Richard C. Schroeppel (born 1948) is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

born in

Illinois Illinois ( ) is a state in the Midwestern United States. Its largest metropolitan areas include the Chicago metropolitan area, and the Metro East section, of Greater St. Louis. Other smaller metropolitan areas include, Peoria and Rockf ...

. His research has included magic squares, elliptic curves, and

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

. In 1964, Schroeppel won first place in the United States among over 225,000 high school students in the Annual High School Mathematics Examination, a contest sponsored by the Mathematical Association of America and the Society of Actuaries. In both 1966 and 1967, Schroeppel scored among the top 5 in the U.S. in the William Lowell Putnam Mathematical Competition. In 1973 he discovered that there are 275,305,224 normal magic squares of order 5. In 1998–1999 he designed the Hasty Pudding Cipher, which was a candidate for the

Advanced Encryption Standard The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a varian ...

, and he is one of the designers of the SANDstorm hash, a submission to the NIST SHA-3 competition. Among other contributions, Schroeppel was the first to recognize the sub-exponential running time of certain integer factoring algorithms. While not entirely rigorous, his proof that Morrison and Brillhart's continued fraction factoring algorithm ran in roughly

e^

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 In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than . Heuristically, its complexity for factoring an integer (consisting of bits) is of the form :\exp\left( ...

. Schroeppel analyzed Morrison and Brillhart's algorithm, and saw how to cut the run time to roughly

e^

by modifications that allowed sieving. This improvement doubled the size of numbers that 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 ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since ...

'', Vol. 43, No. 12, December 1996.) Schroeppel's

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

is 2.

References

External links

Brief autobiographical outline

Richard Schroeppel's website
1948 births 20th-century American mathematicians 21st-century American mathematicians American cryptographers Modern cryptographers Putnam Fellows Magic squares Living people International Association for Cryptologic Research fellows {{US-mathematician-stub

See also

References

External links