Universal one-way hash functions and their cryptographic applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
On the design of provably-secure cryptographic hash functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the existence of pseudorandom generators
SIAM Journal on Computing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function
SIAM Journal on Computing
Efficiency improvements in constructing pseudorandom generators from one-way functions
Proceedings of the forty-second ACM symposium on Theory of computing
Universal one-way hash functions via inaccessible entropy
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
A cookbook for black-box separations and a recipe for UOWHFs
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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A universal one-way hash function (UOWHF) is a shrinking function for which finding a second preimage is infeasible. A UOWHF, a fundamental cryptographic primitive from which digital signature can be obtained, can be constructed from any one-way function (OWF). The best known construction from any OWF f:{0,1}n→{0,1}n, due to Haitner et. al. [2], has output length Õ(n7) and Õ(n5) for the uniform and non-uniform models, respectively. On the other hand, if the OWF is known to be injective, i.e., maximally regular, the Naor-Yung construction is simple and practical with output length linear in that of the OWF, and making only one query to the underlying OWF. In this paper, we establish a trade-off between the efficiency of the construction and the assumption about the regularity of the OWF f. Our first result is a construction comparably efficient to the Naor-Yung construction but applicable to any close-to-regular function. A second result shows that if |f−1f(x)| is concentrated on an interval of size 2s(n), the construction obtained has output length Õ(n·s(n)6) and Õ(n ·s(n)4) for the uniform and non-uniform models, respectively.