Eric Bach is an Americancomputer scientist who has made contributions tocomputational number theory.

Bach completed his undergraduate studies at theUniversity of Michigan, Ann Arbor, and got hisPh.D. in computer science from theUniversity of California, Berkeley, in 1984 under the supervision ofManuel Blum.^[1] He is currently a professor at the Computer Science Department,University of Wisconsin–Madison.

Among other work, he gave explicit bounds for theChebotarev density theorem, which imply that if one assumes thegeneralized Riemann hypothesis then${\displaystyle {\left(\mathbb{Z}/n\mathbb{Z}\right)}^{\ast }}$ is generated by its elements smaller than 2(log n)².^[2] This result shows that the generalized Riemann hypothesis implies tight bounds for the necessary run-time of the deterministic version of theMiller–Rabin primality test. Bach also did some of the first work on pinning down the actual expected run-time of thePollard rho method where previous work relied on heuristic estimates and empirical data.^[3] He is the namesake ofBach's algorithm for generating random factored numbers.

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