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Toy implementation of FHE algorithms

License: Other

Julia 100.00%

homomorphic-encryption encryption cryptography readability julia bfv bgv julialang ckks i-see-nothing-nothing

toyfhe.jl's Introduction

ToyFHE.jl - A toy implementation of FHE algorithms

I frequently hear music in the heart of noise. - George Gershwin

Documentation	Build Status

Installation

This package currently depends on a number of modifications to upstream packages. The included Manifest.toml lists known working versions for these packages. To use those versions, first clone this package to a location of your choice:

$ git clone https://github.com/JuliaCrypto/ToyFHE.jl ToyFHE

Then load up the project within Julia:

$ julia --project=ToyFHE

If you do not have the correct versions of the dependencies installed, you may be asked to install them via instantiate:

julia> using Pkg

julia> Pkg.instantiate()

Examples

julia> cd("ToyFHE/examples/encrypted_mnist")

julia> include("train.jl")

julia> include("infer.jl")

Documentation

DEVEL — documentation of the in-development version.

Features

WARNING: The code in this repository is in an extremely alpha quality. You may want to check back in a little bit once things have been cleaned up.

This repository is a playground for exploring homomorphic encryption protocols. The design goal is ease of use and ease of readability over absolute performance or suitability for production HE applications. The goal of this code is to aid in research and the quick exploration of HE applications.

This package currently contains (partial) implementations of the following HE schemes:

Brakerski/Fan-Vercauteren (BFV)
Brakerski-Gentry-Vaikuntanathan (BGV)
Cheon-Kim-Kim-Song (CKKS)

Both power-of-two and general cyclotomic rings are supported for homomorphic operations. The former is based on a pure Julia FFT implementation and thus likely suitable for multi-threading and GPU applications with little additional effort (those this has not been done so far). The latter is based on the Nemo stack of Julia packages, which are ultimately using FLINT as the execution engine.

Disclaimer

Performance notice

This package has not been optimized for performance. The only implementated performance optimizations are those that were absolutely required to perform the desired algorithmic exploration. PRs are welcome to improve performance (as long as readability is preserved), but such work is not currently on the roadmap.

Security Notice

This package currently has known issues (weak RNG, known timing side channels) that make it unsuitable for use other than for algorithmic research. DO NOT USE FOR PRODUCTION APPLICATIONS (I mean it). As with the performance consideration, these issues are addressable, but not currently on the roadmap.

Omnibus

I am not a cryptographer. I am not your cryptographer. This code is a toy. This code is not intended for production use. This code has not been audited or validated. Consult a professional cryptographer, before using cryptography. No warranty (see LICENSE). Don't sue me.

toyfhe.jl's People

Contributors

Stargazers

Watchers

Forkers

lucyio carstenbauer stjordanis techieboy leobewin cryptosl wkjung zeta1999 goldstar111 zgornel standardgalactic 00mjk

toyfhe.jl's Issues

MNIST example does not work on Julia master

I think the issue is that the manifest uses an old version of CuArrays that does not work on Julia master.

