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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 generalize the concept of exponentiation to group elements. We show how powers can be computed efficiently using repeated squaring. We also consider a reverse operation, namely the discrete logarithm which is much harder to compute. In
Chapter 16 we will see that this makes a lot of public key cryptography work.
