椭圆曲线密码学引论

Overview The book has a strong focus on efficient methods for finite field arithmetic<br>(Chapter 2) and elliptic curve arithmetic (Chapter 3). Next, Chapter 4 surveys the<br>known attacks on the ECDLP, and describes the generation and validation of domain<br>parameters and key pairs, and selected elliptic curve protocols for digital signature,<br>public-key encryption and key establishment. We chose not to include the mathemat-<br>ical details of the attacks on the ECDLP, or descriptions of algorithms for counting<br>the points on an elliptic curve, because the relevant mathematics is quite sophisticated.<br>(Presenting these topics in a readable and concise form is a formidable challenge post-<br>poned for another day.) The choice of material in Chapters 2, 3 and 4 was heavily<br>influenced by the contents of ECC standards that have been developed by accred-<br>ited standards bodies, in particular the FIPS 186-2 standard for the Elliptic Curve<br>Digital Signature Algorithm (ECDSA) developed by the U.S. government’s National<br>Institute for Standards and Technology (NIST). Chapter 5 details selected aspects of<br>efficient implementations in software and hardware, and also gives an introduction to<br>side-channel attacks and their countermeasures. Although the coverage in Chapter 5<br>is admittedly narrow, we hope that the treatment provides a glimpse of engineering<br>considerations faced by software developers and hardware designers.<br>