Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Communication complexity
Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Compact Rijndael Hardware Architecture with S-Box Optimization
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On the evaluation of powers and related problems
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
Extremal Combinatorics: With Applications in Computer Science
Extremal Combinatorics: With Applications in Computer Science
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Boolean Function Complexity: Advances and Frontiers
Boolean Function Complexity: Advances and Frontiers
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We study the notion of "cancellation-free" circuits. This is a restriction of linear Boolean circuits (XOR-circuits), but can be considered as being equivalent to previously studied models of computation. The notion was coined by Boyar and Peralta in a study of heuristics for a particular circuit minimization problem. They asked how large a gap there can be between the smallest cancellation-free circuit and the smallest linear circuit. We show that the difference can be a factor Ω(n/log2n). This improves on a recent result by Sergeev and Gashkov who have studied a similar problem. Furthermore, our proof holds for circuits of constant depth. We also study the complexity of computing the Sierpinski matrix using cancellation-free circuits and give a tight Ω(nlogn) lower bound.