fully-homomorphic-encryption
coq
fully-homomorphic-encryption | coq | |
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19 | 87 | |
3,455 | 4,616 | |
0.3% | 0.7% | |
7.0 | 10.0 | |
about 2 months ago | about 4 hours ago | |
C++ | OCaml | |
Apache License 2.0 | GNU Lesser General Public License v3.0 only |
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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)
coq
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Change of Name: Coq –> The Rocq Prover
The page summarizing the considered new names and their pros/cons is interesting: https://github.com/coq/coq/wiki/Alternative-names
Naming is hard...
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The First Stable Release of a Rust-Rewrite Sudo Implementation
Are those more important than, say:
- Proven with Coq, a formal proof management system: https://coq.inria.fr/
See in the real world: https://aws.amazon.com/security/provable-security/
And check out Computer-Aided Verification (CAV).
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Why Mathematical Proof Is a Social Compact
To be ruthlessly, uselessly pedantic - after all, we're mathematicians - there's reasonable definitions of "academic" where logical unsoundness is still academic if it never interfered with the reasoning behind any proofs of interest ;)
But: so long as we're accepting that unsoundness in your checker or its underlying theory are intrinsically deal breakers, there's definitely a long history of this, perhaps more somewhat more relevant than the HM example, since no proof checkers of note, AFAIK, have incorporated mutation into their type theory.
For one thing, the implementation can very easily have bugs. Coq itself certainly has had soundness bugs occasionally [0]. I'm sure Agda, Lean, Idris, etc. have too, but I've followed them less closely.
But even the underlying mathematics have been tricky. Girard's Paradox broke Martin-Löf's type theory, which is why in these dependently typed proof assistants you have to deal with the bizarre "Tower of Universes"; and Girard's Paradox is an analogue of Russell's Paradox which broke more naive set theories. And then Russell himself and his system of universal mathematics was very famously struck down by Gödel.
But we've definitely gotten it right this time...
[0] https://github.com/coq/coq/issues/4294
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In Which I Claim Rich Hickey Is Wrong
Dafny and Whiley are two examples with explicit verification support. Idris and other dependently typed languages should all be rich enough to express the required predicate but might not necessarily be able to accept a reasonable implementation as proof. Isabelle, Lean, Coq, and other theorem provers definitely can express the capability but aren't going to churn out much in the way of executable programs; they're more useful to guide an implementation in a more practical functional language but then the proof is separated from the implementation, and you could also use tools like TLA+.
https://dafny.org/
https://whiley.org/
https://www.idris-lang.org/
https://isabelle.in.tum.de/
https://leanprover.github.io/
https://coq.inria.fr/
http://lamport.azurewebsites.net/tla/tla.html
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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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Functional Programming in Coq
What ever happened to the effort [1] to rename Coq in order to make it less offensive? There were a number of excellent proposals [2] that seemed to die on the vine.
[1] https://github.com/coq/coq/wiki/Alternative-names
[2] https://github.com/coq/coq/wiki/Alternative-names#c%E1%B5%A3...
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Mark Petruska has requested 250000 Algos for the development of a Coq-avm library for AVM version 8
Information about the Coq proof assistant: https://coq.inria.fr/ , https://en.wikipedia.org/wiki/Coq
- How are people like Andrew Wiles and Grigori Perelman able to work on popular problems for years without others/the research community discovering the same breakthroughs? Is it just luck?
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Basic SAT model of x86 instructions using Z3, autogenerated from Intel docs
This type of thing can help you formally verify code.
So, if your proof is correct, and your description of the (language/CPU) is correct, you can prove the code does what you think it does.
Formal proof systems are still growing up, though, and they are still pretty hard to use. See Coq for an introduction: https://coq.inria.fr/
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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.
What are some alternatives?
SEAL - Microsoft SEAL is an easy-to-use and powerful homomorphic encryption library.
coc.nvim - Nodejs extension host for vim & neovim, load extensions like VSCode and host language servers.
differential-privacy - Google's differential privacy libraries.
kok.nvim - Fast as FUCK nvim completion. SQLite, concurrent scheduler, hundreds of hours of optimization.
i2pd - 🛡 I2P: End-to-End encrypted and anonymous Internet
FStar - A Proof-oriented Programming Language
monero - Monero: the secure, private, untraceable cryptocurrency
Agda - Agda is a dependently typed programming language / interactive theorem prover.
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.
lean4 - Lean 4 programming language and theorem prover
EVA - Compiler for the SEAL homomorphic encryption library
tlaplus - TLC is a model checker for specifications written in TLA+. The TLA+Toolbox is an IDE for TLA+.