Modern Cryptography and Elliptic CurvesThis book offers the beginning undergraduate student some of the vista of modern mathematics by developing and presenting the tools needed to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual introduction also makes a significant effort to teach students how to produce or discover a proof by presenting mathematics as an exploration, and at the same time, it provides the necessary mathematical underpinnings to investigate the practical and implementation side of elliptic curve cryptography (ECC). |
Contents
1 | |
Chapter 2 Back to the Beginning | 9 |
Chapter 3 Some Elementary Number Theory | 45 |
Z_n and U_n | 73 |
Chapter 5 PublicKey Cryptography and RSA | 101 |
Chapter 6 A Little More Algebra | 127 |
Chapter 7 Curves in Affine and Projective Space | 147 |
Chapter 8 Applications of Elliptic Curves | 189 |
Appendix A Deeper Results and Concluding Thoughts | 203 |
Appendix B Answers to Selected Exercises | 219 |
245 | |
249 | |
Back Cover | 253 |