Andrew Odlyzko: Papers on Computational Number Theory

• The past, evolving present and future of discrete logarithm, A. Joux, A. Odlyzko, and C. Pierrot, Open Problems in Mathematical and Computational Sciences, C. K. Koc, ed., Springer, 2014, pp. 5-36. [preprint, PDF]

• Discrete logarithms over finite fields, A. Odlyzko. In Handbook of Finite Fields, G. Mullen and D. Panario, eds., CRC Press, 2013, pp. 393-401. [preprint, PDF]

• Alan Turing and the Riemann zeta function, D. A. Hejhal and A. M. Odlyzko. In Alan Turing - His Work and Impact, S. Barry Cooper and Jan van Leeuwen, eds., Elsevier, 2013, pp. 265-279. [PDF]

• Numerical study of the derivative of the Riemann zeta function at zeros, G. A. Hiary and A. M. Odlyzko, Commentarii Mathematici Universitatis Sancti Pauli, vol. 60, no. 1-2, 2011, pp. 47-60. [PDF]

• The zeta function on the critical line: Numerical evidence for moments and random matrix theory models, G. A. Hiary and A. M. Odlyzko, Math. Comp., vol. 81, no. 279, July 2012, pp. 1723-1752. [preprint, PDF]

• The 10^22-nd zero of the Riemann zeta function, A. M. Odlyzko. Dynamical, Spectral, and Arithmetic Zeta Functions, M. van Frankenhuysen and M. L. Lapidus, eds., Amer. Math. Soc., Contemporary Math. series, no. 290, 2001, pp. 139-144. [Abstract] [PDF]

• An improved bound for the de Bruijn-Newman constant, A. M. Odlyzko, Numerical Algorithms, 25 (2000), pp. 293-303. [Abstract] [PDF]

• Discrete logarithms: The past and the future, A. M. Odlyzko, Designs, Codes, and Cryptography 19 (2000), pp. 129-145. Reprinted in Towards a Quarter-Century of Public Key Cryptography, N. Koblitz, ed., Kluwer, 2000, pp. 59-75. [Abstract] [PDF]

• Jumping champions, A. Odlyzko, M. Rubinstein, and M. Wolf, Experimental Math., 8 (no. 2) (1999), pp. 107-118. [PDF, 2 MB] [Exp. Math. version]

• A nonlinear equation and its application to nearest neighbor spacings for zeros of the zeta function and eigenvalues of random matrices, P. J. Forrester and A. M. Odlyzko, in Organic Mathematics, J. Borwein, P. Borwein, L. Jorgenson, and R. Corless, eds., Amer. Math. Soc. 1997, pp. 239-250. Electronic version available at http://www.cecm.sfu.ca/projects/OMP/. [PDF] A condensed version, GUE eigenvalues and Riemann zeta function zeros: A non-linear equation for a new statistic has appeared in Phys. Rev. E 54 (1996), pp. R4493-R4495. [PDF]

• The future of integer factorization, A. M. Odlyzko, CryptoBytes (The technical newsletter of RSA Laboratories) 1 (no. 2) (1995), pp. 5-12. [PDF] [CryptoBytes issue]

• Discrete logarithms and smooth polynomials, A. M. Odlyzko, pp. 269-278 in Finite Fields: Theory, Applications and Algorithms, G. L. Mullen and P. Shiue, eds., Amer. Math. Soc., Contemporary Math. #168 (1994). [PDF]

• Analytic computations in number theory, A. M. Odlyzko, Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics, W. Gautschi (ed.), Amer. Math. Soc., Proc. Symp. Appl. Math. #48 (1994), pp. 451-463. [PDF]

• Public key cryptography, A. M. Odlyzko, AT&T Tech. J., 73:5 (Sept.-Oct. 1994), pp. 17-23. [PDF]

• A New Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant LAMBDA, G. Csordas, A. M. Odlyzko, W. Smith, and R. S. Varga, Electr. Trans. Num. Anal., 1 (1993), pp. 104-111. [PDF] [comments]

• Iterated absolute values of differences of consecutive primes, A. M. Odlyzko, Math. Comp., 61 (1993), pp. 373-380. [online journal version]

• Improved low-density subset sum algorithms, M. J. Coster, A. Joux, B. A. LaMacchia, A. M. Odlyzko, C. P. Schnorr, and J. Stern, Computational Complexity, 2 (1992), pp. 111-128. [PDF]

• An improved low-density subset sum algorithm, M. J. Coster, B. A. LaMacchia, A. M. Odlyzko, and C. P. Schnorr, pp. 54-67 in Advances in Cryptology - EUROCRYPT '91, D. W. Davies (ed.), Springer Verlag, Lecture Notes in Computer Science #547 (1991). [PDF]

