Solinas Primes

They are also called Generalized Mersenne Primes, which are prime numbers of the form:

• $2^k-1$ (Mersenne Primes)
• $2^k-c$

Examples

• NIST “Recommended Elliptic Curves for Federal Government Use”
  • p-192: $2^{192}-2^{64}-1$
  • p-224: $2^{224}-2^{96}+1$
  • p-256: $2^{256}-2^{224}+2^{192}+2^{96}-1$
  • p-384: $2^{384}-2^{128}-2^{96}+2^{32}-1$
• Curve448
  • $2^{448}-2^{224}+1$