been recently proposed. In this paper, we propose a new design for FCSRs suitable for software applications. Using this approach, we present a new version of X-FCSR-128 suitable for software applications which is really efficient in software.

[1]  Rainer A. Rueppel Advances in Cryptology — EUROCRYPT’ 92 , 2001, Lecture Notes in Computer Science.

[2]  Jongsung Kim,et al.  Related-Key Rectangle Attacks on Reduced Versions of SHACAL-1 and AES-192 , 2005, FSE.

[3]  François Arnault,et al.  Some Results on FCSR Automata With Applications to the Security of FCSR-Based Pseudorandom Generators , 2008, IEEE Transactions on Information Theory.

[4]  Josef Pieprzyk,et al.  Advances in Cryptology - ASIACRYPT 2008, 14th International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, Australia, December 7-11, 2008. Proceedings , 2008, ASIACRYPT.

[5]  Makoto Matsumoto,et al.  Twisted GFSR generators , 1992, TOMC.

[6]  Andrea Röck,et al.  Stream Ciphers Using a Random Update Function: Study of the Entropy of the Inner State , 2008, AFRICACRYPT.

[7]  François Arnault,et al.  A New Approach for FCSRs , 2009, Selected Areas in Cryptography.

[8]  Tor Helleseth,et al.  Sequences and Their Applications - SETA 2006, 4th International Conference, Beijing, China, September 24-28, 2006, Proceedings , 2006, SETA.

[9]  Mark Goresky,et al.  Fibonacci and Galois representations of feedback-with-carry shift registers , 2002, IEEE Trans. Inf. Theory.

[10]  Jean-Jacques Quisquater,et al.  Advances in Cryptology — EUROCRYPT ’89 , 1991, Lecture Notes in Computer Science.

[11]  François Arnault,et al.  Update on F-FCSR Stream Cipher , 2006 .

[12]  Mark Goresky,et al.  Periodicity and Distribution Properties of Combined FCSR Sequences , 2006, SETA.

[13]  François Arnault,et al.  X-FCSR - A New Software Oriented Stream Cipher Based Upon FCSRs , 2007, INDOCRYPT.

[14]  Pierre L'Ecuyer,et al.  On the xorshift random number generators , 2005, TOMC.

[15]  Mark Goresky,et al.  Arithmetic crosscorrelations of feedback with carry shift register sequences , 1997, IEEE Trans. Inf. Theory.

[16]  Eli Biham,et al.  New Types of Cryptanalytic Attacks Using related Keys (Extended Abstract) , 1994, EUROCRYPT.

[17]  Serge Vaudenay Progress in Cryptology - AFRICACRYPT 2008, First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008. Proceedings , 2008, AFRICACRYPT.

[18]  Jason Wittenberg,et al.  Clarify: Software for Interpreting and Presenting Statistical Results , 2003 .

[19]  François Arnault,et al.  F-FCSR: Design of a New Class of Stream Ciphers , 2005, FSE.

[20]  Martin Hell,et al.  Breaking the F-FCSR-H Stream Cipher in Real Time , 2008, ASIACRYPT.

[21]  Martin Hell,et al.  An Efficient State Recovery Attack on X-FCSR-256 , 2009, FSE.

[22]  C. Pandu Rangan,et al.  Progress in Cryptology - INDOCRYPT 2007, 8th International Conference on Cryptology in India, Chennai, India, December 9-13, 2007, Proceedings , 2007, INDOCRYPT.

[23]  Yves Roggeman,et al.  Varying Feedback Shift Registers , 1990, EUROCRYPT.

[24]  H. Niederreiter The Multiple-Recursive Matrix Method for Pseudorandom Number Generation , 1995 .

[25]  Éric Levieil,et al.  Pseudorandom Permutation Families over Abelian Groups , 2006, FSE.

[26]  Anne Canteaut,et al.  Sosemanuk, a Fast Software-Oriented Stream Cipher , 2008, The eSTREAM Finalists.

[27]  Henri Gilbert,et al.  On the Security of IV Dependent Stream Ciphers , 2007, FSE.

[28]  Gerhard Goos,et al.  Fast Software Encryption , 2001, Lecture Notes in Computer Science.

[29]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[30]  Ted G. Lewis,et al.  Generalized Feedback Shift Register Pseudorandom Number Algorithm , 1973, JACM.

[31]  Ronald L. Rivest,et al.  The RC4 encryption algorithm , 1992 .

[32]  Mark Goresky,et al.  2-Adic Shift Registers , 1993, FSE.