Cryptology and Error Correction

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.

“This is a really nice way of introducing students to abstract algebra. It is evident that the author has spent much time polishing the presentation including large amount of details (and numerous examples) which make the book ideal for self-study. Even though the book starts out very elementary (basically requiring no prior knowledge beyond integer arithmetic), it gets to some sophisticated results towards the end. So in summary, I can warmly recommend this book as a first introduction to algebra.” (G. Teschl, Monatshefte für Mathematik, Vol. 196 (3), November, 2021)