• Computation of discrete logarithms in prime fields, B. A. LaMacchia and A. M. Odlyzko, Designs, Codes, and Cryptography, 1 (1991), pp. 46-62, Extended abstract in Advances in Cryptology - CRYPTO '90, A. J. Menezes, and S. A. Vanstone (eds.), Springer Verlag, Lecture Notes in Computer Science #537, 1991, pp. 616-618. [PDF]

• Solving large sparse linear systems over finite fields, B. A. LaMacchia and A. M. Odlyzko, pp. 109-133 in Advances in Cryptology - CRYPTO '90, A. J. Menezes and S. A. Vanstone (eds.), Springer Verlag, Lecture Notes in Computer Science #537 (1991). [PDF]

• Primes, quantum chaos, and computers, A. M. Odlyzko, pp. 35-46 in Number Theory, National Research Council (1990). [PDF]

• The rise and fall of knapsack cryptosystems, A. M. Odlyzko, pp. 75-88 in Cryptology and Computational Number Theory, C. Pomerance (ed.), Am. Math. Soc., Proc. Symp. Appl. Math. #42 (1990). [PDF]

• Supercomputers and the Riemann zeta function, A. M. Odlyzko, pp. 348-352 in Supercomputing '89: Supercomputing Structures & Computations, Proc. 4-th Intern. Conf. on Supercomputing, L. P. Kartashev and S. I. Kartashev (eds.), Intern. Supercomputing Inst. (1989). [PDF]

• Fast algorithms for multiple evaluations of the Riemann zeta function, A. M. Odlyzko and A. Schoenhage, Trans. Am. Math. Soc., 309 (1988), pp. 797-809. [online journal version]

• New analytic algorithms in number theory, A. M. Odlyzko, pp. 466-475 in Proceedings 1986 International Congress of Mathematicians, Amer. Math. Soc., 1987, [PDF]

• On the distribution of spacings between zeros of the zeta function, A. M. Odlyzko, Math. Comp., 48 (1987), pp. 273-308. [online journal version]

• Computing pi(x): An analytic method, J. C. Lagarias and A. M. Odlyzko, J. Algorithms, 8 (1987), pp. 173-191. [PDF]

• On the complexity of computing discrete logarithms and factoring integers, A. M. Odlyzko, pp. 113-116 in Open Problems in Communication and Computation, T. M. Cover and B. Gopinath (eds.), Springer, 1987. [PDF]

• Discrete logarithms in GF(p), D. Coppersmith, A. M. Odlyzko, and R. Schroeppel, Algorithmica, 1 (1986), pp. 1-15.

• Discrete logarithms in finite fields and their cryptographic significance , A. M. Odlyzko, pp. 224-314 in Advances in Cryptology: Proceedings of EUROCRYPT 84, T. Beth, N. Cot, and I. Ingemarsson (eds.), Springer-Verlag, Lecture Notes in Computer Science #209, 1985. [PDF]

• Disproof of the Mertens conjecture, A. M. Odlyzko and H. J. J. te Riele, J. reine angew. Math., 357 (1985), pp. 138-160. [PDF]

• Computing pi(x): The Meissel-Lehmer method, J. C. Lagarias, V. S. Miller, and A. M. Odlyzko, Math. Comp., 44 (1985), pp. 537-560. [online journal version]

• Solving low-density subset sum problems, J. C. Lagarias and A. M. Odlyzko, J. ACM, 32 (1985), pp. 229-246. Preliminary version in Proc. 24th IEEE Foundations Computer Science Symp., pp. 1-10, 1983.

• Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir's signature scheme, A. M. Odlyzko, IEEE Trans. Information Theory, IT-30 (1984), pp. 594-601. [PDF]

• Evaluation of the Adleman attack on multiply iterated knapsack cryptosystems, E. F. Brickell, J. C. Lagarias, and A. M. Odlyzko, pp. 39-42 in Advances in Cryptology: Proceedings of Crypto 83, D. Chaum (ed.), Plenum Press, 1984.

• New algorithms for computing pi(x), J. C. Lagarias and A. M. Odlyzko, pp. 176-193 in Number Theory: New York 1982, D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn and M. B. Nathanson (eds.), Springer-Verlag, Lecture Notes in Mathematics #1052, 1984.

• Gaps between zeros of the zeta function, H. L. Montgomery and A. M. Odlyzko, pp. 1079-1106 in Topics in Classical Number Theory: Coll. Math. Soc. Janos Bolyai 34., G. Halasz (ed.), North-Holland, 1984.

• Irreducibility testing and factorization of polynomials, L. M. Adleman and A. M. Odlyzko, Math. Comp., 41 (1983), pp. 699-709. Preliminary version in Proc. 22nd IEEE Foundations Computer Science Symp., pp. 409-418, 1981. [online Math. Comp. version]

• On computing Artin L-functions in the critical strip, J. C. Lagarias and A. M. Odlyzko, Math. Comp., 33 (1979), pp. 1081-1095. [online journal version]