5.0 Elliptic Curve groups and the Discrete Logarithm Problem At the foundation of every cryptosystem is a hard mathematical problem that is computationally infeasible to solve. The discrete logarithm problem is the basis for the security of many cryptosystems including the Elliptic Curve Cryptosystem. More specifically, the ECC relies upon the difficulty of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Recall that elliptic curve groups have two major operations: addition and multiplication. These two operations may be combined to express scalar multiplication. The ECDLP is based upon the intractability of scalar multiplication products.
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