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Electronic Colloquium on Computational Complexity

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All reports by Author Pravesh Kothari:

TR23-098 | 5th July 2023
Andrej Bogdanov, Pravesh Kothari, Alon Rosen

Public-Key Encryption, Local Pseudorandom Generators, and the Low-Degree Method

The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics.

We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis ... more >>>

TR22-101 | 15th July 2022
Omar Alrabiah, Venkatesan Guruswami, Pravesh Kothari, Peter Manohar

A Near-Cubic Lower Bound for 3-Query Locally Decodable Codes from Semirandom CSP Refutation

Revisions: 1

A code $C \colon \{0,1\}^k \to \{0,1\}^n$ is a $q$-locally decodable code ($q$-LDC) if one can recover any chosen bit $b_i$ of the message $b \in \{0,1\}^k$ with good confidence by randomly querying the encoding $x = C(b)$ on at most $q$ coordinates. Existing constructions of $2$-LDCs achieve $n = ... more >>>

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