Robert J. McEliece

Robert J. McEliece (born May 21, 1942 in Washington, DC - † May 8, 2019 ) was an American mathematician and electrical engineer . He was a professor of electrical engineering at Caltech . He is known for contributions to algebraic coding theory .

life and work

McEliece studied at Caltech with a bachelor's degree in 1964 and a doctorate in mathematics from Marshall Hall in 1967 ( linear recurring sequences over finite fields ). He also studied for a year at Trinity College at the University of Cambridge in 1964/65 . McEliece was an engineer at the Jet Propulsion Laboratory from 1963 , from 1970 to 1978 supervisor of the information processing group and from 1978 a consultant. During this time he was visiting professor at Caltech from 1972 to 1976. He was Professor of Mathematics at the University of Illinois at Urbana-Champaign from 1978 to 1982 , before becoming Professor at Caltech in 1982, where he was Robert E. Puckett Professor .

He developed error-correcting codes based on convolutional codes ( convolution codes ), the z. B. were used in the Galileo probe. He was also involved in the error-correcting codes of the Voyager program . When there were data transmission problems on the Galileo mission that jeopardized the transmission of photos from Jupiter, he was on the team at the Jet Propulsion Laboratory that successfully reprogrammed the decoder on board. He also developed RLL encodings for hard drives and flash memories at Sony .

In 1978 he and Elwyn Berlekamp developed a public key cryptosystem named after him ( McEliece cryptosystem ) based on linear codes (he used Goppa codes ). A corresponding digital signature is the McEliece-Niederreiter signature (additionally after Harald Niederreiter ).

It did not prevail against RSA encryption due to the key lengths in the range of a few megabytes, but the McEliece cryptosystem is considered to be secure against attempts at decryption with a quantum computer .

McEliece is known for important results in mathematical coding theory, including the Solomon-McEliece formula (with Gustave Solomon ), the MRRW bounds (McEliece, R. Rodemick, Howard Rumsey, Lloyd R. Welch ), for binary codes and the theorem by McEliece on weight polynomials of codes. He also wrote a standard work on information and coding theory.

McEliece published with Paul Erdős in 1971 and thus has Erdős number 1. In 2004 he received the Claude E. Shannon Award , in 2000 the IEEE Third Millennium Award and in 2009 the IEEE Alexander Graham Bell Medal . He is a Life Fellow of the IEEE , which he became a Fellow in 1984. In 1984 he was President of the IEEE Information Theory Group . In 1998 he became a member of the National Academy of Engineering . He is a fellow of the American Mathematical Society . For error-correcting codes in NASA space missions, he received the NASA Group Achievement Award twice (1981 and 1992) and once (1981) for his contributions to the Voyager mission.

Fonts

• The theory of information and coding: A mathematical framework for communication. Addison-Wesley, 1977.

Web links

• Homepage at Caltech
• Biography on the IEEE Global History Network

Individual evidence

1. ^ Mathematics Genealogy Project
2. ^ E. Berlekamp, ​​R. McEliece, H. van Tilborg: On the inherent intractability of certain coding problems . In: IEEE Transactions on Information Theory . tape 24 , no. 3 , May 1978, p. 384-386 , doi : 10.1109 / TIT.1978.1055873 .
3. ^ McEliece: A Public-Key Cryptosystem Based on Algebraic Coding Theory. In: JPL Deep Space Network Progress Report. No. 42-44, 1978, pp. 114-116.
4. ^ R. McEliece, E. Rodemich, H. Rumsey, L. Welch: New Upper Bounds on the Rate of a Code via the Delsarte-MacWilliams Inequalities . In: IEEE Transactions on Information Theory . tape 23 , no. 2 , March 1977, p. 157–166 , doi : 10.1109 / TIT.1977.1055688 ( PDF [accessed February 17, 2013]).
5. ^ Erdős, Paul, Robert McEliece, and Herbert Taylor: Ramsey bounds for graph products . In: Pacific Journal of Mathematics . tape 37.1 , 1971, p. 45-46 , doi : 10.2140 / pjm.1971.37.45 .