Revision #2 Authors: Yanyi Liu, Rafael Pass

Accepted on: 24th September 2020 09:13

Downloads: 831

Keywords:

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.

Revision #1 Authors: Yanyi Liu, Rafael Pass

Accepted on: 25th April 2020 01:16

Downloads: 466

Keywords:

We prove the equivalence of two fundamental

problems in the theory of computation:

-Existence of one-way functions: the existence of one-way functions

(which in turn is equivalent to the existence of secure private-key

encryption schemes, digital signatures, pseudorandom generators, pseudorandom functions, commitment schemes, and more).

-Mild average-case hardness of $K^{\poly}$-complexity: the existence of polynomials

$t,p>0$ such that no $\PPT$ algorithm can determine the $t$-time

bounded Kolmogorov Complexity, $K^t$, 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.

TR20-052 Authors: Yanyi Liu, Rafael Pass

Publication: 18th April 2020 12:44

Downloads: 742

Keywords:

We prove the equivalence of two fundamental problems in the theory of computation:

- Existence of one-way functions: the existence of one-way functions (which in turn are equivalent to pseudorandom generators, pseudorandom functions, private-key encryption schemes, digital signatures, commitment schemes, and more).

- Mild average-case hardness of $K^{poly}$-complexity: the existence of polynomials $t,p$ such that no PPT algorithm can determine the $t$-time bounded Kolmogorov Complexity, $K^t$, 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 ``non-trivial'' complexity-based Cryptography: ``Non-trivial'' complexity-based Cryptography is possible iff $K^{poly}$ is mildly hard-on average.