Language Log

If you're interested in one-way functions and Kolmogorov complexity, you'll probably want to read this mind-crunching article:

"Researchers Identify ‘Master Problem’ Underlying All Cryptography", by Erica Klarreich, Quanta Magazine (April 6, 2022)

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

To ease our way, here are brief descriptions of the two key terms:

In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. Not being one-to-one is not considered sufficient for a function to be called one-way….

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In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963.

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