In digital signature schemes, what the security advantage of using Elliptic Curve over Integer Factorization and Discrete Logarithm schemes?
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ECC still uses the discrete logarithm problem, it just gets there a different way. – b degnan Sep 30 '16 at 01:11
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A large advantage of EC vs RSA is a substantially shorter key (and data length due to padding). Starting to handle 4096-bit keys (512-bytes) is getting burdensome. Equivalent security of a 3072 RSA key can be achieved with a 256 bit EC key, source NIST.
If a large number of large keys are being stored there can be memory limitations and for a longer key and thus longer data this may be a communications issue.
For the same key size EC provides a higher level of security.
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Also a shorter key is likely to fit in a faster CPU cache, making implementations on embedded systems faster and reducing the ease of side-channel attacks on larger systems. – SAI Peregrinus Sep 30 '16 at 03:49