Joseph H. Silverman
Encyclopedia
Joseph Hillel Silverman (born March 27, 1955, New York City
)
is currently a professor of mathematics at Brown University
. Joseph Silverman received an Sc.B.
from Brown University in 1977 and a Ph.D.
from Harvard University
in 1982 under the direction of John Tate
. He taught at M.I.T.
(1982-1986) and at Boston University
(1986-1988) before taking a position at Brown in 1988.
Silverman's work has been in number theory
, arithmetic geometry, arithmetic dynamics
and cryptography
. He has published more than 100 research articles, written or coauthored six books, and edited three conference proceedings.
In 1996, Silverman, along with Jeffrey Hoffstein, Jill Pipher
and Daniel Lieman, founded NTRU Cryptosystems, Inc.
to market their cryptographic algorithms, NTRUEncrypt
and NTRUSign
. Silverman remains a co-VP of NTRU Cryptosystems.
, which cited them by saying that “Silverman's volumes have become standard references on one of the most exciting areas of algebraic geometry and number theory.” Silverman has also written three undergraduate texts: Rational Points on Elliptic Curves (1992, co-authored with John Tate
), A Friendly Introduction to Number Theory (3rd ed. 2005), and An Introduction to Mathematical Cryptography (2008, co-authored with Jeffrey Hoffstein and Jill Pipher
). Additional graduate-level texts authored by Silverman are Diophantine Geometry: An Introduction (2000, co-authored with Marc Hindry) and The Arithmetic of Dynamical Systems (2007).
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
)
is currently a professor of mathematics at Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
. Joseph Silverman received an Sc.B.
Bachelor of Science
A Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...
from Brown University in 1977 and a Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1982 under the direction of John Tate
John Tate
John Torrence Tate Jr. is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry.-Biography:...
. He taught at M.I.T.
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
(1982-1986) and at Boston University
Boston University
Boston University is a private research university located in Boston, Massachusetts. With more than 4,000 faculty members and more than 31,000 students, Boston University is one of the largest private universities in the United States and one of Boston's largest employers...
(1986-1988) before taking a position at Brown in 1988.
Silverman's work has been in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, arithmetic geometry, arithmetic dynamics
Arithmetic dynamics
Arithmetic dynamicsis a field that amalgamates two areas of mathematics, dynamical systems and number theory.Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line...
and cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
. He has published more than 100 research articles, written or coauthored six books, and edited three conference proceedings.
In 1996, Silverman, along with Jeffrey Hoffstein, Jill Pipher
Jill Pipher
Jill Pipher is president of the Association of Women in Mathematics , and she is the first director of the Institute for Computational and Experimental Research in Mathematics , an NSF-funded mathematics institute based in Providence, RI.She is currently a professor of mathematics at Brown...
and Daniel Lieman, founded NTRU Cryptosystems, Inc.
NTRU Cryptosystems, Inc.
Ntru Cryptosystems, Inc. is a provider of embedded security solutions. It was founded in 1996 by Joseph H. Silverman, Jeffrey Hoffstein, Jill Pipher and Daniel Lieman, four mathematicians at Brown University...
to market their cryptographic algorithms, NTRUEncrypt
NTRUEncrypt
The NTRUEncrypt public key cryptosystem, also known as the NTRU encryption algorithm, is a lattice-based alternative to RSA and ECC and is based on the shortest vector problem in a lattice...
and NTRUSign
NTRUSign
NTRUSign, also known as the NTRU Signature Algorithm, is a public key cryptography digital signature algorithm based on the GGH signature scheme. It was first presented at the rump session of Asiacrypt 2001 and published in peer-reviewed form at the RSA Conference 2003. The 2003 publication...
. Silverman remains a co-VP of NTRU Cryptosystems.
Books
Silverman has written two graduate texts on elliptic curves, The Arithmetic of Elliptic Curves (1986) and Advanced Topics in the Arithmetic of Elliptic Curves (1994). For these two books he received a Steele Prize for Mathematical Exposition from the American Mathematical SocietyAmerican Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
, which cited them by saying that “Silverman's volumes have become standard references on one of the most exciting areas of algebraic geometry and number theory.” Silverman has also written three undergraduate texts: Rational Points on Elliptic Curves (1992, co-authored with John Tate
John Tate
John Torrence Tate Jr. is an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry.-Biography:...
), A Friendly Introduction to Number Theory (3rd ed. 2005), and An Introduction to Mathematical Cryptography (2008, co-authored with Jeffrey Hoffstein and Jill Pipher
Jill Pipher
Jill Pipher is president of the Association of Women in Mathematics , and she is the first director of the Institute for Computational and Experimental Research in Mathematics , an NSF-funded mathematics institute based in Providence, RI.She is currently a professor of mathematics at Brown...
). Additional graduate-level texts authored by Silverman are Diophantine Geometry: An Introduction (2000, co-authored with Marc Hindry) and The Arithmetic of Dynamical Systems (2007).