A COMPUTATIONAL INTRODUCTION TO NUMBER THEORY AND ALGEBRA

A COMPUTATIONAL INTRODUCTION TO NUMBER THEORY AND ALGEBRA (2004)

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by Victor Shoup

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@MISC{Shoup04acomputational,
    author = {Victor Shoup},
    title = {A COMPUTATIONAL INTRODUCTION TO NUMBER THEORY AND ALGEBRA},
    year = {2004}
}

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2507	A method for obtaining digital signatures and public-key cryptosystems - Rivest, Shamir, et al.
1404	How to share a secret - Shamir - 1979
756	Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer - Shor - 1997
284	New Hash Functions and their Use in Authentication and Set Equality - Wegman, Carter - 1981
255	Polynomial Codes Over Certain Finite Fields - Reed, Solomon - 1960
240	Approximate formulas for some functions of prime numbers - Rosser, Schoenfeld - 1962
184	Lower bounds for discrete logarithms and related problems - Shoup - 1997
154	Elliptic curves over finite fields and the computation of square roots mod p - Schoof - 1985
122	A fast Monte-Carlo test for primality - Solovay, Strassen - 1977
113	Cryptanalysis of short RSA secret exponents - Wiener - 1990
61	A new polynomial factorization algorithm and its implementation - Shoup - 1995
60	Schnelle berechnung von kettenbruchentwicklungen - Schönhage - 1971
55	New algorithms for finding irreducible polynomials over finite fields - Shoup - 1990
43	Class number, a theory of factorization, and genera - Shanks - 1970
40	Fast construction of irreducible polynomials over finite fields - Shoup
30	Searching for primitive roots in finite fields - Shoup - 1992
22	Computational Problems Associated with Racah Algebra - Stein - 1967
21	Discrete logarithm: the effectiveness of the index calculus method, Algorithmic number theory - Schirokauer, Weber, et al. - 1996
19	P-adic reconstruction of rational numbers - Wang, Guy, et al. - 1982
14	Continued fractions and Berlekamp’s algorithm - Welch - 1979
11	Factoring numbers in O(log n) arithmetic steps - Shamir - 1979
10	Universal hashing and authentication codes. Designs, Codes and Cryptography - Stinson - 1994
7	On the least primitive root of a prime - Wang - 1959
7	Solving sparse linear systems over finite fields - Wiedemann - 1986
6	1 + i)-ary GCD computation in Z[i] as an analogue to the binary GCD algorithm - Weilert
4	Construction of irreducible polynomials over finite fields with linearly independent roots - Semaev - 1988
2	Asymptotically fast GCD computation in Z[i - Weilert - 2000