cc: @Keno

julia> cd("ToyFHE.jl/examples/encrypted_mnist")
julia rm("mnist_conv.bson"; force = true)
julia> include("train.jl")
[ Info: Precompiling CuArrays [3a865a2d-5b23-5a0f-bc46-62713ec82fae]
┌ Warning: Assignment to `name` in soft scope is ambiguous because a global variable by the same name exists: `name` will be treated as a new local. Disambiguate by using `local name` to suppress this warning or `global name` to assign to the existing global variable.
└ @ ~/.julia/packages/CUDAdrv/WqkY2/src/error.jl:83
┌ Warning: `@get!(dict, key, default)` at /users/daluthge/.julia/packages/Requires/9Jse8/src/require.jl:11 is deprecated, use `get!(()->default, dict, key)` instead.
│   caller = include(::Function, ::Module, ::String) at Base.jl:380
└ @ Base ./Base.jl:380
ERROR: LoadError: LoadError: syntax: invalid keyword argument syntax "(escape (= threads nthreads))"
Stacktrace:
 [1] top-level scope at /users/daluthge/.julia/packages/CuArrays/dY5ry/src/array.jl:318
 [2] include(::Function, ::Module, ::String) at ./Base.jl:380
 [3] include at ./Base.jl:368 [inlined]
 [4] include(::String) at /users/daluthge/.julia/packages/CuArrays/dY5ry/src/CuArrays.jl:1
 [5] top-level scope at /users/daluthge/.julia/packages/CuArrays/dY5ry/src/CuArrays.jl:22
 [6] include(::Function, ::Module, ::String) at ./Base.jl:380
 [7] include(::Module, ::String) at ./Base.jl:368
 [8] top-level scope at none:2
 [9] eval at ./boot.jl:331 [inlined]
 [10] eval(::Expr) at ./client.jl:451
 [11] top-level scope at ./none:3
in expression starting at /users/daluthge/.julia/packages/CuArrays/dY5ry/src/array.jl:318
in expression starting at /users/daluthge/.julia/packages/CuArrays/dY5ry/src/CuArrays.jl:22
ERROR: LoadError: Failed to precompile CuArrays [3a865a2d-5b23-5a0f-bc46-62713ec82fae] to /users/daluthge/.julia/compiled/v1.5/CuArrays/7YFE0_YKowg.ji.
Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] compilecache(::Base.PkgId, ::String) at ./loading.jl:1288
 [3] _require(::Base.PkgId) at ./loading.jl:1029
 [4] require(::Base.PkgId) at ./loading.jl:927
 [5] require(::Module, ::Symbol) at ./loading.jl:922
 [6] include(::String) at ./client.jl:441
 [7] top-level scope at REPL[10]:1
in expression starting at /gpfs_home/daluthge/Desktop/ToyFHE.jl/examples/encrypted_mnist/train.jl:9

julia> versioninfo(verbose = true)
Julia Version 1.5.0-DEV.274
Commit 8eb0f9fefb (2020-02-15 12:41 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
      "Red Hat Enterprise Linux Server release 7.3 (Maipo)"
  uname: Linux 3.10.0-957.5.1.el7.x86_64 #1 SMP Wed Dec 19 10:46:58 EST 2018 x86_64 x86_64
  CPU: Intel(R) Xeon(R) Gold 5122 CPU @ 3.60GHz:
              speed         user         nice          sys         idle          irq
       #1  3601 MHz  302347066 s        170 s   53586390 s  337540460 s          0 s
       #2  3601 MHz  235401396 s        383 s   47128775 s  410325724 s          0 s
       #3  3601 MHz  103237285 s        288 s   30844130 s  559882062 s          0 s
       #4  3601 MHz   63412689 s        364 s   22978592 s  607626432 s          0 s
       #5  3601 MHz  315443735 s        113 s   49256804 s  329997494 s          0 s
       #6  3601 MHz  155708333 s        578 s   37188177 s  501770058 s          0 s
       #7  3601 MHz   54762847 s        546 s   15693504 s  624338616 s          0 s
       #8  3601 MHz   46859843 s        550 s   14616044 s  632741590 s          0 s

