Strong Prime - Definition in Cryptography

Definition in Cryptography

In cryptography, a prime number is strong if the following conditions are satisfied.

1. is sufficiently large to be useful in cryptography; typically this requires to be too large for plausible computational resources to enable a cryptanalyst to factorise products of multiplied by other strong primes.
2. has large prime factors. That is, for some integer and large prime .
3. has large prime factors. That is, for some integer and large prime .
4. has large prime factors. That is, for some integer and large prime .

Sometimes a prime that satisfies a subset of the above conditions is also called strong. In some cases, some additional conditions may be included. For example, or, etc.