Education
Massachusetts Institute of Technology.
Massachusetts Institute of Technology.
His research has included magic squares, elliptic curves, and cryptography. In both 1966 and 1967, Schroeppel scored among the top 5 in the United States. in the William Lowell Putnam mathematics competition. In 1973 he discovered the number of 5x5 normal magic squares, in 1998–1999 he designed the Hasty Pudding Cipher which was a candidate for the Advanced Encryption Standard, and he is one of the designers of the SANDstorm hash, a submission to the The National Institute of Standards and Technology SHA-3 competition.
Among other contributions, Schroeppel was the first to recognize the sub-exponential running time of certain factoring algorithms.
Not only did Schroeppel analyze Morrison and Brillhart"s algorithm, he also saw how to cut the run time to roughly 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 Republic of South Africa 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 American Mathematical Society, Volume(s) 43, Number 12, December 1996).