Abstract :
While proving compositeness of a natural number is a computational task that can be easily done in polynomial time, proving primality of an arbitrary positive integer is a harder task. Only two main streams of useful algorithms are known in this direction: elliptic curve primality provers (ECPPs, [F. Morain, Advances in Cryptology, EUROCRYPT ʹ90, Lecture Notes in Computer Science, vol. 473, 1990, pp. 110–123]) and cyclotomy [W. Bosma, M. Der Hulst, Primality proving with cyclotomy, Ph.D. Thesis, 12278 University van Amsterdam, Holland, 1990; P.M. Mihăilescu, Cyclotomy of rings and primality testing, Ph.D. Thesis, Dissertation no., ETH Zürich, 1997].