  Memory: 93.04103088378906 GB (74548.9140625 MB free)
  Uptime: 6.958699e6 sec
  Load Avg:  1.20654296875  1.44921875  1.22314453125
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-9.0.1 (ORCJIT, skylake)
Environment:
  CPLUS_INCLUDE_PATH = /gpfs/runtime/opt/gcc/8.3/include
  MANPATH = /gpfs/runtime/opt/python/3.7.4/share/man:/gpfs/runtime/opt/git/2.20.2/share/man:/gpfs/runtime/opt/gcc/8.3/share/man:/gpfs/runtime/opt/binutils/2.31/share/man:/gpfs/runtime/opt/intel/2017.0/man/common/man1:
  TERM = xterm-256color
  LIBRARY_PATH = /gpfs/runtime/opt/cuda/10.2/cuda/lib64:/gpfs/runtime/opt/cuda/10.2/cuda/lib:/gpfs/runtime/opt/cudnn/7.6.5/lib64:/gpfs/runtime/opt/python/3.7.4/lib:/gpfs/runtime/opt/binutils/2.31/lib:/gpfs/runtime/opt/intel/2017.0/lib/intel64:/gpfs/runtime/opt/intel/2017.0/mkl/lib/intel64
  INCLUDE_PATH = /gpfs/runtime/opt/cudnn/7.6.5/include
  CUDA_HOME = /gpfs/runtime/opt/cuda/10.2/cuda
  LD_LIBRARY_PATH = /gpfs/runtime/opt/cuda/10.2/src/lib64:/gpfs/runtime/opt/cuda/10.2/src/lib:/gpfs/runtime/opt/cudnn/7.6.5/lib64:/gpfs/runtime/opt/python/3.7.4/lib:/gpfs/runtime/opt/gcc/8.3/lib64:/gpfs/runtime/opt/binutils/2.31/lib:/gpfs/runtime/opt/intel/2017.0/lib/intel64:/gpfs/runtime/opt/intel/2017.0/mkl/lib/intel64:/gpfs/runtime/opt/java/8u111/jre/lib/amd64
  CPATH = /gpfs/runtime/opt/cuda/10.2/cuda/include:/gpfs/runtime/opt/cudnn/7.6.5/include:/gpfs/runtime/opt/python/3.7.4/include:/gpfs/runtime/opt/gcc/8.3/include:/gpfs/runtime/opt/binutils/2.31/include:/gpfs/runtime/opt/intel/2017.0/mkl/include
  NLSPATH = /gpfs/runtime/opt/intel/2017.0/lib/intel64/locale/en_US:/gpfs/runtime/opt/intel/2017.0/mkl/lib/intel64/locale/en_US
  PATH = /gpfs/runtime/opt/cuda/10.2/cuda/bin:/users/daluthge/bin:/gpfs/runtime/opt/python/3.7.4/bin:/gpfs/runtime/opt/git/2.20.2/bin:/gpfs/runtime/opt/gcc/8.3/bin:/gpfs/runtime/opt/binutils/2.31/bin:/gpfs/runtime/opt/intel/2017.0/bin:/gpfs/runtime/opt/matlab/R2017b/bin:/gpfs/runtime/opt/java/8u111/bin:/usr/lib64/qt-3.3/bin:/usr/local/bin:/usr/bin:/usr/local/sbin:/usr/sbin:/usr/lpp/mmfs/bin:/usr/lpp/mmfs/sbin:/opt/ibutils/bin:/gpfs/runtime/bin
  C_INCLUDE_PATH = /gpfs/runtime/opt/cudnn/7.6.5/include:/gpfs/runtime/opt/gcc/8.3/include
  LD_RUN_PATH = /gpfs/runtime/opt/cuda/10.2/cuda/lib64:/gpfs/runtime/opt/cuda/10.2/cuda/lib:/gpfs/runtime/opt/cudnn/7.6.5/lib64:/gpfs/runtime/opt/cudnn/7.6.5/lib:/gpfs/runtime/opt/python/3.7.4/lib:/gpfs/runtime/opt/gcc/8.3/lib64:/gpfs/runtime/opt/binutils/2.31/lib:/gpfs/runtime/opt/intel/2017.0/lib/intel64:/gpfs/runtime/opt/intel/2017.0/mkl/lib/intel64
  JAVA_HOME = /gpfs/runtime/opt/java/8u111
  MODULEPATH = /gpfs/runtime/modulefiles
  HOME = /users/daluthge
  IPP_PATH = /gpfs/runtime/opt/intel/2017.0/ipp
  MODULEHOME = /gpfs/runtime/pymodules
  PKG_CONFIG_PATH = /gpfs/runtime/opt/python/3.7.4/lib/pkgconfig
  QT_PLUGIN_PATH = /usr/lib64/kde4/plugins:/usr/lib/kde4/plugins

