Decrypted.txt

In public key cryptography each user or the device taking part in the communication generally have a pair of keys, a public key and a private key, and a set of operations associated with the keys to do the cryptographic operations. Only the particular user knows the private key whereas the public key is distributed to all users taking part in the communication.

The public key is a point on the curve and the private key is a random number. The public key is obtained by multiplying the private key with a generator point G in the curve.

The mathematical operations of ECC is defined over the elliptic curve y^2 = x^3 + ax + b, where 4a^3 + 27b^2 ≠ 0. Each value of the ‘a’ and ‘b’ gives a different elliptic curve.

One main advantage of ECC is its small key size. A 160-bit key in ECC is considered to be as secured as 1024-bit key in RSA.