Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2006-12-12
2006-12-12
Malzahn, D. H. (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
07149763
ABSTRACT:
A random prime number is generated within a predetermined interval by precalculating and storing a single value that functions as a universal parameter for generating prime numbers of any desired size. The value, π, is chosen as a product of k prime numbers. A number a is also chosen such that is co-prime with π. Once the values for π and a have been determined they can be stored and used for all subsequent iterations of the prime number generating algorithm. To generate a prime number, a random number x is chosen with uniform distribution, and a candidate prime number within the predetermined interval is calculated on the basis of the random number. This candidate is tested for primality, and returned as the result if it is prime. If the candidate is not prime, the random number x is multiplied by a, and used to generate a new candidate. This procedure is repeated, until the candidate is prime. Since a single value, namely π, needs to be precalculated, economies of storage are achieved. In addition, the interval of interest is approximated with a higher degree of resolution. Moreover, it is possible to utilize the same value of π for a number of different intervals.
REFERENCES:
patent: 6141668 (2000-10-01), Shimada
patent: 6718536 (2004-04-01), Dupaquis
patent: 02/05483 (2002-01-01), None
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.
Joye Marc
Paillier Pascal
Buchanan & Ingersoll & Rooney PC
Gemplus
Malzahn D. H.
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