Reducing elliptic curve logarithms to logarithms in a finite field

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Reducing elliptic curve logarithms to logarithms in a finite field

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Annual ACM Symposium on Theory of Computing archive
Proceedings of the twenty-third annual ACM symposium on Theory of computing table of contents

New Orleans, Louisiana, United States

Pages: 80 - 89

Year of Publication: 1991

ISBN:0-89791-397-3

Authors

Alfred Menezes	Univ. of Waterloo, Ontario, CANADA
Scott Vanstone	Univ. of Waterloo, Ontario, CANADA
Tatsuaki Okamoto	NTT Labs., Yokosuka-Shi, Japan

Sponsor

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 36, Downloads (12 Months): 145, Citation Count: 7

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	L. Adleman, K. Manders and G. Miller, "On taking roots in finite fields", Proceedings of the 20th Annual Symposium on the Foundations of Computer Science (1979), 175-178.
	2	Andreas Bender , Guy Castagnoli, On the implementation of elliptic curve cryptosystems, Proceedings on Advances in cryptology, p.186-192, July 1989, Santa Barbara, California, United States
	3	D. Coppersmith, "Fast evaluation of logarithxm in fields of characteristic two", IEEE Transactions on Information Theory, IT-30 (1984), 587-594.
	4	Don Coppersmith , Andrew M. Odlyzko , Richard Schroeppel, Discrete logarithms in GF(p), Algorithmica, v.1 n.1, p.1-15, Jan. 1986 [doi>10.1007/BF01840433]
	5	T. E1Gamal, "A subexponential-time algorithm for computing discrete logarithms over GF(p2)'', IEEE Transactions on Information Theory, IT-31 (1985), 473-481.
	6	Burton S. Kaliski, Jr., A pseudo-random bit generator based on elliptic logarithms, Proceedings on Advances in cryptology---CRYPTO '86, p.84-103, January 1987, Santa Barbara, California, United States
	7	B. Kaliski, "Elliptic curves a#rtd cryptography: A pseudorandom bit generator and other tools", PhD thesis, M. I. T., January 1988.
	8	N. Koblitz, "Elliptic curve cryptosystems', Mathematics of Computation, 48 (1987), 203- 209.
	9	Alfred Menezes , Scott A. Vanstone, The implementation of elliptic curve cryptosystems, Proceedings of the international conference on cryptology on Advances in cryptology, p.2-13, September 1990, Sydney, Australia
	10	A. Menezes and S. Vanstorte, "Elliptic curve cryptosystems and their implementation", in preparation.
	11	V. Miller, "Short programs for functions on curves", unpublished manuscript, 1986.
	12	Victor S Miller, Use of elliptic curves in cryptography, Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85, p.417-426, June 1986, Santa Barbara, California, United States
	13	A M Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques, p.224-314, December 1985, Paris, France
	14	C. Pomeraxtce, "Fast, rigorous factorization and discrete logarithms algorithms", Discrete Algorithms and Complezity (1987), 119-143.
	15	M. Rabin, "Probabilistic algorithms in finite fields", SIAM Journal on Computing, 9 (1980), 273-280.
	16	J. Rosser and L. Schoentield, "Approximate formulas for some functions of prime numbers", Illinois Journal of Mathematics, 6 (1962), 64-94.
	17	R. School, "Elliptic curves over fimte fields and the computation of square roots rood p", Mathematics of Computation, 44 (1985), 483- 494.
	18	René Schoof, Nonsingular plane cubic curves over finite fields, Journal of Combinatorial Theory Series A, v.46 n.2, p.183-211, Nov. 1987 [doi>10.1016/0097-3165(87)90003-3]
	19	J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, New York, 1986.
	20	R. Silverman, "The multiple polynomial quadratic sieve'# Mathematics of Computation, 48 (1987), 329-339.

CITED BY 7

	Pu Duan , Shi Cui , Choong Wah Chan, Special polynomial families for generating more suitable pairing-friendly elliptic curves, Proceedings of the 5th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications, p.187-192, February 15-17, 2006, Madrid, Spain
	Fabien Laguillaumie , Damien Vergnaud, Multi-designated verifiers signatures: anonymity without encryption, Information Processing Letters, v.102 n.2-3, p.127-132, April, 2007
	Jung Hee Cheon , Nicholas Hopper , Yongdae Kim , Ivan Osipkov, Provably Secure Timed-Release Public Key Encryption, ACM Transactions on Information and System Security (TISSEC), v.11 n.2, p.1-44, March 2008
	Hao Li , Jian Huang , Philip Sweany , Dijiang Huang, FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field, Journal of Systems Architecture: the EUROMICRO Journal, v.54 n.12, p.1077-1088, December, 2008
	Amitabh Saxena , Ben Soh, One-Way Signature Chaining: a new paradigm for group cryptosystems, International Journal of Information and Computer Security, v.2 n.3, p.268-296, October 2008
	David J. Malan , Matt Welsh , Michael D. Smith, Implementing public-key infrastructure for sensor networks, ACM Transactions on Sensor Networks (TOSN), v.4 n.4, p.1-23, August 2008
	Toshiya Nakajima , Tetsuya Izu , Tsuyoshi Takagi, Reduction Optimal Trinomials for Efficient Software Implementation of the ηT Pairing, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, v.E91-A n.9, p.2379-2386, September 2008