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| 1 | .\" $OpenBSD: ec.3,v 1.4 2016/12/08 21:48:50 jmc Exp $ | ||
| 2 | .\" | ||
| 3 | .Dd $Mdocdate: December 8 2016 $ | ||
| 4 | .Dt EC 3 | ||
| 5 | .Os | ||
| 6 | .Sh NAME | ||
| 7 | .Nm ec | ||
| 8 | .Nd Elliptic Curve functions | ||
| 9 | .Sh SYNOPSIS | ||
| 10 | .In openssl/ec.h | ||
| 11 | .Sh DESCRIPTION | ||
| 12 | This library provides an extensive set of functions for performing | ||
| 13 | operations on elliptic curves over finite fields. | ||
| 14 | In general an elliptic curve is one with an equation of the form: | ||
| 15 | .Pp | ||
| 16 | .Dl y^2 = x^3 + ax + b | ||
| 17 | .Pp | ||
| 18 | An | ||
| 19 | .Vt EC_GROUP | ||
| 20 | structure is used to represent the definition of an elliptic curve. | ||
| 21 | Points on a curve are stored using an | ||
| 22 | .Vt EC_POINT | ||
| 23 | structure. | ||
| 24 | An | ||
| 25 | .Vt EC_KEY | ||
| 26 | is used to hold a private/public key pair, where a private key is simply a | ||
| 27 | .Vt BIGNUM | ||
| 28 | and a public key is a point on a curve represented by an | ||
| 29 | .Vt EC_POINT . | ||
| 30 | .Pp | ||
| 31 | The library contains a number of alternative implementations of the | ||
| 32 | different functions. | ||
| 33 | Each implementation is optimised for different scenarios. | ||
| 34 | No matter which implementation is being used, the interface remains the | ||
| 35 | same. | ||
| 36 | The library handles calling the correct implementation when an interface | ||
| 37 | function is invoked. | ||
| 38 | An implementation is represented by an | ||
| 39 | .Vt EC_METHOD | ||
| 40 | structure. | ||
| 41 | .Pp | ||
| 42 | The creation and destruction of | ||
| 43 | .Vt EC_GROUP | ||
| 44 | objects is described in | ||
| 45 | .Xr EC_GROUP_new 3 . | ||
| 46 | Functions for manipulating | ||
| 47 | .Vt EC_GROUP | ||
| 48 | objects are described in | ||
| 49 | .Xr EC_GROUP_copy 3 . | ||
| 50 | .Pp | ||
| 51 | Functions for creating, destroying and manipulating | ||
| 52 | .Vt EC_POINT | ||
| 53 | objects are explained in | ||
| 54 | .Xr EC_POINT_new 3 , | ||
| 55 | whilst functions for performing mathematical operations and tests on | ||
| 56 | .Vt EC_POINT Ns s | ||
| 57 | are covered in | ||
| 58 | .Xr EC_POINT_add 3 . | ||
| 59 | .Pp | ||
| 60 | For working with private and public keys refer to | ||
| 61 | .Xr EC_KEY_new 3 . | ||
| 62 | Implementations are covered in | ||
| 63 | .Xr EC_GFp_simple_method 3 . | ||
| 64 | .Pp | ||
| 65 | For information on encoding and decoding curve parameters to and | ||
| 66 | from ASN.1 see | ||
| 67 | .Xr d2i_ECPKParameters 3 . | ||
| 68 | .Sh SEE ALSO | ||
| 69 | .Xr crypto 3 , | ||
| 70 | .Xr d2i_ECPKParameters 3 , | ||
| 71 | .Xr EC_GFp_simple_method 3 , | ||
| 72 | .Xr EC_GROUP_copy 3 , | ||
| 73 | .Xr EC_GROUP_new 3 , | ||
| 74 | .Xr EC_KEY_new 3 , | ||
| 75 | .Xr EC_POINT_add 3 , | ||
| 76 | .Xr EC_POINT_new 3 , | ||
| 77 | .Xr EVP_PKEY_CTX_set_ec_paramgen_curve_nid 3 | ||