How to construct random functions
Journal of the ACM (JACM)
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The complexity of Boolean functions
The complexity of Boolean functions
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
Simulating threshold circuits by majority circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Cryptographic limitations on learning Boolean formulae and finite automata
Journal of the ACM (JACM)
Cryptographic primitives based on hard learning problems
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On lower bounds for read-k-times branching programs
Computational Complexity
On the computational power of depth-2 circuits with threshold and modulo gates
Theoretical Computer Science
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Computing Boolean functions by polynomials and threshold circuits
Computational Complexity
Approximations by OBDDs and the Variable Ordering Problem
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Proceedings of the Third International Workshop on Fast Software Encryption
On the Security of Remotely Keyed Encryption
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
Synthesizers and their application to the parallel construction of pseudo-random functions
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Threshold circuits of bounded depth
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Cryptography in constant parallel time
Cryptography in constant parallel time
Hash-based RFID security protocol using randomly key-changed identification procedure
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part IV
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A set F of Boolean functions is called a pseudorandom function generator (PRFG) if communicating with a randomly chosen secret function from F cannot be efficiently distinguished from communicating with a truly random function. We ask for the minimal hardware complexity of a PRFG. This question is motivated by design aspects of secure secret key cryptosystems. These should be efficient in hardware, but often are required to behave like PRFGs. By constructing efficient distinguishing schemes we show for a wide range of basic nonuniform complexity classes (including TC20, that they do not contain PRFGs. On the other hand we show that the PRFG proposed by Naor and Reingold in [24] consists of TC40-functions. The question if TC30-functions can form PRFGs remains as an interesting open problem. We further discuss relations of our results to previous work on cryptographic limitations of learning and Natural Proofs.