Lindsay N. Childs is Professor Emeritus at the University of Albany where he earned recognition as a much-loved mentor of students, and as an expert in Galois field theory. Capping his tenure at Albany, he was named a Collins Fellow for his extraordinary devotion to the University at Albany and the people in it over a sustained period of time. Post University of Albany, Professor Childs has taught a sequence of online courses whose content evolved into this book. Lindsay Childs is author of A Concrete Introduction to Higher Algebra, published in Springer's Undergraduate Texts in Mathematics series, as well as a monograph, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (American Mathematical Society), and more than 60 research publications in abstract algebra.

Preface.- 1. Secure, Reliable Information.- 2. Modular Arithmetic.- 3. Linear Equations Modulo m.- 4. Unique Factorization in Z.- 5. Rings and Fields.- 6. Polynomials.- 7. Matrices and Hamming Codes.- 8. Orders and Euler's theorem.- 9. RSA Cryptography and Prime Numbers.- 10. Groups, Cosets, and Lagrange's theorem.- 11. Solving Systems of Congruences.- 12. Homomorphisms and Euler's Phi function.- 13. Cyclic Groups and Cryptography.- 14. Applications of Cosets.- 15. An Introduction to Reed-Solomon codes.- 16. Blum-Goldwasser Cryptography.- 17. Factoring by the Quadratic Sieve.- 18. Polynomials and Finite Fields.- 19. Reed-Solomon Codes II.- Bibliography.