Module ec.group

EC_GROUP module for Lua OpenSSL binding.

This module provides a complete wrapper for OpenSSL’s EC_GROUP operations, enabling elliptic curve group mathematical operations similar to BIGNUM.

Usage:

    group = require('openssl').ec.group

Functions

new (curve[, form[, flag]]) Create EC group and generator point from curve specification
dup () Duplicate an EC_GROUP.
generator () Get the generator point of the group.
order () Get the order of the group.
cofactor () Get the cofactor of the group.
degree () Get the degree of the group (field size in bits).
curve_name () Get the curve name NID.
asn1_flag ([flag]) Get or set the ASN1 flag.
point_conversion_form ([form]) Get or set the point conversion form.
curve () Get curve parameters (p, a, b).
seed () Get the seed value for the group.
parse () Parse the EC group to extract all parameters.
equal (other) Compare two EC groups for equality.
point_new () Create a new EC point on this group.
point_dup (point) Duplicate an EC point on this group.
point_equal (a, b) Compare two EC points for equality.
point2oct (point[, form]) Convert EC point to octet string.
oct2point (oct) Convert octet string to EC point.
point2bn (point[, form]) Convert EC point to BIGNUM.
bn2point (bn) Convert BIGNUM to EC point.
point2hex (point[, form]) Convert EC point to hexadecimal string.
hex2point (hex) Convert hexadecimal string to EC point.
affine_coordinates (group, point[, x[, y]]) Get or set affine coordinates of an EC point.
set_to_infinity (group) Set EC point to infinity.
is_at_infinity (group) Check if EC point is at infinity.
is_on_curve (group) Check if EC point is on the curve.
point_add (group, a, b) Add two EC points.
point_dbl (group) Double an EC point.
point_invert (group) Invert an EC point.
point_mul (group, n[, q[, m]]) Multiply EC point by a scalar.
generate_key () Generate EC key pair from this group.
list () List all available elliptic curve names.


Functions

new (curve[, form[, flag]])
Create EC group and generator point from curve specification

Parameters:

  • curve string, table or number curve specification (name, parameters, or NID)
  • form string or number point_conversion_form (optional)
  • flag string or number asn1_flag (optional)

Returns:

    openssl.ec_group the elliptic curve group

Or

    openssl.ec_point the generator point

Or

  1. nil on error
  2. string error message — @see OpenSSL function: EC_GROUP_new_by_curve_name — @see OpenSSL function: EC_GROUP_new_curve_GFp

Usage:

    local group = require('openssl').group

-- Create group from curve name
local ec_group, generator = group.new('prime256v1')

-- Create group from NID
local ec_group2, generator2 = group.new(415)  -- NID for prime256v1

-- Create group with parameters
local ec_group3, generator3 = group.new({
  p = '0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF',
  a = '0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC',
  b = '0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B',
  order = '0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551',
  generator = '046B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C2964FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5',
  cofactor = 1
})
dup ()
Duplicate an EC_GROUP.

Returns:

    openssl.ec_group duplicated elliptic curve group
generator ()
Get the generator point of the group.

Returns:

    openssl.ec_point generator point of the curve
order ()
Get the order of the group.

Returns:

    openssl.bn order of the group
cofactor ()
Get the cofactor of the group.

Returns:

    openssl.bn cofactor of the group
degree ()
Get the degree of the group (field size in bits).

Returns:

    number degree of the group
curve_name ()
Get the curve name NID.

Returns:

    number NID of the curve
asn1_flag ([flag])
Get or set the ASN1 flag.

Parameters:

  • flag string or number ASN1 flag (“explicit” or “named_curve”) (optional)

Returns:

  1. string or number current ASN1 flag (when getting)
  2. openssl.ec_group self (when setting)
point_conversion_form ([form])
Get or set the point conversion form.

Parameters:

  • form string or number point conversion form (“compressed”, “uncompressed”, or “hybrid”) (optional)

Returns:

  1. string or number current conversion form (when getting)
  2. openssl.ec_group self (when setting)
curve ()
Get curve parameters (p, a, b).

Returns:

    table containing p, a, b as BIGNUM objects
seed ()
Get the seed value for the group.

Returns:

    string or nil seed value or nil if not set
parse ()
Parse the EC group to extract all parameters.

