A library for lattice cryptography.

Latest on Hackage:

This package is not currently in any snapshots. If you're interested in using it, we recommend adding it to Stackage Nightly. Doing so will make builds more reliable, and allow to host generated Haddocks.

GPL-2 licensed by Eric Crockett, Chris Peikert
Maintained by Eric Crockett

This package is primarily a library providing interfaces for lattice cryptography
primitives. There are two main interfaces: 'Cyclotomic' and 'Tensor'. The
Cyclotomic interface is the outward-facing API that is used to build cryptographic
applications like pseudo-random functions, encryption, etc. The Tensor interface allows
multiple backends to implement the functionality used by the Cyclotomic interface.
Unless you are writing a new backend implementation, you shouldn't need to
understand the Tensor interface. However, you *will* need an implementation of the
Tensor interface in order to test, benchmark, and run applications.

Most of the functionality in Lol is exported by two modules:

* 'Crypto.Lol' exports the primary *interfaces* of Lol

* 'Crypto.Lol.Types' exports concrete types that would be used by most

For a brief introduction to relevant mathematical notation, see 'Crypto.Lol'.

Overview of key modules, roughly from highest- to lowest-level:

Cyclotomic layer:
* 'Crypto.Lol.Cyclotomic.Cyc', which defines an interface for using cyclotomic
fields, rings \( R \), and quotient rings \( R_q=R/qR \); as well as many
other commonly used operations, e.g., converting
between rings, decoding and decomposing elements, modulus
reduction/rounding, etc. 'Cyc' is a safe wrapper around the
'UCyc' type, which exposes some representation-dependent operations.
'UCyc' (and hence 'Cyc') is implemented using a generic 'Tensor'
(described below).

Tensor layer:
* 'Crypto.Lol.Cyclotomic.Tensor', which defines a class that encapsulates all
the necessary linear transformations for operating on representations of
\( R \)- and \( R_q \)-elements, e.g., the CRT transform, converting between
the powerful and decoding bases, generating error terms, etc.

* You will need an implementation of the 'Tensor' interface in order to use Lol.
Two implementations can be found at
< lol-cpp>
and < lol-repa>.

Base ring layer:
* 'Crypto.Lol.Types.FiniteField', which gives an unoptimized implementation of
finite field arithmetic. To use this module, you will need an instance of
'IrreduciblePoly'. These instances provide irreducible polynomials
for various degrees and base fields. One (orphan) instance is provided for
characteristic 2 fields of size up to 2^128 in
'Crypto.Lol.Types.IrreducibleChar2', and is exported by 'Crypto.Lol.Types'.
If you need to use an unsupported finite field, define your own
instance of 'IrreduciblePoly' and do **not** import 'IrreducibleChar2'.

* 'Crypto.Lol.Types.Unsafe.ZqBasic', which is a basic implementation of
\( \Z_q=\Z/q\Z \) arithmetic.

* 'Crypto.Lol.Factored', which contains type-level support code for
factored integers. It also supports "reifying" 'Int's at runtime as static
types and "reflecting" those types as integers back to the code..
'Factored' types are mainly used to represent cyclotomic indices.

Tests and benchmarks can be found in the packages < lol-tests> and < lol-benches>,
respectively, though they are instantiated in individual tensors.


Changelog for lol project

  • Support for serializing ring products, linear functions, and TypeReps.
  • Split previous lol package into separate tensor packages lol-cpp and lol-repa and utility packages lol-benches and lol-tests.
  • Moved test and benchmark code to packages lol-tests and lol-benches, respectively.
  • Simpler tests and benchmarks (though microbenchmarks might be slightly slower than
  • Fixed minor bug in IrreducibleChar2.hs
  • Moved tensor-specific instances (Elt, Unbox, etc) to tensor packages (lol-cpp and lol-repa).

  • Updates to README.

  • Benchmarks now compile.

  • Dramatically improved CT performance using Haskell INLINE/INLINABLE pragmas.
  • Removed fmapTM from Tensor.
  • Removed valuePPs, totientPPs, radicalPPs, oddRadicalPPs from Factored.
  • K_q (i.e. base ring RRq) is now serialized with a discrete modulus.
  • Fixed a bug in UCyc.divG. The result is divG is now split into divGPow divGDec, and divGCRTC.
  • Added UCycPC type synonym to UCyc.
  • Added data-level interface for Factored.
  • Added Random instance for FiniteField.

  • Added support for GHC 8.0, also compatible with 7.10.3
  • Converted documentation to MathJax
  • Renamed Tensor.Matrix -> Tensor.Kron
  • Added Crypto.Lol.Types interface file

  • Support for protocol-buffers
  • Support for reifying Factored types
  • Support for reals (RR) mod q
  • Replaced C backend with C++ backend
  • Renamed LatticePrelude -> Prelude
  • Added monad argument to CRTrans

  • Added benchmarks
  • Better performance for C backend with RNS base ring
  • UCyc exposes bases as type for safety
  • Other safety improvements throughout
  • Easier index representation with TemplateHaskell
  • Split SymmSHE into new package lol-apps.

  • Fixed bug in Box-Muller sampling routine.
  • Changed how we lift linear functions for better noise control.
  • Split entailment functions in Tensor.
  • Increased performance in FastCyc by better handling Sub constructors.
comments powered byDisqus