caa a22 4500 475807529 CHVBK 20180406123751.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1023/A:1008354106356 doi (NATIONALLICENCE)springer-10.1023/A:1008354106356 The State of Elliptic Curve Cryptography [Elektronische Daten] [Neal Koblitz, Alfred Menezes, Scott Vanstone] Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffie and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers modulo a prime, this idea can be extended to arbitrary groups and, in particular, to elliptic curve groups. The resulting public-key systems provide relatively small block size, high speed, and high security. This paper surveys the development of elliptic curve cryptosystems from their inception in 1985 by Koblitz and Miller to present day implementations. Kluwer Academic Publishers, 2000 Elliptic curves nationallicence public-key cryptography nationallicence Koblitz Neal Dept. of Mathematics, University of Washington, Box 354350, 98195, Seattle, WA, USA aut Menezes Alfred Dept. of C&O, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Vanstone Scott Dept. of C&O, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Designs, Codes and Cryptography Kluwer Academic Publishers 19/2-3(2000-03-01), 173-193 0925-1022 19:2-3<173 2000 19 10623 https://doi.org/10.1023/A:1008354106356 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008354106356 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Koblitz Neal Dept. of Mathematics, University of Washington, Box 354350, 98195, Seattle, WA, USA aut NATIONALLICENCE 700 1- Menezes Alfred Dept. of C&O, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 700 1- Vanstone Scott Dept. of C&O, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 19/2-3(2000-03-01), 173-193 0925-1022 19:2-3<173 2000 19 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer