R. K. Guy, "How to factor a number", Congressus Numerantum XVI, Proc. Fifth Manitoba Conference on Numerical Mathematics, Winnipeg, 1976, 49-89. Home/Search Document Not in Database Summary Related Articles Check |
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Security and Efficiency Analyses of Public Key Cryptosystems - Kunihiro (2001) (Correct)
....the effectiveness of the proposed method. For example, the proposed method runs 3 or 4 times faster than the original ECM. 3.1 Introduction It is important to find efficient factoring algorithms for evaluating the security of cryptosystems. The ae method [50] p 0 1 method [49] p 1 method [21], continued fraction method [51] quadratic sieve method [45] number field sieve method [34] elliptic curve factoring method [33] 43] etc. have been proposed. These methods have been classified into two types: algorithms depending on prime factors and algorithms depending on composite numbers. ....
R. K. Guy, "How to factor a number," Proc. of the Manitoba Conf. on Numerical Math., pp. 49--89, 1975.
New Methods of Generating Primes Secure against Both - And Methods Yoshizo (Correct)
....forit ing method [1] This method is widely re#ered to as P 1 method. Factoring the composite number N , P 1 method is very e#ective when P 1 isf)L: P into small primes, where P is af( of the N. In 1975, Guy suggested P 1 method which is a similar algorithm to P 1 method [2]. Since cryptosystem based on the problemof fblemP( the composite number N can be attacked with P 1 and P 1 methods, it is required that P 1 and P 1 should be di#cult to be f : PB into many small primes. The trial division method is well known as an e# cient methodf= generating ....
R.K.Guy , "How to factor a number," Proc. 5th Manitoba Conf. on Numerical Math., pp.49--89, 1975.
Open Problems in Number Theoretic Complexity, II - Adleman, McCurley (5 citations) (Correct)
....94 Problem O1b has been settled in the affirmative by Adleman and Huang [AH92] As a result of the work of H. Maier on gaps between consecutive primes, the exact formulation of Cram er s conjecture has now been called into question, however the conjecture required for [GK86] is unaffected. Ref1 [Guy77], Knu81] Len81] CL84] Pom81] Rab80a] Rie85b] Rie85a] Wil78] 2 Testing an infinite set of primes Let S ae N. C2 Input n 2 N. Output 1 if n 2 S, 0 otherwise. O2 Does there exist an infinite set S ae Primes such that C2 is in P Rem2 86 In light of Rem1 86 it is remarkable that ....
....and Schroeppel. See [Adl91] Cop90] Cou93] LL93] and the references cited therein. In a very recent development Peter Shor [Shoar] has shown that factoring can be done in polynomial time on a quantum computer . It is premature to judge the implications of this development. Ref5 [Dix81] [Guy77], Knu81] Len87] MB75] Pom82] Rie85b] Rie85a] Sha71] Sch82] SL84] Wil84] 6 Factoring a set of positive density Let S ae N. C6 Input n 2 N. Output p 1 ; p 2 ; p k 2 Primes and e 1 ; e 2 ; e k 2 N such that n = k Y i=1 p e i i if n 1 and n 2 S : O6 ....
Richard Guy. How to factor a number. Congressus Numeratium, XXVII:49--89, 1977. Proceedings of the Fifth Manitoba Conference on Numerical Mathematics, University of Manitoba.
Factorizations of a^n±1, 13 ≤ a < 100 - Brent, Riele (1992) (Correct)
....program factor for IBM PC and compatible computers [3] The program factor should be considered primarily as a means of accessing a file of known factors, rather than as a general purpose factorization program. For surveys of factorization algorithms and programs, we refer the reader to [1, 2, 7, 8, 10, 13, 14, 16, 17, 18, 19, 20]. Over the past few years we have systematically extended our list of factors, concentrating on numbers a n Sigma 1 for 13 a 100, n 100, but also considering some larger values of the exponent n for the smaller bases a. The tables are now complete for n 46 and include no composites with ....
R. K. Guy, "How to factor a number", Congressus Numerantum XVI, Proc. Fifth Manitoba Conference on Numerical Mathematics, Winnipeg, 1976, 49-89.
The Magic Words Are Squeamish Ossifrage (Extended Abstract) - Atkins, Graff, Lenstra.. (Correct)
.... the scenes of this world wide computing effort (Section 5) and some concluding remarks (Section 6) 2 Predicting the difficulty of factoring r Back in 1976, Richard Guy wrote I shall be surprised if anyone regularly factors numbers of size 10 80 without special form during the present century [8]. In 1977, Rivest estimated in [20] that factoring a 125 digit number which is the product of two 63 digit prime numbers would require at least 40 quadrillion years using the best factoring algorithm known, assuming that a b (modc) could be computed in 1 nanosecond, for 125 digit numbers a, b, ....
R. K. Guy, How to factor a number, Proc. Fifth Manitoba Conf. Numer. Math., Congressus Numerantium 16 (1976) 49--89.
Factorizations of a - Richard Brent Computer (Correct)
No context found.
R. K. Guy, "How to factor a number", Congressus Numerantum XVI, Proc. Fifth Manitoba Conference on Numerical Mathematics, Winnipeg, 1976, 49-89.
Factorizations of a^n ± 1, 13 ≤ a < 100 - Brent, Riele (1992) (Correct)
No context found.
R. K. Guy, "How to factor a number", Congressus Numerantum XVI, Proc. Fifth Manitoba Conference on Numerical Mathematics, Winnipeg, 1976, 49-89.
Are `Strong' Primes Needed for RSA? - Rivest, Silverman (1999) (1 citation) (Correct)
No context found.
Richard K. Guy. How to factor a number. In Proceedings Fifth Manitoba Conference on Numerical Mathematics, pages 49--89, 1975. 20
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