@hackage lol0.5.0.2

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 instantiations including tensors, base rings, and cryptographic

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.

• 'Crypto.Lol.Cyclotomic.Tensor.RepaTensor', which gives an implementation of the 'Tensor' class based on the "repa" package, a highly optimized and parallelizable array library.

• 'Crypto.Lol.Cyclotomic.Tensor.CTensor', which gives an implementation of the 'Tensor' class using a C++ backend via Haskell's FFI.

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.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.