# Russell Impagliazzo

**Russell Impagliazzo** is a professor of computer science at the University of California, San Diego. He received his doctorate from the University of California, Berkeley. His advisor was Manuel Blum. He spent two (2) years as a postdoc at the University of Toronto. He is a 2004 Guggenheim fellow.

Russell Impagliazzo | |
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Russell Impagliazzo at the DIMACS Workshop on Cryptography, July 2016. |

Impagliazzo's contributions to the field of computational complexity include: The construction of a pseudorandom number generator from any one-way function, his proof of Yao's XOR lemma via "hard core sets," his work on break through results in propositional proof complexity, such as the exponential size lower bound for constant-depth Hilbert proofs of the pigeonhole principle and the introduction of the polynomial calculus system, his work on connections between computational hardness and de-randomization, and recent break-through work on the construction of multi-source seedless extractors.

Impagliazzo has contributed to more than 40 papers on topics within his specialties. He also stated the well-known and much-used exponential time hypothesis, stating that 3-SAT cannot be solved in subexponential time in the number of variables. This hypothesis is used to show many lower bounds on algorithms in computer science.

His "five worlds" are well known in computational complexity theory.