Is There a Shortage of Primes for Cryptography?

Cryptographic algorithms often prescribe the use of primes whose length in bits is a power of 2. Recently, we proved that for m > 1, there is no prime number with 2m significant bits, exactly two of which are 0 bits. Here we generalize this theorem to impose many more restrictions on primes whose length in bits is a power of 2. No similar restrictions apply to primes of other lengths. We consider whether the restrictions on primes with length 2m bits are so great that one should choose other lengths for primes to be used in cryptography.

• Type: Journal
• Year: 2006
• Where: IJNSEC
• Authors: Samuel S. Wagstaff Jr.
• Keywords: Cryptographic Algorithms, IJNSEC 2006, Primes, Significant Bits