Richard Schroeppel

Richard Schroeppel
Richard Schroeppel
Born	1948; Illinois
Nationality	American
Alma mater	MIT
Awards	IACR Fellow (2011) ; Putnam Fellow (1966, 1967)
	Scientific career
Fields	Mathematics
Institutions	University of Arizona

Richard C. Schroeppel (born 1948) is an American

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^{\sqrt {2\ln {n}\ln {\ln {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.

Schroeppel analyzed Morrison and Brillhart's algorithm,^[4] and saw how to cut the run time to roughly $e^{\sqrt {\ln {n}\ln {\ln {n}}}}$ 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

, Vol. 43, No. 12, December 1996.)

Schroeppel's Erdős number is 2.^[5]

References

^ "Lane Student Wins Top U.S. Math Award""Chicago Tribune, June 20, 1964".
^ "The Mathematical Association of America's William Lowell Putnam Competition" (PDF).
^ Sloane, N. J. A. (ed.). "Sequence A006052 (Number of magic squares of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
JSTOR 2005475
.

^ "Erdős Number Project". Oakland University. Retrieved 16 August 2023.

External links

Brief autobiographical outline

Richard Schroeppel's website

Authority control databases: Academics

DBLP

zbMATH

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[1] "Lane Student Wins Top U.S. Math Award""Chicago Tribune, June 20, 1964".

[2] "The Mathematical Association of America's William Lowell Putnam Competition" (PDF).

[3] Sloane, N. J. A. (ed.). "Sequence A006052 (Number of magic squares of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[4] JSTOR 2005475
.

[5] "Erdős Number Project". Oakland University. Retrieved 16 August 2023.

[4]

[5]

See also

References

External links