Abstract Algebra Theory and Applications - Computer Science ...

EXERCISES 71Programming Exercises1. Write a computer program that will write any decimal number as the sumof distinct powers of 2. What is the largest integer that your program willhandle?2. Write a computer program to calculate a x (mod n) by the method of repeatedsquares. What are the largest values of n and x that your programwill accept?References and Suggested Readings[1] Koblitz, N. A Course in Number Theory and Cryptography. Springer-Verlag,New York, 1987.[2] Pomerance, C. “Cryptology and Computational Number Theory—An Introduction,”in Cryptology and Computational Number Theory, Pomerance, C.,ed. Proceedings of Symposia in Applied Mathematics, vol. 42, AmericanMathematical Society, Providence, RI, 1990. This book gives an excellentaccount of how the method of repeated squares is used in cryptography.