Linear Weaknesses in T-functions

We find linear (as well as quadratic) relations in a very large class of T-functions. The relations may be used in analysis of T-function-based stream ciphers.

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

[2]  Tor Helleseth,et al.  Linear Properties in T-Functions , 2006, IEEE Transactions on Information Theory.

[3]  Andrei Khrennikov,et al.  Applied Algebraic Dynamics , 2009 .

[4]  Adi Shamir,et al.  Guaranteeing the Diversity of Number Generators , 2001, Inf. Comput..

[6]  Aggelos Kiayias,et al.  Polynomial Reconstruction Based Cryptography , 2001, Selected Areas in Cryptography.

[7]  Qi Wen-feng.  On the algebraic structure of Klimov-Shamir T-function , 2008 .

[8]  Christof Paar,et al.  Cryptographic Hardware and Embedded Systems - CHES 2002 , 2003, Lecture Notes in Computer Science.

[9]  Vladimir Anashin,et al.  Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers , 1998 .

[10]  M. V. Larin,et al.  Transitive polynomial transformations of residue class rings , 2002 .

[11]  Adi Shamir,et al.  Cryptographic Applications of T-Functions , 2003, Selected Areas in Cryptography.

[12]  Adi Shamir,et al.  A New Class of Invertible Mappings , 2002, CHES.

[13]  Fabien Durand,et al.  Minimal polynomial dynamics on the set of 3‐adic integers , 2009, 1208.2016.

[14]  Wen-Feng Qi,et al.  Linear Equation on Polynomial Single Cycle T-Functions , 2007, Inscrypt.

[15]  Kai-Thorsten Wirt.  ASC – A Stream Cipher with Built – In MAC Functionality , 2007 .

[16]  Dong Hoon Lee,et al.  A New Class of Single Cycle T-Functions , 2005, FSE.

[17]  Adi Shamir,et al.  New Applications of T-Functions in Block Ciphers and Hash Functions , 2005, FSE.

[18]  V. S. Anachin.  Uniformly distributed sequences ofp-adic integers , 1994 .

[19]  Nicholas Kolokotronis.  Cryptographic properties of nonlinear pseudorandom number generators , 2008, Des. Codes Cryptogr..

[20]  Adi Shamir,et al.  New Cryptographic Primitives Based on Multiword T-Functions , 2004, FSE.

[21]  Vladimir Anashin,et al.  Uniformly distributed sequences of p-adic integers, II , 2002, math/0209407.

[22]  Andrey Bogdanov,et al.  ABC: A New Fast Flexible Stream Cipher , 2005 .

[23]  Tor Helleseth,et al.  Alinear weakness in the Klimov-Shamir T-function , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[24]  Vladimir Anashin,et al.  Non-Archimedean Ergodic Theory and Pseudorandom Generators , 2007, Comput. J..