Richard Schroeppel
Encyclopedia
United States
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mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
born in Illinois
Illinois
Illinois is the fifth-most populous state of the United States of America, and is often noted for being a microcosm of the entire country. With Chicago in the northeast, small industrial cities and great agricultural productivity in central and northern Illinois, and natural resources like coal,...
. His research has included magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
s, elliptic curves, and cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
. In 1973 he discovered the number of 5x5 normal magic squares, in 1998–1999 he designed the Hasty Pudding Cipher
Hasty Pudding Cipher
The Hasty Pudding Cipher is a variable-block-size block cipher designed by Richard Schroeppel, which was an unsuccessful candidate in the competition for selecting the U.S. Advanced Encryption Standard...
which was a candidate for the Advanced Encryption Standard
Advanced Encryption Standard
Advanced Encryption Standard is a specification for the encryption of electronic data. It has been adopted by the U.S. government and is now used worldwide. It supersedes DES...
, and he is one of the designers of the SANDstorm hash
SANDstorm hash
The SANDstorm hash is a cryptographic hash function designed in 2008 by Mark Torgerson, Richard Schroeppel, Tim Draelos, Nathan Dautenhahn, Sean Malone, Andrea Walker, Michael Collins, and Hilarie Orman for the NIST SHA-3 competition....
, a submission to the NIST SHA-3 competition. He currently works at Sandia National Laboratories
Sandia National Laboratories
The Sandia National Laboratories, managed and operated by the Sandia Corporation , are two major United States Department of Energy research and development national laboratories....
.
Among other contributions, Schroeppel was the first to recognize the sub-exponential running time of certain factoring algorithms. While not entirely rigorous, his proof that Morrison and Brillhart's continued fraction factoring algorithm ran in roughly exp{SQRT[2 ln(n) lnln(n)]} steps was an important milestone in factoring and laid a foundation for much later work, including the current "champion" factoring algorithm, the Number Field Sieve.
Not only did Schroeppel analyze Morrison and Brillhart's algorithm, he also saw how to cut the run time to roughly exp{SQRT[ln(n) lnln(n)]} by modifications which allowed sieving. This improvement doubled the size of numbers which could be factored in a given amount of time. Coming around the time of the RSA algorithm, which depends on the difficulty of factoring for its security, this was a critically important result.
Due to Schroeppel's apparent prejudice against publishing (though he freely circulated his ideas within the research community), and in spite of Pomerance noting that his quadratic sieve factoring algorithm owed a debt to Schroeppel's earlier work, the latter's contribution is often overlooked. (See the section on "Smooth Numbers" on pages 1476-1477 of Pomerance's "A Tale of Two Sieves," Notices of the AMS, Vol. 43, No. 12, December 1996.)
His Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
is 2.