Primality tests for using elliptic curves

Author:
Yu Tsumura

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2697-2703

MSC (2010):
Primary 11Y11; Secondary 14H52

Published electronically:
January 14, 2011

MathSciNet review:
2801608

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Abstract | References | Similar Articles | Additional Information

Abstract: Using the properties of elliptic curves, we propose primality tests for integers of the form , where is a prime number.

**1.**John Brillhart, D. H. Lehmer, and J. L. Selfridge,*New primality criteria and factorizations of 2^{𝑚}±1*, Math. Comp.**29**(1975), 620–647. MR**0384673**, 10.1090/S0025-5718-1975-0384673-1**2.**Robert Denomme and Gordan Savin,*Elliptic curve primality tests for Fermat and related primes*, J. Number Theory**128**(2008), no. 8, 2398–2412. MR**2394827**, 10.1016/j.jnt.2007.12.009**3.**Benedict H. Gross,*An elliptic curve test for Mersenne primes*, J. Number Theory**110**(2005), no. 1, 114–119. MR**2114676**, 10.1016/j.jnt.2003.11.011**4.**Hans-Georg Rück,*A note on elliptic curves over finite fields*, Math. Comp.**49**(1987), no. 179, 301–304. MR**890272**, 10.1090/S0025-5718-1987-0890272-3**5.**Lawrence C. Washington,*Elliptic curves*, 2nd ed., Discrete Mathematics and its Applications (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2008. Number theory and cryptography. MR**2404461**

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Additional Information

**Yu Tsumura**

Affiliation:
Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907-2067

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10839-6

Keywords:
Elliptic curve,
primality tests

Received by editor(s):
January 12, 2010

Received by editor(s) in revised form:
July 15, 2010, and August 3, 2010

Published electronically:
January 14, 2011

Communicated by:
Ken Ono

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.