Public-key Cryptography: Theory and Practice

3. Algebraic and Number-theoretic Computations

3.1	Introduction
3.2	Complexity Issues
3.3	Multiple-precision Integer Arithmetic
3.4	Elementary Number-theoretic Computations
3.5	Arithmetic in Finite Fields
3.6	Arithmetic on Elliptic Curves
3.7	Arithmetic on Hyperelliptic Curves
3.8	Random Numbers
	Chapter Summary
	Sugestions for Further Reading

From the start there has been a curious affinity between mathematics, mind and computing . . . It is perhaps no accident that Pascal and Leibniz in the seventeenth century, Babbage and George Boole in the nineteenth, and Alan Turing and John von Neumann in the twentieth – seminal figures in the history of computing – were all, among their other accomplishments, mathematicians, possessing a natural affinity for symbol, ...