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Chapter 15 Powers and Logarithms
Objectives
Compute powers of group elements.
Compute powers whose exponent is a power of 2 using repeated squaring.
Compute powers of group elements using fast exponentiation.
Compute discrete logarithms of group elements.
In this chapter we extend exponentiation to group elements. We show how to compute powers efficiently using repeated squaring. We also study the reverse operation, the discrete logarithm, which is much harder to compute. In
Chapter 16 we will see why this difference makes much of public key cryptography work.
