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www.jeremykun.com | ||
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www.daniellowengrub.com
[AI summary] The text discusses the implementation of homomorphic operations in the context of RLWE (Ring Learning With Errors) and GSW (Gentry-Sahai-Waters) encryption schemes. Key concepts include the use of encryptions of zero to facilitate homomorphic multiplication, the structure of GSW ciphertexts as matrices of RLWE ciphertexts, and the role of scaling factors to manage error growth during multiplication. The main goal is to enable secure computation of polynomial products without revealing the underlying plaintexts. |
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jeremykun.com
In this article I'll derive a trick used in FHE called sample extraction. In brief, it allows one to partially convert a ciphertext in the Ring Learning With Errors (RLWE) scheme to the Learning With Errors (LWE) scheme. Here are some other articles I've written about other FHE building blocks, though they are not prerequisites... |
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cp4space.hatsya.com
A couple of years ago I described a primep which possesses various properties that renders it useful for computing number-theoretic transforms over the field $latex \mathbb{F}_p$. Specifically, we have: $latex p = \Phi_{192}(2) = \Phi_6(2^{32}) = 2^{64} - 2^{32} + 1$ where the first of these equalities uses the identity that: $latex \Phi_{k}(x) = \Phi_{rad(k)}(x^{k/rad(k)})$... |
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nfil.dev
I've been reading up on the Double Ratchet algorithm and its implementations lately, as it's an exciting piece of crypto that offers some very nice guarantees: forward secrecy (ie. by breaking a key at some point you can't read older messages), eventual break-in recovery (ie. by breaking a key you can only read a few messages before the protocol recovers), and of course confidentiality and deniability. It's all done through the use of "ratchets", which are used to update the key used with each message. The algorithm comes at a nice time, when consumers are becoming more privacy-aware and governments more determined to perform mass surveillance, which is where E2E encryption becomes the only way to protect your data. |
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