TY - GEN

T1 - On one-way functions and kolmogorov complexity

AU - Liu, Yanyi

AU - Pass, Rafael

N1 - Publisher Copyright:
© 2020 IEEE.

PY - 2020/11

Y1 - 2020/11

N2 - We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial t(n) geq(1+ varepsilon)n, varepsilon > 0, the following are equivalent: •One-way functions exists (which in turn is equivalent to the existence of secure private-key encryption schemes, digital signatures, pseudorandom generators, pseudorandom functions, commitment schemes, and more); •t-time bounded Kolmogorov Complexity, K{t}, is mildly hard-on-average (i.e., there exists a polynomial p(n) > 0 such that no PPT algorithm can compute K{t}, for more than a 1-frac{1}{p(n)} fraction of n-bit strings). In doing so, we present the first natural, and well-studied, computational problem characterizing the feasibility of the central private-key primitives and protocols in Cryptography.

AB - We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial t(n) geq(1+ varepsilon)n, varepsilon > 0, the following are equivalent: •One-way functions exists (which in turn is equivalent to the existence of secure private-key encryption schemes, digital signatures, pseudorandom generators, pseudorandom functions, commitment schemes, and more); •t-time bounded Kolmogorov Complexity, K{t}, is mildly hard-on-average (i.e., there exists a polynomial p(n) > 0 such that no PPT algorithm can compute K{t}, for more than a 1-frac{1}{p(n)} fraction of n-bit strings). In doing so, we present the first natural, and well-studied, computational problem characterizing the feasibility of the central private-key primitives and protocols in Cryptography.

KW - n/a

UR - http://www.scopus.com/inward/record.url?scp=85100338719&partnerID=8YFLogxK

U2 - 10.1109/FOCS46700.2020.00118

DO - 10.1109/FOCS46700.2020.00118

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AN - SCOPUS:85100338719

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 1243

EP - 1254

BT - Proceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020

PB - IEEE Computer Society

T2 - 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020

Y2 - 16 November 2020 through 19 November 2020

ER -