TY - GEN
T1 - A Direct PRF Construction from Kolmogorov Complexity
AU - Liu, Yanyi
AU - Pass, Rafael
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - While classic results in the 1980s establish that one-way functions (OWF) imply the existence of pseudorandom generators (PRG) which in turn imply pseudorandom functions (PRF), the constructions (most notably the one from OWFs to PRGs) is complicated and inefficient. Consequently, researchers have developed alternative direct constructions of PRFs from various different concrete hardness assumptions. In this work, we continue this thread of work and demonstrate the first direct construction of PRFs from average-case hardness of the time-bounded Kolmogorov complexity problem MKtP[s], where given a threshold, s(·), and a polynomial time-bound, t(·), MKtP[s] denotes the language consisting of strings x with t-bounded Kolmogorov complexity, Kt(x), bounded by s(|x|). In more detail, we demonstrate a direct PRF construction with quasi-polynomial security from mild avg-case of hardness of MKtP[2O(logn)] w.r.t the uniform distribution. We note that by earlier results, this assumption is known to be equivalent to the existence of quasi-polynomially secure OWFs; as such, our results yield the first direct (quasi-polynomially secure) PRF construction from a natural hardness assumptions that also is known to be implied by (quasi-polynomially secure) PRFs. Perhaps surprisingly, we show how to make use of the Nisan-Wigderson PRG construction to get a cryptographic, as opposed to a complexity-theoretic, PRG.
AB - While classic results in the 1980s establish that one-way functions (OWF) imply the existence of pseudorandom generators (PRG) which in turn imply pseudorandom functions (PRF), the constructions (most notably the one from OWFs to PRGs) is complicated and inefficient. Consequently, researchers have developed alternative direct constructions of PRFs from various different concrete hardness assumptions. In this work, we continue this thread of work and demonstrate the first direct construction of PRFs from average-case hardness of the time-bounded Kolmogorov complexity problem MKtP[s], where given a threshold, s(·), and a polynomial time-bound, t(·), MKtP[s] denotes the language consisting of strings x with t-bounded Kolmogorov complexity, Kt(x), bounded by s(|x|). In more detail, we demonstrate a direct PRF construction with quasi-polynomial security from mild avg-case of hardness of MKtP[2O(logn)] w.r.t the uniform distribution. We note that by earlier results, this assumption is known to be equivalent to the existence of quasi-polynomially secure OWFs; as such, our results yield the first direct (quasi-polynomially secure) PRF construction from a natural hardness assumptions that also is known to be implied by (quasi-polynomially secure) PRFs. Perhaps surprisingly, we show how to make use of the Nisan-Wigderson PRG construction to get a cryptographic, as opposed to a complexity-theoretic, PRG.
UR - http://www.scopus.com/inward/record.url?scp=85192826327&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-58737-5_14
DO - 10.1007/978-3-031-58737-5_14
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AN - SCOPUS:85192826327
SN - 9783031587368
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 375
EP - 406
BT - Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
A2 - Joye, Marc
A2 - Leander, Gregor
PB - Springer Science and Business Media Deutschland GmbH
T2 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2024
Y2 - 26 May 2024 through 30 May 2024
ER -