TY - GEN
T1 - One-Way Functions and the Hardness of (Probabilistic) Time-Bounded Kolmogorov Complexity w.r.t. Samplable Distributions
AU - Liu, Yanyi
AU - Pass, Rafael
N1 - Publisher Copyright:
© 2023, International Association for Cryptologic Research.
PY - 2023
Y1 - 2023
N2 - Consider the recently introduced notion of probabilistic time-bounded Kolmogorov Complexity, pKt (Goldberg et al., CCC’22), and let MpKtP denote the language of pairs (x, k) such that pKt(x) ≤ k. We show the equivalence of the following: MpKpolyP is (mildly) hard-on-average w.r.t. any samplable distribution D ;MpKpolyP is (mildly) hard-on-average w.r.t. the uniform distribution;existence of one-way functions. As far as we know, this yields the first natural class of problems where hardness with respect to any samplable distribution is equivalent to hardness with respect to the uniform distribution. Under standard derandomization assumptions, we can show the same result also w.r.t. the standard notion of time-bounded Kolmogorov complexity, Kt.
AB - Consider the recently introduced notion of probabilistic time-bounded Kolmogorov Complexity, pKt (Goldberg et al., CCC’22), and let MpKtP denote the language of pairs (x, k) such that pKt(x) ≤ k. We show the equivalence of the following: MpKpolyP is (mildly) hard-on-average w.r.t. any samplable distribution D ;MpKpolyP is (mildly) hard-on-average w.r.t. the uniform distribution;existence of one-way functions. As far as we know, this yields the first natural class of problems where hardness with respect to any samplable distribution is equivalent to hardness with respect to the uniform distribution. Under standard derandomization assumptions, we can show the same result also w.r.t. the standard notion of time-bounded Kolmogorov complexity, Kt.
UR - http://www.scopus.com/inward/record.url?scp=85173042592&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-38545-2_21
DO - 10.1007/978-3-031-38545-2_21
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AN - SCOPUS:85173042592
SN - 9783031385445
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 645
EP - 673
BT - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings, Part II
A2 - Handschuh, Helena
A2 - Lysyanskaya, Anna
PB - Springer Science and Business Media Deutschland GmbH
T2 - Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Y2 - 20 August 2023 through 24 August 2023
ER -