Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
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
Constant depth circuits, Fourier transform, and learnability
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
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
Journal of Computer and System Sciences
The Design of Rijndael
Expanding Pseudorandom Functions; or: From Known-Plaintext Security to Chosen-Plaintext Security
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Collective coin flipping, robust voting schemes and minima of Banzhaf values
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
How To Construct Randolli Functions
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
A Fast and Key-Efficient Reduction of Chosen-Ciphertext to Known-Plaintext Security
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
A Leakage-Resilient Mode of Operation
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Gowers Uniformity, Influence of Variables, and PCPs
SIAM Journal on Computing
On Agnostic Learning of Parities, Monomials, and Halfspaces
SIAM Journal on Computing
The Learning with Errors Problem (Invited Survey)
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Poly-logarithmic independence fools bounded-depth boolean circuits
Communications of the ACM
Message authentication, revisited
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Pseudorandom functions and lattices
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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Pseudorandom functions (PRFs) play a fundamental role in symmetric-key cryptography. However, they are inherently complex and cannot be implemented in the class AC0 (MOD2). Weak pseudorandom functions (weak PRFs) do not suffer from this complexity limitation, yet they suffice for many cryptographic applications. We study the minimal complexity requirements for constructing weak PRFs. To this end We conjecture that the function family FA(x) = g(Ax), where A is a random square GF(2) matrix and g is a carefully chosen function of constant depth, is a weak PRF. In support of our conjecture, we show that functions in this family are inapproximable by GF(2) polynomials of low degree and do not correlate with any fixed Boolean function family of subexponential size. We study the class AC0 ○ MOD2 that captures the complexity of our construction. We conjecture that all functions in this class have a Fourier coefficient of magnitude exp(- poly log n) and prove this conjecture in the case when the MOD2 function is typical. We investigate the relation between the hardness of learning noisy parities and the existence of weak PRFs in AC0 ○ MOD2. We argue that such a complexity-driven approach can play a role in bridging the gap between the theory and practice of cryptography.