Public-key Cryptography: Theory and Practice

*3.6. Arithmetic on Elliptic Curves

The recent popularity of cryptographic systems based on elliptic curve groups over stems from two considerations. First, discrete logarithms in can be computed in subexponential time. This demands q to be sufficiently large, typically of length 768 bits or more. On the other hand, if the elliptic curve E over is carefully chosen, the only known algorithms for solving the discrete logarithm problem in are fully ...