In ElGamal system, each user has a private key x. and has three components of public key − prime modulus p, generator g, and public Y = gx mod p. The strength of the ElGamal is based on the difficulty of discrete logarithm problem.
The secure key size is generally > 1024 bits. Today even 2048 bits long key are used. On the processing speed front, Elgamal is quite slow, it is used mainly for key authentication protocols. Due to higher processing efficiency, Elliptic Curve variants of ElGamal are becoming increasingly popular.
Elliptic Curve Cryptography (ECC)
Elliptic Curve Cryptography (ECC) is a term used to describe a suite of cryptographic tools and protocols whose security is based on special versions of the discrete logarithm problem. It does not use numbers modulo p.
ECC is based on sets of numbers that are associated with mathematical objects called elliptic curves. There are rules for adding and computing multiples of these numbers, just as there are for numbers modulo p.
ECC includes a variants of many cryptographic schemes that were initially designed for modular numbers such as ElGamal encryption and Digital Signature Algorithm.
It is believed that the discrete logarithm problem is much harder when applied to points on an elliptic curve. This prompts switching from numbers modulo p to points on an elliptic curve. Also an equivalent security level can be obtained with shorter keys if we use elliptic curve-based variants.
The shorter keys result in two benefits −
- Ease of key management
- Efficient computation
These benefits make elliptic-curve-based variants of encryption scheme highly attractive for application where computing resources are constrained.
RSA and ElGamal Schemes – A Comparison
Let us briefly compare the RSA and ElGamal schemes on the various aspects.
| RSA | ElGamal |
|---|---|
| It is more efficient for encryption. | It is more efficient for decryption. |
| It is less efficient for decryption. | It is more efficient for decryption. |
| For a particular security level, lengthy keys are required in RSA. | For the same level of security, very short keys are required. |
| It is widely accepted and used. | It is new and not very popular in market. |
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