(ToyFHE) pkg> st
Project ToyFHE v0.1.0
Status `/gpfs_home/daluthge/Desktop/ToyFHE.jl/Project.toml`
  [c3fe647b] AbstractAlgebra v0.7.1 #master (https://github.com/Nemocas/AbstractAlgebra.jl.git)
  [15f4f7f2] AutoHashEquals v0.2.0
  [fbb218c0] BSON v0.2.4
  [c3b6d118] BitIntegers v0.2.0 #kf/div (https://github.com/Keno/BitIntegers.jl)
  [3a865a2d] CuArrays v1.3.0 #master (https://github.com/JuliaGPU/CuArrays.jl.git)
  [ab62b9b5] DeepDiffs v1.1.0
  [31c24e10] Distributions v0.21.1 #kf/discretenormal (https://github.com/Keno/Distributions.jl)
  [7a1cc6ca] FFTW v1.0.1
  [587475ba] Flux v0.9.0
  [65ccaadd] FourierTransforms v0.0.0 #master (https://github.com/JuliaComputing/FourierTransforms.jl)
  [0c68f7d7] GPUArrays v1.0.4 #master (https://github.com/JuliaGPU/GPUArrays.jl.git)
  [8d0d7f98] GaloisFields v0.4.0 #master (https://github.com/tkluck/GaloisFields.jl.git)
  [3e1990a7] Hecke v0.6.5 #kf/discard2 (https://github.com/Keno/Hecke.jl)
  [7869d1d1] IRTools v0.3.0 #master (https://github.com/MikeInnes/IRTools.jl.git)
  [aa1ae85d] JuliaInterpreter v0.7.4
  [7475f97c] Mods v0.1.0
  [2edaba10] Nemo v0.15.1 #master (https://github.com/Nemocas/Nemo.jl.git)
  [6fe1bfb0] OffsetArrays v0.11.1
  [f27b6e38] Polynomials v0.5.3
  [27ebfcd6] Primes v0.4.0+ #master (https://github.com/JuliaMath/Primes.jl.git)
  [09ab397b] StructArrays v0.4.0 #kf/fhe (https://github.com/Keno/StructArrays.jl)
  [700de1a5] ZygoteRules v0.2.0 #master (https://github.com/FluxML/ZygoteRules.jl.git)
  [37e2e46d] LinearAlgebra
  [9a3f8284] Random

