Cryptanalysis of RSA
Principal Investigator: Samuel Wagstaff
We study the minimum period of the Bell numbers, which arise in combinatorics, modulo a prime. It is shown that this period is probably always equal to its maximum possible value. Interesting new divisibility theorems are proved for possible prime divisors of the maximum possible period. The conclusion is that these numbers are not suitable for use as RSA public keys.
Other PIs: Peter L. Montgomery
Students: Sangil Nahm
Peter L Montgomery, Sangil Nahm and Samuel S Wagstaff Jr., “The period of the Bell numbers modulo a prime,” Math. Comp. v. 79 (2010), pp. 1793--1800.
Keywords: Bell numbers, divisibility theorems, RSA public keys