Take the 2-minute tour ×  There are elliptic curve variants of
Diffie-Hellman, ElGamal, DSA and possibly other
protocols/algorithms. I know that these elliptic curve variants
have smaller key and ciphertext sizes which will make
communications (or storage) more efficient.  Are there other
advantages to the elliptic curve variants of these standard
protocols/algorithms?  Specifically I am interested in speed and
power consumption, but other potential advantages like
resistance to side-channel attacks are also of interest.
share|improve this question add comment  2 Answers  up vote 4
down vote accepted  Computations on elliptic curves are more
efficient. Roughly speaking, when the base field has size $n$
(for DH/ElGamal/DSA, the size in bits of the modulus $p$; for
elliptic curves, the size of the field for point coordinates)
and a "security level" $t$ (e.g. $t = 80$ for "80-bit security"
as can be expected when using a 160-bit subgroup and a 160-bit
hash function), the computational cost of a private key oper