Cryptography – Key management – Having particular key generator
Reexamination Certificate
2006-05-09
2006-05-09
Sheikh, Ayaz (Department: 2131)
Cryptography
Key management
Having particular key generator
C380S030000, C380S044000, C380S046000, C380S277000, C708S200000, C708S250000
Reexamination Certificate
active
07043018
ABSTRACT:
A prime number generation method for efficiently generating prime numbers that are highly resistant to the P−1 and P+1 methods. These prime numbers are used in a cryptosystem. Prime candidates are first generated, and the generated prime candidates are subjected to prime number judgment by either a probabilistic primality testing method or a deterministic primality testing method. A prime candidate P′ is generated using odd random numbers, a judgment is made as to whether or not that prime candidate P′ satisfies the expression P′≡0, ±1 (mod pi) (where 3≦i≦n) for prime numbers from p3to pn(where pnis the n'th prime). When that expression is satisfied, that prime candidate P′ is excluded. Only those prime candidates P′ that do not satisfy that condition are subjected to the prime number judgment.
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Kasahara Masao
Murakami Yasuyuki
Sato Yoshizo
Arani Taghi T.
Hogan & Hartson LLP
Kasahara Masao
Murata Kikai Kabushiki Kaisha
Sheikh Ayaz
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