منابع مشابه
Very Short Primality Proofs
It is shown that every prime p has a proof of its primality of length 0(logp) multiplications modulo p.
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The first efficient general primality proving method was proposed in the year 1980 by Adleman, Pomerance and Rumely and it used Jacobi sums. The method was further developed by H. W. Lenstra Jr. and more of his students and the resulting primality proving algorithms are often referred to under the generic name of Cyclotomy Primality Proving (CPP). In the present paper we give an overview of the...
متن کاملPrimality proofs with elliptic curves: heuristics and analysis
This paper deals with the heuristic running time analysis of the elliptic curve primality proving (ECPP) algorithm of Atkin and Morain. Our aim is to collect assumptions and the fastest possible algorithms to reduce the heuristic running time and to show that under these assumptions and some plausible conditions the heuristic running time can be reduced down to o(ln n) bit operation for input p...
متن کاملShort Discreet Proofs
We show how to produce short proofs of theorems such that a distrusting Verifier can be convinced that the theorem is true yet obtains no information about the proof itself. The proofs are non-interactive provided that the quadratic residuosity bit commitment scheme is available to the Prover and Verifier. For typical applications, the proofs are short enough to fit on a floppy disk.
متن کاملDescribing proofs by short tautologies
Herbrand’s theorem is one of the most fundamental results about first-order logic. In the context of proof analysis, Herbrand-disjunctions are used for describing the constructive content of cut-free proofs. However, given a proof with cuts, the computation of an Herbrand-disjunction is of significant computational complexity, as the cuts in the proof have to be eliminated first. In this paper ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1987
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1987-0866117-4