Algebraic Aspects of CryptographyThis book is intended as a text for a course on cryptography with emphasis on algebraic methods. It is written so as to be accessible to graduate or advanced undergraduate students, as well as to scientists in other fields. The first three chapters form a self-contained introduction to basic concepts and techniques. Here my approach is intuitive and informal. For example, the treatment of computational complexity in Chapter 2, while lacking formalistic rigor, emphasizes the aspects of the subject that are most important in cryptography. Chapters 4-6 and the Appendix contain material that for the most part has not previously appeared in textbook form. A novel feature is the inclusion of three types of cryptography - "hidden monomial" systems, combinatorial-algebraic sys tems, and hyperelliptic systems - that are at an early stage of development. It is too soon to know which, if any, of these cryptosystems will ultimately be of practical use. But in the rapidly growing field of cryptography it is worthwhile to continually explore new one-way constructions coming from different areas of mathematics. Perhaps some of the readers will contribute to the research that still needs to be done. This book is designed not as a comprehensive reference work, but rather as a selective textbook. The many exercises (with answers at the back of the book) make it suitable for use in a math or computer science course or in a program of independent study. |
Contents
I | 1 |
III | 2 |
IV | 5 |
V | 8 |
VI | 10 |
VII | 12 |
VIII | 13 |
IX | 17 |
XXXVII | 96 |
XXXVIII | 102 |
XXXIX | 103 |
XL | 104 |
XLI | 105 |
XLIII | 109 |
XLIV | 111 |
XLV | 112 |
X | 18 |
XI | 21 |
XII | 22 |
XIII | 23 |
XIV | 24 |
XV | 31 |
XVI | 34 |
XVII | 41 |
XVIII | 44 |
XIX | 45 |
XX | 48 |
XXII | 52 |
XXIII | 53 |
XXIV | 55 |
XXVI | 61 |
XXVII | 63 |
XXVIII | 64 |
XXIX | 65 |
XXX | 70 |
XXXII | 78 |
XXXIII | 80 |
XXXIV | 86 |
XXXV | 87 |
XXXVI | 95 |
Other editions - View all
Algebraic Aspects of Cryptography A. J. Menezes,Y. -H. Wu,R. J. Zuccherato No preview available - 1998 |
Common terms and phrases
3-Coloring a₁ algebraic Alice answer b₁ big-O notation binary C₁ Catherine Chapter choose ciphertext coefficients compute cryptanalysis cryptography curve Y2 D₁ decision problem defined Definition degu denote digits discrete log div(a divides elliptic curve encryption equation Euclidean algorithm Example Exercise field Fq finite field follows g₁ Gaussian integers graph Gröbner basis hence hyperelliptic curve input length instance Integer Factorization irreducible polynomial jacobian leading term Lemma linear m₁ matrix message units modulo monomial multiplication NP-complete number of bit obtain one-way function ordp(G P₁ Perfect Code plaintext point at infinity polynomial function prime number proof prove public key cryptography quadratic random rational function reduced divisor reduced Gröbner basis ring root satisfies search problem semi-reduced divisor signature solution solve splitting field Suppose Theorem Traveling Salesrep variables vector zero