Is RSA algorithm, invented in 1977, losing its power? Will ECC become the de facto cryptographic solution? or its too early to predict?
Public-key systems–or asymmetric cryptography–use two different keys with a mathematical relationship to each other. Their protection relies on the premise that knowing one key will not help you figure out the other. The RSA algorithm uses the fact that it’s easy to multiply two large prime numbers together and get a product. But you can’t take that product and reasonably guess the two original numbers, or guess one of the original primes if only the other is known. The public key and private keys are carefully generated using the RSA algorithm; they can be used to encrypt information or sign it.
whereas
The advantage of elliptic curve cryptography lies in its immunity to the specialised attacks that have eroded the strength of RSA, with the result that smaller keys can be used to provide a given level of protection. “The size of the parameters (essentially the key size) for elliptic curve cryptography (ECC) needed to ensure security (under our current state of understanding) is much lower for ECC than for RSA or ElGamal (another alternative cryptographic method,” said Kohel. Indeed keys 160 bits long provide ECC with the same level of security as 1024 bit keys for RSA.
