## LiDIA

### Summary

LiDIA is a C++ library for computational number theory which provides a collection of highly optimized implementations of various multiprecision data types and time-intensive algorithms.

### Authors

The LiDIA Group

### Vendor

Cryptography and Computer Algebra Group at Darmstadt University of Technology

### Links

### Status

incomplete information or not officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- basic arithmetic
- bit operations
- Buchmann's subexponential algorithm
- Chinese remainder
- computational number theory
- computing classgroups
- counting points on elliptic curves over finite fields
- cryptography
- elliptic curve method
- elliptic curves
- factoring ideals of algebraic number fields
- factorization of polynomials over finite fields
- finite fields linear algebra
- galois fields
- greatest common divisor of polynomials
- hash tables
- integer factorization
- integers
- integration
- Jacobi symbol
- lattice basis reduction
- lattice reductions
- lattices
- Legendre symbol
- linear algebra
- matrices
- matrix
- multiprecision arithmetics
- number theory
- polynomial factorization
- polynomials
- power series
- primality proofing
- prime proofer
- probabilistic primality tests
- proof primality
- quadratic number fields
- quadratic residue
- rational factorization
- rational numbers
- self-initializing multipolynomial quadratic sieve with Lanczos algorithm
- trial division
- trigonometric function
- univariate polynomials
- vectors
- V. Shoup's algorithms