(ToyFHE) pkg> st -m
Project ToyFHE v0.1.0
Status `/gpfs_home/daluthge/Desktop/ToyFHE.jl/Manifest.toml`
  [c3fe647b] AbstractAlgebra v0.7.1 #master (https://github.com/Nemocas/AbstractAlgebra.jl.git)
  [621f4979] AbstractFFTs v0.4.1
  [1520ce14] AbstractTrees v0.2.1
  [79e6a3ab] Adapt v1.0.0
  [7d9fca2a] Arpack v0.3.1
  [15f4f7f2] AutoHashEquals v0.2.0
  [fbb218c0] BSON v0.2.4
  [9e28174c] BinDeps v0.8.10
  [b99e7846] BinaryProvider v0.5.8
  [c3b6d118] BitIntegers v0.2.0 #kf/div (https://github.com/Keno/BitIntegers.jl)
  [fa961155] CEnum v0.2.0
  [3895d2a7] CUDAapi v1.2.0
  [c5f51814] CUDAdrv v4.0.3
  [be33ccc6] CUDAnative v2.5.4
  [da1fd8a2] CodeTracking v0.5.8
  [944b1d66] CodecZlib v0.6.0
  [3da002f7] ColorTypes v0.8.0
  [5ae59095] Colors v0.9.6
  [bbf7d656] CommonSubexpressions v0.2.0
  [34da2185] Compat v2.2.0
  [8f4d0f93] Conda v1.3.0
  [3a865a2d] CuArrays v1.3.0 #master (https://github.com/JuliaGPU/CuArrays.jl.git)
  [9a962f9c] DataAPI v1.1.0
  [864edb3b] DataStructures v0.17.5
  [ab62b9b5] DeepDiffs v1.1.0
  [163ba53b] DiffResults v0.0.4
  [b552c78f] DiffRules v0.0.10
  [31c24e10] Distributions v0.21.1 #kf/discretenormal (https://github.com/Keno/Distributions.jl)
  [7a1cc6ca] FFTW v1.0.1
  [1a297f60] FillArrays v0.7.4
  [53c48c17] FixedPointNumbers v0.6.1
  [587475ba] Flux v0.9.0
  [f6369f11] ForwardDiff v0.10.6
  [65ccaadd] FourierTransforms v0.0.0 #master (https://github.com/JuliaComputing/FourierTransforms.jl)
  [0c68f7d7] GPUArrays v1.0.4 #master (https://github.com/JuliaGPU/GPUArrays.jl.git)
  [8d0d7f98] GaloisFields v0.4.0 #master (https://github.com/tkluck/GaloisFields.jl.git)
  [cd3eb016] HTTP v0.8.8
  [3e1990a7] Hecke v0.6.5 #kf/discard2 (https://github.com/Keno/Hecke.jl)
  [7869d1d1] IRTools v0.3.0 #master (https://github.com/MikeInnes/IRTools.jl.git)
  [83e8ac13] IniFile v0.5.0
  [682c06a0] JSON v0.21.0
  [aa1ae85d] JuliaInterpreter v0.7.4
  [e5e0dc1b] Juno v0.7.2
  [929cbde3] LLVM v1.3.2
  [1914dd2f] MacroTools v0.5.2
  [739be429] MbedTLS v0.7.0
  [e89f7d12] Media v0.5.0
  [e1d29d7a] Missings v0.4.3
  [7475f97c] Mods v0.1.0
  [872c559c] NNlib v0.6.0
  [77ba4419] NaNMath v0.3.2
  [2edaba10] Nemo v0.15.1 #master (https://github.com/Nemocas/Nemo.jl.git)
  [6fe1bfb0] OffsetArrays v0.11.1
  [bac558e1] OrderedCollections v1.1.0
  [90014a1f] PDMats v0.9.10
  [69de0a69] Parsers v0.3.8
  [f27b6e38] Polynomials v0.5.3
  [2dfb63ee] PooledArrays v0.5.2
  [27ebfcd6] Primes v0.4.0+ #master (https://github.com/JuliaMath/Primes.jl.git)
  [1fd47b50] QuadGK v2.1.1
  [3cdcf5f2] RecipesBase v0.7.0
  [189a3867] Reexport v0.2.0
  [ae029012] Requires v0.5.2
  [79098fc4] Rmath v0.6.0
  [a2af1166] SortingAlgorithms v0.3.1
  [276daf66] SpecialFunctions v0.7.2
  [90137ffa] StaticArrays v0.12.1
  [2913bbd2] StatsBase v0.32.0
  [4c63d2b9] StatsFuns v0.8.0
  [09ab397b] StructArrays v0.4.0 #kf/fhe (https://github.com/Keno/StructArrays.jl)
  [a759f4b9] TimerOutputs v0.5.3
  [9f7883ad] Tracker v0.2.5
  [3bb67fe8] TranscodingStreams v0.9.5
  [30578b45] URIParser v0.4.0
  [81def892] VersionParsing v1.1.3
  [a5390f91] ZipFile v0.8.3
  [700de1a5] ZygoteRules v0.2.0 #master (https://github.com/FluxML/ZygoteRules.jl.git)
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8bb1440f] DelimitedFiles
  [8ba89e20] Distributed
  [b77e0a4c] InteractiveUtils
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [44cfe95a] Pkg
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [6462fe0b] Sockets
  [2f01184e] SparseArrays
  [10745b16] Statistics
  [4607b0f0] SuiteSparse
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode

Function for loading a package with a specific manifest

I'm just putting this here since it's semi-relevant, but also because Slack is ephemeral.

julia> import Pkg

julia> function load_manifest(; kwargs...)
           pkg = Pkg.PackageSpec(; kwargs...)
           return load_manifest(pkg)
       end

julia> function load_manifest(pkg::Pkg.Types.PackageSpec, shared::Bool = true)
           ctx = Pkg.Types.Context()
           return load_manifest(ctx, pkg, shared)
       end

julia> function load_manifest(ctx::Pkg.Types.Context, pkg::Pkg.Types.PackageSpec, shared::Bool = true)
           Pkg.Types.handle_repo_develop!(ctx, pkg, shared)
           devpath = Pkg.Types.devpath(ctx, pkg.name, shared)
           Pkg.activate(devpath)
           Pkg.instantiate()
           return devpath
       end

julia> load_manifest(url = "https://github.com/JuliaComputing/ToyFHE.jl")

julia> using ToyFHE

Write documentation

Document the version of Julia that generated the Manifest.toml?

