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jeremykun.wordpress.com
The Learning With Errors problem is the basis of a few cryptosystems, and a foundation for many fully homomorphic encryption (FHE) schemes. In this article I'll describe a technique used in some of these schemes called modulus switching. In brief, an LWE sample is a vector of values in $\mathbb{Z}/q\mathbb{Z}$ for some $q$, and in... |
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unorde.red
[AI summary] This article explains the Diffie-Hellman key exchange algorithm, its mathematical foundation in discrete logarithm problems, and its security implications in modern cryptography. |
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rot256.dev
We start by getting a grasp of how the FFT can be used to quickly compute a change of basis change for the elements of \( \mathbb{F}_p[X] \). Besides being an essential tool in improving the performance of many zero-knowledge proof systems (not just those mentioned in the Introduction), it will also give us some crucial intuition about what is happening in DEEP-FRI over prime fields. But of course we need a finite field with a subgroup of \( 2^k \)-th roots of unity. Since the multiplicative group of a finite field is always cyclic this simply means that \( 2^k \ | \ p - 1 \). Finding such a field can be done using rejection sampling. |
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alanrendall.wordpress.com
The theorem of the title is about dividing smooth functions by other smooth functions or, in other words, representing a given smooth function in terms of products of other smooth functions. A large part of the account which follows is based on that in the book 'Normal Forms and Unfoldings for Local Dynamical Systems' by... |
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