.. _functions-based-on-gf-p:

Functions Based on GF(*p*)
==========================


This section describes functions designed to specify the elliptic curve
cryptosystem and perform various operations on the elliptic curve
defined over a prime finite field. The examples of the operations are
shown below:


- Setting up operations:
  `ECCPSet <eccpset.html>`__
  sets up elliptic curve domain parameters.
  `ECCPSetKeyPair <eccpsetkeypair.html>`__
  sets a pair of public and private keys for the given cryptosystem.
- Computation operations:
  `ECCPAddPoint <eccpaddpoint.html>`__
  adds two points on the elliptic curve.
  `ECCPMulPointScalar <eccpmulpointscalar.html>`__
  performs the scalar multiplication of a point on the elliptic curve.
  `ECCPSignDSA <eccpsigndsa.html>`__
  computes the digital signature of a message.
- Validation operations:
  `ECCPValidate <eccpvalidate.html>`__
  checks validity of the elliptic curve domain parameters.
  `ECCPValidateKeyPair <eccpvalidatekeypair.html>`__
  validates correctness of the public and private keys.
- Generation operations:
  `ECCPGenKeyPair <eccpgenkeypair.html>`__
  generates a private key and computes a public key for the given
  elliptic cryptosystem.
- Retrieval operations:
  `ECCPGet <eccpget.html>`__
  retrieves elliptic curve domain parameters.
  `ECCPGetOrderBitSize <eccpgetorderbitsize.html>`__
  retrieves the size of a base point in bytes.


All functions described in this section employ a context IppsECCPState
that catches several auxiliary components specifying operations
performed on the elliptic curve or entire elliptic cryptosystem. ECCP
stands for Elliptic Curve Cryptography Prime and means that all
functions whose name include this abbreviation perform operations over a
prime finite field GF( *p*).


The IppECCType enumerator lists standard elliptic curves supported. You
can select a particular type in a call to
`ECCPSetStd <eccpsetstd.html>`__.


The table below associates each value of IppECCType with parameters of
the elliptic curve and provides a reference to the appropriate
specification.


.. list-table:: Standard Elliptic Curves
   :header-rows: 1

   * - Value of IppECCType   
     - Name of the Curve    
     - Reference    
   * - ippECarbitrary   
     - Not applicable    
     - No reference because of arbitrary parameters.    
   * - ippECstd112r1   
     - secp112r1   
     - [`SEC2 <bibliography.html>`__]    
   * - ippECstd112r2   
     - secp112r2   
     - [SEC2]    
   * - ippECstd128r1   
     - secp128r1   
     - [SEC2]    
   * - ippECstd128r2   
     - secp128r2   
     - [SEC2]    
   * - ippECstd160r1   
     - secp160r1   
     - [SEC2]    
   * - ippECstd160r2   
     - secp160r2   
     - [SEC2]    
   * - ippECstd192r1   
     - secp192r1   
     - [SEC2]    
   * - ippECstd224r1   
     - secp224r1   
     - [SEC2]    
   * - ippECstd256r1   
     - secp256r1   
     - [SEC2]    
   * - ippECstd384r1   
     - secp384r1   
     - [SEC2]    
   * - ippECstd521r1   
     - secp521r1   
     - [SEC2]    
   * - ippECstdSM2   
     - SM2   
     - [`SM2 <bibliography.html>`__]    




For more information on parameters recommended for the functions, see
[`SEC2 <bibliography.html>`__] and
[`SM2 <bibliography.html>`__].


.. note::


   .. rubric:: Important
      :class: NoteTipHead

   To provide minimum security of the elliptic curve cryptosystem over a
   prime finite field, the length of the underlying prime must be equal
   to or greater than 160 bits.

.. toctree::
   :maxdepth: 1

   
   eccpgetsize
   eccpgetsizestd
   eccpinit
   eccpinitstd
   eccpbindgxytblstd
   eccpset
   eccpsetstd
   eccpget
   eccpgetorderbitsize
   eccpvalidate
   eccppointgetsize
   eccppointinit
   eccpsetpoint
   eccpsetpointatinfinity
   eccpgetpoint
   eccpcheckpoint
   eccpcomparepoint
   eccpnegativepoint
   eccpaddpoint
   eccpmulpointscalar
   eccpgenkeypair
   eccppublickey
   eccpvalidatekeypair
   eccpsetkeypair
   eccpsharedsecretdh
   eccpsharedsecretdhc
   eccpsigndsa
   eccpverifydsa
   eccpsignnr
   eccpverifynr
   eccpsignsm2
   eccpverifysm2
   signing-verification-using-the-elliptic-curve-cryptography-functions-over-a-prime-finite-field