Cryptography Reference
In-Depth Information
References
[1] Leonard M. Adleman and Jonathan Demarrais. A subexponential algorithm for discrete logarithms over all
finite fields. Mathematics of Computation 61 (203): 1-15 (1993).
[2] J. A. Buchmann, J. Loho, and J. Zayer. An implementation of the general number field sieve. In Advances in
Cryptology - Crypto '93, (ed. Douglas R. Stinson), pp. 159-165. Lecture Notes in Computer Science, Vol. 773.
(Springer-Verlag, Berlin, 1993).
[3] J. A. Davis and D. B. Holdridge. Factorization using the quadratic sieve algorithm. In Advances in Crypto-
logy: Proceedings of Crypto '83, (ed. David Chaum), pp. 103-116 (Plenum, New York, 1984).
[4] Whitfield Diffie and Martin E. Hellman. New directions in cryptography. IEEE Transactions on Information
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[5] T. ElGamal. A public key cryptosystem and a signature scheme based on discrete logarithms. In Advances
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[6] Donald E. Knuth. The Art of Computer Programming: Seminumerical Algorithms, Vol. 2, 3rd ed. (Addison
Wesley, Boston, 1998).
[7] H. W. Lenstra, Jr. Factoring integers with elliptic curves. The Annals of Mathematics, 2nd Ser. 126(3):
649-673 (1987).
[8] Arien K. Lenstra and Henrik W. Lenstra, Jr., eds. The Development of the Number Field Sieve, Vol. 554 of
Lecture Notes in Mathematics .(Springer-Verlag, Berlin, 1993).
[9]
Stephen
McMath.
Daniel
Shanks'
Square
Forms
Factorization.
(2004);
ht-
tp://web.usna.navy.mil/~wdj/mcmath/SQUFOF.pdf .
[10] Michael A. Morrison and John Brillhart. A method of factoring and the factorization of f 7 . Mathematics of
Computation 29(129): 183-205 (1975).
[11] John M. Pollard. Monte carlo methods for index computation. Mathematics of Computation 32(143):
918-924 (1978).
[12] John M. Pollard. Theorems of factorization and primality testing. Mathematical Proceedings of the Cam-
bridge Philosophical Society 76: 521-528 (1974).
[13] C. Pomerance. The quadratic sieve factoring algorithm. In Advances in Cryptology: Proceedings of Eur-
oCrypt '84, (eds. Thomas Beth, Norbert Cot, and Ingemar Ingemarsson), pp. 169-182. Lecture Notes in Com-
puter Science, Volume 209. (Springer-Verlag, Berlin, 1984).
[14] Daniel Shanks. Five number-theoretic algorithms. Congressus Numerantium 7 (Utilitas Mathematica,
1973).
[15] Samuel S. Wagstaff. Cryptanalysis for Number Theoretic Ciphers. (Chapman & Hall/CRC, Boca Raton,
FL, 2003).
Notes
1 As my friend Raquel Phillips pointed out, “logarithm” and “algorithm” are anagrams!
 
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