All reports by Author Mikito Nanashima:

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TR24-063
| 6th April 2024
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Shuichi Hirahara, Mikito Nanashima#### One-Way Functions and Zero Knowledge

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TR23-100
| 6th July 2023
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Shuichi Hirahara, Mikito Nanashima#### Learning in Pessiland via Inductive Inference

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TR23-035
| 22nd March 2023
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Shuichi Hirahara, Rahul Ilango, Zhenjian Lu, Mikito Nanashima, Igor Carboni Oliveira#### A Duality Between One-Way Functions and Average-Case Symmetry of Information

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TR22-164
| 20th November 2022
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Shuichi Hirahara, Mikito Nanashima#### Learning versus Pseudorandom Generators in Constant Parallel Time

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TR21-161
| 16th November 2021
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Shuichi Hirahara, Mikito Nanashima#### On Worst-Case Learning in Relativized Heuristica

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TR20-095
| 24th June 2020
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Mikito Nanashima#### On Basing Auxiliary-Input Cryptography on NP-hardness via Nonadaptive Black-Box Reductions

Revisions: 1

Shuichi Hirahara, Mikito Nanashima

The fundamental theorem of Goldreich, Micali, and Wigderson (J. ACM 1991) shows that the existence of a one-way function is sufficient for constructing computational zero knowledge ($\mathrm{CZK}$) proofs for all languages in $\mathrm{NP}$. We prove its converse, thereby establishing characterizations of one-way functions based on the worst-case complexities of ... more >>>

Shuichi Hirahara, Mikito Nanashima

Pessiland is one of Impagliazzo's five possible worlds in which NP is hard on average, yet no one-way function exists. This world is considered the most pessimistic because it offers neither algorithmic nor cryptographic benefits.

In this paper, we develop a unified framework for constructing strong learning algorithms ... more >>>

Shuichi Hirahara, Rahul Ilango, Zhenjian Lu, Mikito Nanashima, Igor Carboni Oliveira

Symmetry of Information (SoI) is a fundamental property of Kolmogorov complexity that relates the complexity of a pair of strings and their conditional complexities. Understanding if this property holds in the time-bounded setting is a longstanding open problem. In the nineties, Longpré and Mocas (1993) and Longpré and Watanabe (1995) ... more >>>

Shuichi Hirahara, Mikito Nanashima

A polynomial-stretch pseudorandom generator (PPRG) in NC$^0$ (i.e., constant parallel time) is one of the most important cryptographic primitives, especially for constructing highly efficient cryptography and indistinguishability obfuscation. The celebrated work (Applebaum, Ishai, and Kushilevitz, SIAM Journal on Computing, 2006) on randomized encodings yields the characterization of sublinear-stretch pseudorandom generators ... more >>>

Shuichi Hirahara, Mikito Nanashima

A PAC learning model involves two worst-case requirements: a learner must learn all functions in a class on all example distributions. However, basing the hardness of learning on NP-hardness has remained a key challenge for decades. In fact, recent progress in computational complexity suggests the possibility that a weaker assumption ... more >>>

Mikito Nanashima

A black-box (BB) reduction is a central proof technique in theoretical computer science. However, the limitations on BB reductions have been revealed for several decades, and the series of previous work gives strong evidence that we should avoid a nonadaptive BB reduction to base cryptography on NP-hardness (e.g., Akavia et ... more >>>