Since the Manifest.toml file is checked in to source control, perhaps we could document somewhere which version of Julia was used to generate the manifest file?

UndefVarError: FmpzModRing not defined

While evaluating using ToyFHE, I see the following:

[ Info: Precompiling ToyFHE [ed6b25c6-c39d-11e9-27fc-075f0335bf0b]

Welcome to Nemo version 0.15.1

Nemo comes with absolutely no warranty whatsoever


Welcome to

    _    _           _
   | |  | |         | |
   | |__| | ___  ___| | _____
   |  __  |/ _ \/ __| |/ / _ \
   | |  | |  __/ (__|   <  __/
   |_|  |_|\___|\___|_|\_\___|

Version 0.6.7 ...
 ... which comes with absolutely no warranty whatsoever
(c) 2015-2019 by Claus Fieker, Tommy Hofmann and Carlo Sircana

WARNING: using Hecke.modulus in module Utils conflicts with an existing identifier.
WARNING: using Hecke.degree in module Utils conflicts with an existing identifier.
ERROR: LoadError: LoadError: UndefVarError: FmpzModRing not defined
Stacktrace:
 [1] getproperty(::Module, ::Symbol) at .\Base.jl:13
 [2] top-level scope at C:\Users\marco\.julia\packages\ToyFHE\EUUTq\src\utils.jl:33
 [3] include at .\boot.jl:328 [inlined]
 [4] include_relative(::Module, ::String) at .\loading.jl:1105
 [5] include at .\Base.jl:31 [inlined]
 [6] include(::String) at C:\Users\marco\.julia\packages\ToyFHE\EUUTq\src\ToyFHE.jl:1
 [7] top-level scope at C:\Users\marco\.julia\packages\ToyFHE\EUUTq\src\ToyFHE.jl:25
 [8] include at .\boot.jl:328 [inlined]
 [9] include_relative(::Module, ::String) at .\loading.jl:1105
 [10] include(::Module, ::String) at .\Base.jl:31
 [11] top-level scope at none:2
 [12] eval at .\boot.jl:330 [inlined]
 [13] eval(::Expr) at .\client.jl:425
 [14] top-level scope at .\none:3
in expression starting at C:\Users\marco\.julia\packages\ToyFHE\EUUTq\src\utils.jl:33
in expression starting at C:\Users\marco\.julia\packages\ToyFHE\EUUTq\src\ToyFHE.jl:25
ERROR: Failed to precompile ToyFHE [ed6b25c6-c39d-11e9-27fc-075f0335bf0b] to C:\Users\marco\.julia\compiled\v1.3\ToyFHE\EfSLj_Hqkgq.ji.
Stacktrace:
 [1] error(::String) at .\error.jl:33
 [2] compilecache(::Base.PkgId, ::String) at .\loading.jl:1283
 [3] _require(::Base.PkgId) at .\loading.jl:1024
 [4] require(::Base.PkgId) at .\loading.jl:922
 [5] require(::Module, ::Symbol) at .\loading.jl:917

Clean up Ring Element type

I don't like the explicit (i)nntt calls in all the various places. A better design would be to have a single ring element struct that keeps both representations as Union{Nothing, T} and produced the appropriate one on demand as required.

Pick smaller instances for the tests

The tests take quite a while to run. For some of the tests I wrote early one, the parameters are from real world instantiations of the schemes. This is unnecessary. We should be able to just cut down the ring dimension and make the tests much faster.

Eventually register this package in the General registry

I know that this will take some time, because currently the package relies on Keno's forked versions of several packages.

But it would be great to eventually get ToyFHE.jl registered in the General Registry.

