Generation of a random number that is non-divisible by a set...

Details Generation of a random number that is non-divisible by a set... Generation of a random number that is non-divisible by a set...

2006-09-26

2006-09-26

Louis-Jacques, Jacques H. (Department: 2134)

Cryptography

Particular algorithmic function encoding

Public key

C380S028000, C380S268000, C380S044000

Reexamination Certificate

active

07113595

ABSTRACT:
A random number that is co-prime with a set of prime numbers is generated, without having to calculate the greatest common denominator of the numbers. The value of 1−xλ(mod π), where x is a randomly generated value and λ is the Carmichael function, is tested to determine whether it is non-zero. If it equals zero, x is chosen as the random number of interest. Otherwise the value for x is updated, and the procedure is repeated. Due to the minimal amount of computation resources required to select x, the process is particularly well suited for generating cryptographic keys in portable electronic devices, such as smart cards.

REFERENCES:
patent: 2001/0036267 (2001-11-01), Paillier
patent: 02/05483 (2002-01-01), None
Davenport, J. H., “Primality Testing Revisited”; Aug. 1992, ACM Press; Papers from the international symposium on Symbolic and algebraic computation, pp. 123-129.
Catalano et al, “Cryptosystems: Paillier's cryptosystem revisited”; Nov. 2001, ACM Press; Proceedings of the 8th ACM conference on Computer and Communications Security, pp. 206-214.
Paillier, U.S. Appl. No. 09/818,658, filed Mar. 28, 2001.
John B. Friedlander et al., “Small Values of the Carmichael Function and Cryptographic Applications”, pp. 1-8.
Fischer Harald et al., “Power Permutations on Prime Residue Classes”, pp. 191-197.

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