论文信息 - Primality Tests Using Algebraic Groups

Primality Tests Using Algebraic Groups

We introduce primality tests using algebraic groups. Some previously known tests are naturally interpreted as special cases of these algebraic group tests. Moreover, in this framework we can generalize Lucas and n + 1 tests in a natural way.

Masanari Kida

[1] Jon Grantham,et al. Frobenius pseudoprimes , 2001, Math. Comput..

[2] Daniel Shanks,et al. Strong primality tests that are not sufficient , 1982 .

[3] S. Gurak. Cubic and biquadratic pseudoprimes of Lucas type , 1989 .

[4] Valentin Evgenʹevich Voskresenskiĭ,et al. Algebraic Groups and Their Birational Invariants , 1998 .

[5] Joe Kilian,et al. Primality testing using elliptic curves , 1999, JACM.

[6] William Ellison,et al. Prime numbers , 1985 .

[7] Manindra Agrawal,et al. PRIMES is in P , 2004 .