# Overview

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VERIFICATUM ELLIPTIC CURVE LIBRARY (VEC)

This library implements elliptic curves based on the GMP library, for
simultaneous or fixed base modular exponentiation. The formulas used
are taken from <http://www.hyperelliptic.org>.

The purpose of this library is twofold. Firstly, we want a
self-contained and relatively small library that we hope can converge
to a static state. Secondly, our particular application allow using

Our code is not intended to be secure against side-channel attacks,
since we do not need it for the applications we have in mind. It is
the responsibility of the user to make sure that this is the case in
their application.

For details on exponentiation techniques, a good source is Handbook of
Applied Cryptography, Menezes, Oorshot, and Vanstone, which is
additional techniques only suitable for very large number of
exponentiations.

We have copied optimized code from the OpenSSL project,
<http://www.openssl.org>, for a few standard curves. These are P-224
(written by Emilia Käsper), P-256 and P-521 (written by David
Langley). This code is in turn heavily inspired by the implementation
of Curve25519 by Dan Bernstein. The optimized code is roughly a factor
of three faster than the code based cleanly on top of GMP, which
explains the difference in running time between curves of the same
size.

Torbjorn Granlund helped us with the benchmarking. Emilia Käsper took
the time to answer our questions about her code and interpreting the
benchmarks. Dan Bernstein gave advice on how to implement the default
curves and pointed to Emilias code.

Some of the algorithms are implemented using macros. This may be
thought of as poor man's C++ templates. The rationale behind this
approach is that it is a way to include specialized add/double
routines implemented by others in such a way that their datatypes need
not be modified. Instead all that is needed is a macro file that maps
actual datatypes to macros.

This is necessary, since any conversion to/from a canonical type,
e.g., based on GMP, is too costly when the curve operations are
aggressively optimized. We avoid C++ to not involve yet another
language.

The following assumes that you are using a release. Developers should

BUILDING

Building has been tested with GMP 6.1.1. Then LIBRARY_PATH must point
to libgmp.la and C_INCLUDE_PATH must point to gmp.h. This is usually
the case automatically after installing GMP.

Then use

\$ ./configure
\$ make

to build the library.

INSTALLING

Use

\$ make install

to install the library libvec.{la,a,so}.

USAGE

The software is supposed to be used by other applications, but you can
use

\$ make check

or

\$ vec test

to test the arithmetic of all implemented curves, and you can use

\$ make bench

or

\$ vec speed

to get some benchmarks. Please consult the code to see exactly what is
measured before drawing any conclusions. Both commands also accept
names of curves as input to restrict the execution to these, e.g.,

\$ vec test P-224 P-256

tests the arithmetic of the curves P-224 and P-256 and nothing else.

API DOCUMENTATION

You may use

\$ make api

to build also some documentation using doxygen (this assumes you have
installed doxygen). The API is not installed anywhere. You can copy it
to any location.

REPORTING BUGS

Minor bugs should be reported in the repository system as issues or
bugs. Security critical bugs, vulnerabilities, etc should be reported
directly to Verificatum AB. We will make best effort to disclose the
information in a responsible way before the finder gets proper credit.
```