CERIAS - Center for Education and Research in Information Assurance and Security

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Purdue University
Center for Education and Research in Information Assurance and Security

Cryptanalysis of RSA

Research Areas: End System Security

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.

Personnel

Other PIs: Peter L. Montgomery

Students: Sangil Nahm

Representative Publications

  • 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