fully-homomorphic-encryption
Agda
fully-homomorphic-encryption | Agda | |
---|---|---|
19 | 27 | |
3,455 | 2,378 | |
0.3% | 0.6% | |
7.0 | 9.8 | |
about 2 months ago | 8 days ago | |
C++ | Haskell | |
Apache License 2.0 | MIT License |
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fully-homomorphic-encryption
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What are the current hot topics in type theory and static analysis?
Secure computing. This includes Fully Homomorphic Encryption AKA FHE, of which there is a language/compiler which just got released and Google's older FHE compiler. FHE is probably more "compiler" than "type system", e.g. Google's compiler works on C++. Also Security Type Systems which include Oblivious data structures and Oblivious ADTs.
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Ask HN: Should we follow what impresses us?
I don't have any advice for you, but I do work on homomorphic encryption at Google and we have an FHE compiler project [1] (though it is likely going to change a lot in the coming year). I happen to have a math PhD, so the transition to this field was not a huge stretch, but before that I worked in supply chain optimization for data centers, and just decided this was too exciting to pass up.
[1]: https://github.com/google/fully-homomorphic-encryption/issue...
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Spiral’s Homomorphic Encryption – Is This the Future of Privacy?
+1, and some compilers already exist to do that for you. See, e.g., Google's compiler (which I work on). https://github.com/google/fully-homomorphic-encryption
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We’re Christian Mouchet, Jean-Philippe Bossuat, Kurt Rohloff, Nigel Smart, Pascal Paillier, Rand Hindi, Wonkyung Jung, various researchers and library developers of homomorphic encryption to answer questions about homomorphic encryption and why it’s important for the future of data privacy! AMA
Once the tools are written, you should be able to take a program written in some language foo and transpile it to a FHE version of foo. See Google's C++ to FHE-C++ transpiler. Thus, you can test/debug your application without FHE before transpiling to something that is FHE.
- Google releases C++ Transpiler for Fully Homomorphic Encryption
- Fully Homomorphic Encryption by Google
- Fully homomorphic encryption (Google GitHub)
- r/crypto - Fully Homomorphic Encryption by Google
- Fully Homomorphic Encryption (FHE)
Agda
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Types versus sets (and what about categories?)
This was recently deemed inappropriate:
"Bye bye Set"
"Set and Prop are removed as keywords"
https://github.com/agda/agda/pull/4629
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If given a list of properties/definitions and relationship between them, could a machine come up with (mostly senseless, but) true implications?
Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.
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What can Category Theory do?
Haskell and Agda are probably the most obvious examples. Ocaml too, but it is much older, so its type system is not as categorical. There is also Idris, which is not as well-known but is very cool.
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What are the current hot topics in type theory and static analysis?
Most of the proof assistants out there: Lean, Coq, Dafny, Isabelle, F*, Idris 2, and Agda. And the main concepts are dependent types, Homotopy Type Theory AKA HoTT, and Category Theory. Warning: HoTT and Category Theory are really dense, you're going to really need to research them.
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Amendmend proposal: Changed syntax for Or patterns
Does this come with plans to separately unify the body with each of the contexts induced by matching on each of the respective patterns (similar to what’s discussed here), or will it behave like the _ pattern and use only the most general context?
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Functional Programming and Maths <|> How can a code monkey learn Agda?
That's absolutely untrue. From the horse's mouth:
- Doom emacs and agda-mode
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FP language idea - would this is possible to infer and type check?
Agda has the so-called mixfix operators (which are powerful enough to cover pre/in/postfix cases with an arbitrary number of arguments), check that out: - https://agda.readthedocs.io/en/v2.6.1/language/mixfix-operators.html - https://github.com/agda/agda/blob/master/examples/Introduction/Operators.agda - https://github.com/agda/agda-stdlib/blob/master/src/Data/Product/Base.agda
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Best Programming Language for Computational Proof
Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones.
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Do you use Idris or Coq, and why?
Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.
What are some alternatives?
SEAL - Microsoft SEAL is an easy-to-use and powerful homomorphic encryption library.
lean - Lean Theorem Prover
differential-privacy - Google's differential privacy libraries.
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
i2pd - 🛡 I2P: End-to-End encrypted and anonymous Internet
open-typerep - Open type representations and dynamic types
monero - Monero: the secure, private, untraceable cryptocurrency
HoleyMonoid - Automatically exported from code.google.com/p/monoid-cont
HElib - HElib is an open-source software library that implements homomorphic encryption. It supports the BGV scheme with bootstrapping and the Approximate Number CKKS scheme. HElib also includes optimizations for efficient homomorphic evaluation, focusing on effective use of ciphertext packing techniques and on the Gentry-Halevi-Smart optimizations.
distributive - Dual Traversable
EVA - Compiler for the SEAL homomorphic encryption library
lean4 - Lean 4 programming language and theorem prover