TY - GEN
T1 - Non-adaptive Universal One-Way Hash Functions from Arbitrary One-Way Functions
AU - Mao, Xinyu
AU - Mazor, Noam
AU - Zhang, Jiapeng
N1 - Publisher Copyright:
© 2023, International Association for Cryptologic Research.
PY - 2023
Y1 - 2023
N2 - In this work we give the first non-adaptive construction of universal one-way hash functions (UOWHFs) from arbitrary one-way functions. Our construction uses O(n9) calls to the one-way function, has a key of length O(n10), and can be implemented in NC1 assuming the underlying one-way function is in NC1. Prior to this work, the best UOWHF construction used O(n13) adaptive calls and a key of size O(n5) (Haitner, Holenstein, Reingold, Vadhan and Wee [Eurocrypt ’10]). By the result of Applebaum, Ishai and Kushilevitz [FOCS ’04], the above implies the existence of UOWHFs in NC0, given the existence of one-way functions in NC1. We also show that the PRG construction of Haitner, Reingold and Vadhan (HRV, [STOC ’10]), with small modifications, yields a relaxed notion of UOWHFs, which is a function family which can be (inefficiently) converted to UOWHF by changing the functions on a negligible fraction of the inputs. In order to analyze this construction, we introduce the notion of next-bit unreachable entropy, which replaces the next-bit pseudoentropy notion used by HRV.
AB - In this work we give the first non-adaptive construction of universal one-way hash functions (UOWHFs) from arbitrary one-way functions. Our construction uses O(n9) calls to the one-way function, has a key of length O(n10), and can be implemented in NC1 assuming the underlying one-way function is in NC1. Prior to this work, the best UOWHF construction used O(n13) adaptive calls and a key of size O(n5) (Haitner, Holenstein, Reingold, Vadhan and Wee [Eurocrypt ’10]). By the result of Applebaum, Ishai and Kushilevitz [FOCS ’04], the above implies the existence of UOWHFs in NC0, given the existence of one-way functions in NC1. We also show that the PRG construction of Haitner, Reingold and Vadhan (HRV, [STOC ’10]), with small modifications, yields a relaxed notion of UOWHFs, which is a function family which can be (inefficiently) converted to UOWHF by changing the functions on a negligible fraction of the inputs. In order to analyze this construction, we introduce the notion of next-bit unreachable entropy, which replaces the next-bit pseudoentropy notion used by HRV.
KW - non-adaptive
KW - one-way function
KW - universal one-way hash function
UR - http://www.scopus.com/inward/record.url?scp=85161633722&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-30634-1_17
DO - 10.1007/978-3-031-30634-1_17
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AN - SCOPUS:85161633722
SN - 9783031306334
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 502
EP - 531
BT - Advances in Cryptology – EUROCRYPT 2023 - 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2023, Proceedings
A2 - Hazay, Carmit
A2 - Stam, Martijn
PB - Springer Science and Business Media Deutschland GmbH
T2 - 42nd Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2023
Y2 - 23 April 2023 through 27 April 2023
ER -