Key lengths of asymmetric encryption: ElGamal and ECC Recently I have been researching asymmetric encryption algorithms for a class, I cannot find any information anywhere on the key lengths used in any of the algorithms I'm looking into (ElGamal &amp; Elliptic Curve Cryptography).

Is there a range of valid key sizes?
Key size and encryption system

Encryption systems are often grouped into families. Common families
 include symmetric systems (e.g. AES) and asymmetric systems (e.g.
 RSA); they may alternatively be grouped according to the central
 algorithm used (e.g. elliptic curve cryptography).

As each of these is of a different level of cryptographic complexity,
 it is usual to have different key sizes for the same level of
 security, depending upon the algorithm used. For example, the security
 available with a 1024-bit key using asymmetric RSA is considered
 approximately equal in security to an 80-bit key in a symmetric
 algorithm.

The actual degree of security achieved over time varies, as more
 computational power and more powerful mathematical analytic methods
 become available. For this reason cryptologists tend to look at
 indicators that an algorithm or key length shows signs of potential
 vulnerability, to move to longer key sizes or more difficult
 algorithms. For example, as of May 2007, a 1039 bit integer was
 factored with the special number field sieve using 400 computers over
 11 months. The factored number was of a special form; the special
 number field sieve cannot be used on RSA keys. The computation is
 roughly equivalent to breaking a 700 bit RSA key. However, this might
 be an advance warning that 1024 bit RSA used in secure online commerce
 should be deprecated, since they may become breakable in the near
 future. Cryptography professor Arjen Lenstra observed that "Last time,
 it took nine years for us to generalize from a special to a
 nonspecial, hard-to-factor number" and when asked whether 1024-bit RSA
 keys are dead, said: "The answer to that question is an unqualified
 yes."

The 2015 Logjam attack revealed additional dangers in using
 Diffie-Helman key exchange when only one or a few common 1024-bit or
 smaller prime moduli are in use. This common practice allows large
 amounts of communications to be compromised at the expense of
 attacking a small number of primes.

Acording to this Wiki Page 

Also here are some more links to visit if you want to learn more about asymmetric cryptography:

asymmetric cryptography (public key cryptography) 

Elliptic-curve cryptography

Elliptic-curve Cryptography Key Sizes

This 3rd link for Key Sizes is where it gets into some pretty complex methods, but if you really want to know Key length / sizes, then you will want to review that section.