000			02624 a2200265 4500
999			_c2918 _d2918
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008			250604b ||||| |||| 00| 0 eng d
020			_a9780521516440
041			_aeng
082			_a004.0151 SHO/C
100			_aShoup, Victor _913157
245			_aA computational introduction to number theory and algebra
250			_a2nd ed.
260			_bCambridge University Press _cc2009 _aCambridge
300			_axvii, 580p.; 25cm.
500			_aTable of Contents: Preface Preliminaries 1. Basic properties of the integers 2. Congruences 3. Computing with large integers 4. Euclid's algorithm 5. The distribution of primes 6. Abelian groups 7. Rings 8. Finite and discrete probability distributions 9. Probabilistic algorithms 10. Probabilistic primality testing 11. Finding generators and discrete logarithms in Z*p 12. Quadratic reciprocity and computing modular square roots 13. Modules and vector spaces 14. Matrices 15. Subexponential-time discrete logarithms and factoring 16. More rings 17. Polynomial arithmetic and applications 18. Linearly generated sequences and applications 19. Finite fields 20. Algorithms for finite fields 21. Deterministic primality testing Appendix: some useful facts Bibliography Index of notation Index.
520			_aNumber theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
650			_aComputer science _xMathematical principles _913158
650			_aComputer algebra _913159
650			_aComputational geometry _94337
650			_aMathematics _xAlgorithmics _xComplexity _913160
650			_aInformation theory and coding _913161
856			_uhttps://www.cambridge.org/core/books/computational-introduction-to-number-theory-and-algebra/6DBE79226210EB629448E57A1C65E985
942			_cBK