`decrypt(circshift(c, gk))` does not work with Julia 1.5.0-beta1

I've tried to run the introductory examples on https://juliacomputing.com/blog/2019/11/22/encrypted-machine-learning.html with Julia 1.5.0-beta1. When I reached the circshift test, Julia threw the following error:

julia> decrypt(circshift(c, gk))
ERROR: MethodError: no method matching decrypt(::CipherText{CKKSEncoding{FixedRational{1099511627776,T} where T},CKKSParams,ToyFHE.NTT.RingElement{ℤ₁₃₂₉₂₂₇₉₉₇₅₆₈₀₈₁₄₅₇₄₀₂₇₀₁₂₀₇₁₀₄₂₄₈₂₅₇/(x¹⁶ + 1),ToyFHE.CRTEncoded{3,Tuple{𝔽₁₀₉₉₅₁₁₆₂₇₈₇₃,𝔽₁₀₉₉₅₁₁₆₂₈₁₆₁,𝔽₁₀₉₉₅₁₁₆₂₈₇₆₉}},StructArrays.StructArray{ToyFHE.CRTEncoded{3,Tuple{𝔽₁₀₉₉₅₁₁₆₂₇₈₇₃,𝔽₁₀₉₉₅₁₁₆₂₈₁₆₁,𝔽₁₀₉₉₅₁₁₆₂₈₇₆₉}},1,Tuple{Array{𝔽₁₀₉₉₅₁₁₆₂₇₈₇₃,1},Array{𝔽₁₀₉₉₅₁₁₆₂₈₁₆₁,1},Array{𝔽₁₀₉₉₅₁₁₆₂₈₇₆₉,1}},Int64}},2})
Closest candidates are:
  decrypt(::PrivKey, ::CipherText{T,P,T1,N} where N where T1 where P<:ToyFHE.SHEShemeParams) where T at /home/mschlott/gdrive/work/code/CryptoSim.jl/ToyFHE.jl/src/rlwe_she.jl:199
  decrypt(::KeyPair, ::Any) at /home/whatever/ToyFHE.jl/src/rlwe_she.jl:217
Stacktrace:
 [1] top-level scope at REPL[21]:1

Here's an MWE:

julia> using ToyFHE

julia> N = 8;

julia> ℛ = NegacyclicRing(2N, (40, 40, 40))
ℤ₁₃₂₉₂₂₇₉₉₇₅₆₈₀₈₁₄₅₇₄₀₂₇₀₁₂₀₇₁₀₄₂₄₈₂₅₇/(x¹⁶ + 1)

julia> params = CKKSParams(ℛ)
CKKS parameters

julia> Tscale = FixedRational{2^40}
FixedRational{1099511627776,T} where T

julia> plain = CKKSEncoding{Tscale}(zero(ℛ))
8-element CKKSEncoding{FixedRational{1099511627776,T} where T} with indices 0:7:
 0.0 + 0.0im
 0.0 + 0.0im
 0.0 + 0.0im
 0.0 + 0.0im
 0.0 + 0.0im
 0.0 + 0.0im
 0.0 + 0.0im
 0.0 + 0.0im

julia> kp = keygen(params)
CKKS key pair

julia> kp.priv
CKKS private key

julia> kp.pub
CKKS public key

julia> foreach(i->plain[i] = i+1, 0:7); plain
8-element CKKSEncoding{FixedRational{1099511627776,T} where T} with indices 0:7:
 1.0 + 0.0im
 2.0 + 0.0im
 3.0 + 0.0im
 4.0 + 0.0im
 5.0 + 0.0im
 6.0 + 0.0im
 7.0 + 0.0im
 8.0 + 0.0im

julia> c = encrypt(kp.pub, plain)
CKKS ciphertext (length 2, encoding CKKSEncoding{FixedRational{1099511627776,T} where T})

julia> gk = keygen(GaloisKey, kp.priv; steps=2)
CKKS galois key (element 25)

julia> decrypt(circshift(c, gk))

Any idea what the problem could be?

I wonder which is your julia verision

I'm using julia 1.0.0 to run your code in Ubuntu18.04
however, when i input "include("train.jl")"
I encounter some problems:

I guess that I use diferent version, so i wonder which version is your julia.'
Thank you!

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