Problems complete for deterministic logarithmic space
Journal of Algorithms
Founding crytpography on oblivious transfer
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Computing algebraic formulas using a constant number of registers
SIAM Journal on Computing
Subquadratic Simulations of Balanced Formulae by Branching Programs
SIAM Journal on Computing
The complexity of iterated multiplication
Information and Computation
On the (Im)possibility of Obfuscating Programs
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
On the randomness complexity of efficient sampling
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Protecting cryptographic keys against continual leakage
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Securing computation against continuous leakage
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Protecting circuits from leakage: the computationally-bounded and noisy cases
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Leakage-Resilient circuits without computational assumptions
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
How to Compute in the Presence of Leakage
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
Shielding circuits with groups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We show that if NC1 ≠ L, then for every element α of the alternating group At, circuits of depth O(log t) cannot distinguish between a uniform vector over (At)t with product = α and one with product = identity. Combined with a recent construction by the author and Viola in the setting of leakage-resilient cryptography [STOC '13], this gives a compiler that produces circuits withstanding leakage from NC1 (assuming NC1 ≠ L). For context, leakage from NC1 breaks nearly all previous constructions, and security against leakage from P is impossible. We build on work by Cook and McKenzie [J. Algorithms '87] establishing the relationship between L = logarithmic space and the symmetric group St. Our techniques include a novel algorithmic use of commutators to manipulate the cycle structure of permutations in At.