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 & 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 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.
ElGamal encryption using arithmetic modulo a prime $p$ is fine till year 2030 regarding parameter size according to the recommendations of many (if not all) major security authorities, if:
This is believed to be on the safe side by a large margin, if we discount the possibility that quantum computers become usable for cryptanalysis.
Similarly, for ElGamal encryption using Elliptic Curve groups over field $\mathbb Z_p$ with $p$ prime, both $p$ and the order of the generator $g$ should be at least 256 bits; and the Elliptic Curve should obey a number of complex criteria, still being debated.
The classical reference site surveying recommendations on key size is keylength.
The Right answer is the one that crpyto developers use as a standard which is the RFC and usually related to FIPS within the US, National Instittue for standards and technology (NIST). http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf see page 27 for example, is probably the biggest defacto standard for how to do ECDSA outside the of the RFC's themselves.
And one of the RFCs for ECDSA Mathmatics: https://www.rfc-editor.org/rfc/rfc6090
EC is different because different standard specify different curves, and I think the can very depending on what your using it for.
