The Blum Blum Shub algorithm serves as a fundamental cryptographic tool for generating pseudo-random numbers, marking a significant intersection between theoretical mathematics and computational practice. Born in Brooklyn in 1943, Michael Ira Shub has spent his career examining the complexities of real number algorithms and dynamical systems, shaping contemporary understandings of computability and stability within rigorous mathematical frameworks.
Early Academic Development
Shub attended the University of California, Berkeley, where he earned his Ph.D. in 1967. His doctoral thesis, Endomorphisms of Compact Differentiable Manifolds, was completed under the supervision of Stephen Smale. During this research, he identified the concept of expanding maps, providing initial examples of structurally stable strange attractors. Following this period, he held positions at Brandeis University, the University of California, Santa Cruz, and Queens College at the City University of New York.
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In 1974, Shub proposed the Entropy Conjecture, an open problem within the study of dynamical systems. His 1987 volume, Global Stability of Dynamical Systems, serves as a primary reference in both introductory and advanced curricula. This work bridged various theoretical gaps in the field, further refined by later analytical research conducted alongside Stephen Smale in 1993 regarding homotopy-based algorithms for nonlinear algebraic equation systems.
Computational Theory and IBM Tenure
During his tenure at IBM's Thomas J. Watson Research Center from 1985 to 2004, Shub expanded his work into computational theory. He co-authored the Blum Blum Shub random number generator with Lenore and Manuel Blum in 1986. By 1989, he joined Lenore Blum and Stephen Smale to introduce the Blum-Shub-Smale machine, an alternative to the classical Turing model designed for analyzing function computability. He also served as the founding chair of the Society for the Foundations of Computational Mathematics and helped establish its affiliated journal.
Recent Appointments and Professional Recognition
After leaving IBM in 2004, Shub joined the University of Toronto for a six-year period. Since 2010, he has held research roles at the University of Buenos Aires and the Graduate Center of the City University of New York. In 2016, he became the Martin and Michele Cohen Professor and Chair of the Mathematics Department at City College of New York. His professional memberships include the American Mathematical Society, which named him a Fellow in 2015.
Fast facts
- Born: 1943, Brooklyn, United States
- Ph.D.: University of California, Berkeley (1967)
- Key Publication: Global Stability of Dynamical Systems (1987)
- Founding Chair: Society for the Foundations of Computational Mathematics (1995)
- Academic Roles: University of Toronto, Brandeis University, City University of New York
- Notable Recognition: Fellow of the American Mathematical Society (2016)
Questions readers ask
What is the Blum Blum Shub algorithm?
It is a pseudo-random number generator developed in 1986 by Michael Shub alongside Lenore and Manuel Blum, recognized for being both unpredictable and secure.
What is the Blum-Shub-Smale machine?
Proposed in 1989, it is a theoretical model of computation using real numbers, developed as an alternative to the classical Turing machine model.
Achievements
- Notable work: Blum Blum Shub
- Held posts at City University of New York, University of Toronto and Brandeis University
- Fields: mathematics
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