Guaranteeing the Diversity of Number Generators

A major problem in using iterative number generators of the form xi=f (xi-1) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called sequence diversity, which generalizes the notion of cycle-length for noniterative generators. We then introduce the class of counter-assisted generators and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter-assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong. 2001 Elsevier Science

[1]  K. Kjeldsen,et al.  On the Cycle Structure of a Set of Nonlinear Shift Registers with Symmetric Feedback Functions , 1976, J. Comb. Theory, Ser. A.

[2]  Ethan M. Coven,et al.  Periods of Some Nonlinear Shift Registers , 1979, J. Comb. Theory, Ser. A.

[3]  Andrew Chi-Chih Yao,et al.  Theory and application of trapdoor functions , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[4]  Andrew Chi-Chih Yao,et al.  Theory and Applications of Trapdoor Functions (Extended Abstract) , 1982, FOCS.

[5]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[6]  U. Vazirani.  Randomness, adversaries and computation (random polynomial time) , 1986 .

[7]  Ralph Howard,et al.  Data Encryption Standard , 1987, Definitions.

[8]  Michael Luby,et al.  How to Construct Pseudo-Random Permutations from Pseudo-Random Functions (Abstract) , 1986, CRYPTO.

[9]  Dieter Gollmann,et al.  Clock-controlled shift registers: a review , 1989, IEEE J. Sel. Areas Commun..

[10]  W. G. Chambers.  On Random Mappings and Random Permutations , 1994, FSE.

[11]  Ronald L. Rivest,et al.  The RC5 Encryption Algorithm , 1994, FSE.

[12]  Stefan Lucks,et al.  Faster Luby-Rackoff Ciphers , 1996, FSE.

[13]  Michael Luby,et al.  Pseudorandomness and cryptographic applications , 1996, Princeton computer science notes.

[14]  염흥렬,et al.  [서평]「Applied Cryptography」 , 1997 .

[15]  C. Ding,et al.  Stream Ciphers and Number Theory , 1998 .

[16]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[17]  Boaz Tsaban.  Bernoulli Numbers and the Probability of a Birthday Surprise , 2003, Discret. Appl. Math..

[18]  Boaz Tsaban,et al.  Efficient linear feedback shift registers with maximal period , 2002, IACR Cryptol. ePrint Arch..