TY - GEN
T1 - Distributional collision resistance beyond one-way functions
AU - Bitansky, Nir
AU - Haitner, Iftach
AU - Komargodski, Ilan
AU - Yogev, Eylon
N1 - Publisher Copyright:
© International Association for Cryptologic Research 2019.
PY - 2019
Y1 - 2019
N2 - Distributional collision resistance is a relaxation of collision resistance that only requires that it is hard to sample a collision (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. The notion lies between one-wayness and collision resistance, but its exact power is still not well-understood. On one hand, distributional collision resistant hash functions cannot be built from one-way functions in a black-box way, which may suggest that they are stronger. On the other hand, so far, they have not yielded any applications beyond one-way functions. Assuming distributional collision resistant hash functions, we construct constant-round statistically hiding commitment scheme. Such commitments are not known based on one-way functions, and are impossible to obtain from one-way functions in a black-box way. Our construction relies on the reduction from inaccessible entropy generators to statistically hiding commitments by Haitner et al. (STOC ’09). In the converse direction, we show that two-message statistically hiding commitments imply distributional collision resistance, thereby establishing a loose equivalence between the two notions. A corollary of the first result is that constant-round statistically hiding commitments are implied by average-case hardness in the class SZK (which is known to imply distributional collision resistance). This implication seems to be folklore, but to the best of our knowledge has not been proven explicitly. We provide yet another proof of this implication, which is arguably more direct than the one going through distributional collision resistance.
AB - Distributional collision resistance is a relaxation of collision resistance that only requires that it is hard to sample a collision (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. The notion lies between one-wayness and collision resistance, but its exact power is still not well-understood. On one hand, distributional collision resistant hash functions cannot be built from one-way functions in a black-box way, which may suggest that they are stronger. On the other hand, so far, they have not yielded any applications beyond one-way functions. Assuming distributional collision resistant hash functions, we construct constant-round statistically hiding commitment scheme. Such commitments are not known based on one-way functions, and are impossible to obtain from one-way functions in a black-box way. Our construction relies on the reduction from inaccessible entropy generators to statistically hiding commitments by Haitner et al. (STOC ’09). In the converse direction, we show that two-message statistically hiding commitments imply distributional collision resistance, thereby establishing a loose equivalence between the two notions. A corollary of the first result is that constant-round statistically hiding commitments are implied by average-case hardness in the class SZK (which is known to imply distributional collision resistance). This implication seems to be folklore, but to the best of our knowledge has not been proven explicitly. We provide yet another proof of this implication, which is arguably more direct than the one going through distributional collision resistance.
UR - http://www.scopus.com/inward/record.url?scp=85065909222&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-17659-4_23
DO - 10.1007/978-3-030-17659-4_23
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AN - SCOPUS:85065909222
SN - 9783030176587
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 667
EP - 695
BT - Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
A2 - Ishai, Yuval
A2 - Rijmen, Vincent
PB - Springer Verlag
T2 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019
Y2 - 19 May 2019 through 23 May 2019
ER -