Undergraduate Texts in Mathematics
Editors
S. Axler
K.A. Ribet
Undergraduate Texts in Mathematics
Abbott: Understanding Analysis.
Anglin: Mathematics: A Concise History and
Philosophy.
Readings in Mathematics.
Anglin/Lambek: The Heritage of Thales.
Readings in Mathematics.
Apostol: Introduction to Analytic Number Theory.
Second edition.
Armstrong: Basic Topology.
Armstrong: Groups and Symmetry.
Axler: Linear Algebra Done Right. Second edition.
Beardon: Limits: A New Approach to Real Analysis.
Bak/Newman: Complex Analysis. Second edition.
Banchoff/Wermer: Linear Algebra Through
Geometry. Second edition.
Beck/Robins: Computing the Continuous Discretely
Berberian: A First Course in Real Analysis.
Bix: Conics and Cubics: A Concrete Introduction to
Algebraic Curves. Second edition.
Br
`
emaud: An Introduction to Probabilistic Modeling.
Bressoud: Factorization and Primality Testing.
Bressoud: Second Year Calculus.
Readings in Mathematics.
Brickman: Mathematical Introduction to Linear
Programming and Game Theory.
Browder: Mathematical Analysis: An Introduction.
Buchmann: Introduction to Cryptography. Second
Edition.
Buskes/van Rooij: Topological Spaces: From
Distance to Neighborhood.
Callahan: The Geometry of Spacetime: An
Introduction to Special and General Relavitity.
Carter/van Brunt: The Lebesgue– Stieltjes Integral:
A Practical Introduction.
Cederberg: A Course in Modern Geometries. Second
edition.
Chambert-Loir: A Field Guide to Algebra
Childs: A Concrete Introduction to Higher Algebra.
Second edition.
Chung/AitSahlia: Elementary Probability Theory:
With Stochastic Processes and an Introduction to
Mathematical Finance. Fourth edition.
Cox/Little/O’Shea: Ideals, Varieties, and Algorithms.
Second edition.
Croom: Basic Concepts of Algebraic Topology.
Cull/Flahive/Robson: Difference Equations. From
Rabbits to Chaos
Curtis: Linear Algebra: An Introductory Approach.
Fourth edition.
Daepp/Gorkin: Reading, Writing, and Proving:
A Closer Look at Mathematics.
Devlin: The Joy of Sets: Fundamentals
of-Contemporary Set Theory. Second edition.
Dixmier: General Topology.
Driver: Why Math?
Ebbinghaus/Flum/Thomas: Mathematical Logic.
Second edition.
Edgar: Measure, Topology, and Fractal Geometry.
Second edition.
Elaydi: An Introduction to Difference Equations.
Third edition.
Erdo´´s/Sur
´
anyi: Topics in the Theory of Numbers.
Estep: Practical Analysis on One Variable.
Exner: An Accompaniment to Higher Mathematics.
Exner: Inside Calculus.
Fine/Rosenberger: The Fundamental Theory
of Algebra.
Fischer: Intermediate Real Analysis.
Flanigan/Kazdan: Calculus Two: Linear and
Nonlinear Functions. Second edition.
Fleming: Functions of Several Variables. Second
edition.
Foulds: Combinatorial Optimization for
Undergraduates.
Foulds: Optimization Techniques: An Introduction.
Franklin: Methods of Mathematical
Economics.
Frazier: An Introduction to Wavelets Through Linear
Algebra.
Gamelin: Complex Analysis.
Ghorpade/Limaye: A Course in Calculus and Real
Analysis
Gordon: Discrete Probability.
Hairer/Wanner: Analysis by Its History.
Readings in Mathematics.
Halmos: Finite-Dimensional Vector Spaces. Second
edition.
Halmos: Naive Set Theory.
H
¨
ammerlin/Hoffmann: Numerical Mathematics.
Readings in Mathematics.
Harris/Hirst/Mossinghoff: Combinatorics and
Graph Theory.
Hartshorne: Geometry: Euclid and Beyond.
Hijab: Introduction to Calculus and Classical
Analysis. Second edition.
Hilton/Holton/Pedersen: Mathematical Reflections:
In a Room with Many Mirrors.
Hilton/Holton/Pedersen: Mathematical Vistas: From
a Room with Many Windows.
Hoffstein/Pipher/Silverman: An Introduction to
Mathematical Cryptography.
Iooss/Joseph: Elementary Stability and Bifurcation
Theory. Second Edition.
(continued after index)
Jeffrey Hoffstein
Jill Pipher
Joseph H. Silverman
An Introduction to
Mathematical Cryptography
123
Jeffrey Hoffstein Jill Pipher
Department of Mathematics Department of Mathematics
Brown University Brown University
151 Thayer St. 151 Thayer St.
Providence, RI 02912 Providence, RI 02912
USA USA
jhoff@math.brown.edu jpipher@math.brown.edu
Joseph H. Silverman
Department of Mathematics
Brown University
151 Thayer St.
Providence, RI 02912
USA
jhs@math.brown.edu
Editorial Board
S. Axler K.A. Ribet
Mathematics Department Department of Mathematics
San Francisco State University University of California
San Francisco, CA 94132 at Berkeley
USA Berkeley, CA 94720
axler@sfsu.edu USA
ribet@math.berkeley.edu
ISBN: 978-0-387-77993-5 e-ISBN: 978-0-387-77994-2
DOI: 10.1007/978-0-387-77994-2
Library of Congress Control Number: 2008923038
Mathematics Subject Classification (2000): 94A60, 11T71, 14G50, 68P25
c
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