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Proving primality in essentially quartic random time
 Math. Comp
, 2003
"... Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1. ..."
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Cited by 18 (0 self)
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Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1.
Proving Primality In Essentially Quartic Expected Time
, 2003
"... This paper presents a randomized algorithm that, given a prime n, nds and veri es a proof of the primality of n in expected time (lg n) . ..."
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Cited by 7 (0 self)
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This paper presents a randomized algorithm that, given a prime n, nds and veri es a proof of the primality of n in expected time (lg n) .
Doublyfocused enumeration of pseudosquares and pseudocubes
 In Proceedings of the 7th International Algorithmic Number Theory Symposium (ANTS VII
, 2006
"... Abstract. This paper offers numerical evidence for a conjecture that primality proving may be done in (log N) 3+o(1) operations by examining the growth rate of quantities known as pseudosquares and pseudocubes. In the process, a novel method of solving simultaneous congruencesâ€” doublyfocused enumer ..."
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Cited by 1 (0 self)
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Abstract. This paper offers numerical evidence for a conjecture that primality proving may be done in (log N) 3+o(1) operations by examining the growth rate of quantities known as pseudosquares and pseudocubes. In the process, a novel method of solving simultaneous congruencesâ€” doublyfocused enumeration â€” is examined. This technique, first described by D. J. Bernstein, allowed us to obtain recordsetting sieve computations in software on general purpose computers. 1
ELLIPTIC PERIODS AND PRIMALITY PROVING (EXTENTED VERSION)
, 810
"... Abstract. We construct extension rings with fast arithmetic using isogenies between elliptic curves. As an application, we give an elliptic version of the AKS primality criterion. ..."
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Abstract. We construct extension rings with fast arithmetic using isogenies between elliptic curves. As an application, we give an elliptic version of the AKS primality criterion.
Elliptic periods and primality proving
, 2009
"... We define the ring of elliptic periods modulo an integer n and give an elliptic version of the AKS primality criterion. ..."
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We define the ring of elliptic periods modulo an integer n and give an elliptic version of the AKS primality criterion.