Very short primality proofs

Very short primality proofs
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by Carl Pomerance PDF

Math. Comp. 48 (1987), 315-322 Request permission

It is shown that every prime p has a proof of its primality of length $O(\log p)$ multiplications modulo p.

References

Eric Bach, Analytic methods in the analysis and design of number-theoretic algorithms, ACM Distinguished Dissertations, MIT Press, Cambridge, MA, 1985. MR 807772

Sequences of Numbers Generated by Addition in Formal Groups and New Primality and Factorization Tests

Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197–272 (German). MR 5125, DOI 10.1007/BF02940746

Almost All Primes Can Be Quickly Certified

Gary L. Miller, Riemann’s hypothesis and tests for primality, J. Comput. System Sci. 13 (1976), no. 3, 300–317. MR 480295, DOI 10.1016/S0022-0000(76)80043-8
Peter L. Montgomery, Speeding the Pollard and elliptic curve methods of factorization, Math. Comp. 48 (1987), no. 177, 243–264. MR 866113, DOI 10.1090/S0025-5718-1987-0866113-7
Vaughan R. Pratt, Every prime has a succinct certificate, SIAM J. Comput. 4 (1975), no. 3, 214–220. MR 391574, DOI 10.1137/0204018

Acta Inform.

J. Combin. Theory

Daniel Shanks, Solved and unsolved problems in number theory, 3rd ed., Chelsea Publishing Co., New York, 1985. MR 798284
John T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179–206. MR 419359, DOI 10.1007/BF01389745
William C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969), 521–560. MR 265369
Andrew Chi Chih Yao, On the evaluation of powers, SIAM J. Comput. 5 (1976), no. 1, 100–103. MR 395331, DOI 10.1137/0205008