Eric Bach
Encyclopedia
Eric Bach is an American
computer scientist
who has made contributions to computational number theory
. Bach did his undergraduate studies at the University of Michigan, Ann Arbor, and got his Ph.D.
in computer science from the University of California, Berkeley
, in 1984 under the supervision of Manuel Blum
. He is currently a professor at the Computer Science Department, University of Wisconsin–Madison
. Among other work, he gave explicit bounds for the Chebotarev density theorem which imply that if one assumes the generalized Riemann hypothesis
then
is generated by its elements smaller than 2(log n)2. This result shows that the generalized Riemann hypothesis implies tight bounds for the necessary run-time of the deterministic version of the Miller–Rabin primality test. Bach also did some of the first work on pinning down the actual expected run-time of the Pollard rho method
where previous work relied on heuristic estimates and empirical data.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
who has made contributions to computational number theory
Computational number theory
In mathematics, computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations...
. Bach did his undergraduate studies at the University of Michigan, Ann Arbor, and got his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in computer science from the University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, in 1984 under the supervision of Manuel Blum
Manuel Blum
Manuel Blum is a computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking".-Biography:Blum attended MIT, where he received his bachelor's degree and...
. He is currently a professor at the Computer Science Department, University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
. Among other work, he gave explicit bounds for the Chebotarev density theorem which imply that if one assumes the generalized Riemann hypothesis
Generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function...
then
is generated by its elements smaller than 2(log n)2. This result shows that the generalized Riemann hypothesis implies tight bounds for the necessary run-time of the deterministic version of the Miller–Rabin primality test. Bach also did some of the first work on pinning down the actual expected run-time of the Pollard rho methodPollard's rho algorithm
Pollard's rho algorithm is a special-purpose integer factorization algorithm. It was invented by John Pollard in 1975. It is particularly effective at splitting composite numbers with small factors.-Core ideas:...
where previous work relied on heuristic estimates and empirical data.