Returns:

    table containing all group parameters (generator, order, cofactor, degree, curve_name, etc.)
equal (other)
Compare two EC groups for equality.

Parameters:

  • other openssl.ec_group EC group to compare

Returns:

    boolean true if equal, false otherwise
point_new ()
Create a new EC point on this group.

Returns:

    openssl.ec_point new elliptic curve point (at infinity)
point_dup (point)
Duplicate an EC point on this group.

Parameters:

  • point openssl.ec_point the EC point to duplicate

Returns:

    openssl.ec_point duplicated EC point
point_equal (a, b)
Compare two EC points for equality.

Parameters:

  • a openssl.ec_point first EC point
  • b openssl.ec_point second EC point

Returns:

    boolean true if equal, false otherwise
point2oct (point[, form])
Convert EC point to octet string.

Parameters:

  • point openssl.ec_point the EC point
  • form string point conversion form (“compressed”, “uncompressed”, or “hybrid”) (optional)

Returns:

    string or nil octet string representation or nil on failure
oct2point (oct)
Convert octet string to EC point.

Parameters:

  • oct string octet string representation

Returns:

    ec_point or nil the resulting EC point or nil on failure
point2bn (point[, form])
Convert EC point to BIGNUM.

Parameters:

  • point openssl.ec_point the EC point
  • form string point conversion form (“compressed”, “uncompressed”, or “hybrid”) (optional)

Returns:

    bn or nil the resulting BIGNUM or nil on failure
bn2point (bn)
Convert BIGNUM to EC point.

Parameters:

  • bn openssl.bn the BIGNUM to convert

Returns:

    ec_point or nil the resulting EC point or nil on failure
point2hex (point[, form])
Convert EC point to hexadecimal string.

Parameters:

  • point openssl.ec_point the EC point
  • form string point conversion form (“compressed”, “uncompressed”, or “hybrid”) (optional)

Returns:

    string or nil hexadecimal string representation or nil on failure
hex2point (hex)
Convert hexadecimal string to EC point.

Parameters:

  • hex string hexadecimal string representation

Returns:

    ec_point or nil the resulting EC point or nil on failure
affine_coordinates (group, point[, x[, y]])
Get or set affine coordinates of an EC point.

Parameters:

  • group openssl.ec_group the EC group
  • point openssl.ec_point the EC point
  • x openssl.bn x coordinate (for setting) (optional)
  • y openssl.bn y coordinate (for setting) (optional)

Returns:

  1. openssl.bn x coordinate (when getting)
  2. openssl.bn y coordinate (when getting)
set_to_infinity (group)
Set EC point to infinity.

Parameters:

  • group openssl.ec_group the EC group

Returns:

    openssl.ec_point self
is_at_infinity (group)
Check if EC point is at infinity.

Parameters:

  • group openssl.ec_group the EC group

Returns:

    boolean true if at infinity, false otherwise
is_on_curve (group)
Check if EC point is on the curve.

Parameters:

  • group openssl.ec_group the EC group

Returns:

    boolean true if on curve, false otherwise
point_add (group, a, b)
Add two EC points.

Parameters:

  • group openssl.ec_group the EC group
  • a openssl.ec_point first point
  • b openssl.ec_point second point

Returns:

    openssl.ec_point result point (a + b)
point_dbl (group)
Double an EC point.

Parameters:

  • group openssl.ec_group the EC group

Returns:

    openssl.ec_point result point (2 * point)
point_invert (group)
Invert an EC point.

Parameters:

  • group openssl.ec_group the EC group

Returns:

    openssl.ec_point self (inverted)
point_mul (group, n[, q[, m]])
Multiply EC point by a scalar.

Parameters:

  • group openssl.ec_group the EC group
  • n bn or number scalar multiplier
  • q openssl.ec_point optional point for double scalar multiplication (optional)
  • m openssl.bn optional second scalar for double scalar multiplication (optional)

Returns:

    openssl.ec_point result point (n point) or (n point + m * q)
generate_key ()
Generate EC key pair from this group.

Returns:

    ec_key generated EC key object or nil if failed
list ()
List all available elliptic curve names.

Returns:

    table array of curve names and descriptions
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