Understanding Incompressibility & Next-Block Pseudoentropy in Cryptography 🔐

Iftach Haitner (Tel Aviv University)
https://simons.berkeley.edu/talks/iftach-haitner-tel-aviv-university-2023-05-02
Minimal Complexity Assumptions for Cryptography

A distribution is k-incompressible, Yao [FOCS ’82], if no efficient compression scheme compresses it to less than k bits. While being a natural measure, its relation to other computational analogs of entropy such as pseudoentropy, Hastad, Impagliazzo, Levin, and Luby [SICOMP 99], and to other cryptographic hardness assumptions, was unclear.

We advance towards a better understating of this notion, showing that a k-incompressible distribution has (k-2) bits of next-block pseudoentropy, a refinement of pseudoentropy introduced by Haitner, Reingold, and Vadhan [SICOMP ’13]. We deduce that a samplable distribution X that is (H(X) + 2)-incompressible, implies the existence of one-way functions.