I know that this depends on which techniques you're using, but roughly speaking, when modern cryptography makes use of so-called "large prime numbers", how large (in bits or digits) are these primes typically?


For example, recent versions of OpenSSH typically use either

  • ECDSA with a curve size of 256, 384, or 521 bits, which requires a prime of the same size, give or take a couple bits, or
  • RSA with a key size of 1024, 2048, or 4096 bits, which requires two (distinct) primes of half the key size (e.g., a 2048-bit RSA key requires two distinct 1024-bit primes).

The reason for the difference in size is that RSA can be broken significantly faster than by brute force, which means it requires larger keys to achieve the same level of security.

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    $\begingroup$ I would like to point out that RSA-1024 shouldn't be used anymore because it isn't consider secure enough (deprecated since 2010) because it only garanty 80 bits of security. The same thing should happen to RSA-2048 after 2020, when the minimum security recommendation will go from 112 bits to 128 bits. You can also find (even if it is not common) RSA-3072 which is equivalent to 128 bits of security. $\endgroup$ – Faulst Aug 28 '18 at 7:07

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