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1 | =pod |
2 | ||
3 | =head1 NAME | |
4 | ||
5 | EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy, EC_POINT_dup, EC_POINT_method_of, EC_POINT_set_to_infinity, EC_POINT_set_Jprojective_coordinates, EC_POINT_get_Jprojective_coordinates_GFp, EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp, EC_POINT_set_compressed_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m, EC_POINT_get_affine_coordinates_GF2m, EC_POINT_set_compressed_coordinates_GF2m, EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex, EC_POINT_hex2point - Functions for creating, destroying and manipulating B<EC_POINT> objects. | |
6 | ||
7 | =head1 SYNOPSIS | |
8 | ||
9 | #include <openssl/ec.h> | |
10 | #include <openssl/bn.h> | |
11 | ||
12 | EC_POINT *EC_POINT_new(const EC_GROUP *group); | |
13 | void EC_POINT_free(EC_POINT *point); | |
14 | void EC_POINT_clear_free(EC_POINT *point); | |
15 | int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src); | |
16 | EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group); | |
17 | const EC_METHOD *EC_POINT_method_of(const EC_POINT *point); | |
18 | int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point); | |
19 | int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, | |
20 | const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx); | |
21 | int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, | |
22 | const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx); | |
23 | int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, | |
24 | const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx); | |
25 | int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, | |
26 | const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); | |
27 | int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, | |
28 | const BIGNUM *x, int y_bit, BN_CTX *ctx); | |
29 | int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, | |
30 | const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx); | |
31 | int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, | |
32 | const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); | |
33 | int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, | |
34 | const BIGNUM *x, int y_bit, BN_CTX *ctx); | |
35 | size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p, | |
36 | point_conversion_form_t form, | |
37 | unsigned char *buf, size_t len, BN_CTX *ctx); | |
38 | int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p, | |
39 | const unsigned char *buf, size_t len, BN_CTX *ctx); | |
40 | BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *, | |
41 | point_conversion_form_t form, BIGNUM *, BN_CTX *); | |
42 | EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *, | |
43 | EC_POINT *, BN_CTX *); | |
44 | char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *, | |
45 | point_conversion_form_t form, BN_CTX *); | |
46 | EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *, | |
47 | EC_POINT *, BN_CTX *); | |
48 | ||
49 | ||
50 | =head1 DESCRIPTION | |
51 | ||
52 | An EC_POINT represents a point on a curve. A new point is constructed by calling the function EC_POINT_new and providing the B<group> | |
53 | object that the point relates to. | |
54 | ||
55 | EC_POINT_free frees the memory associated with the EC_POINT. | |
8fdc3734 | 56 | if B<point> is NULL nothing is done. |
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57 | |
58 | EC_POINT_clear_free destroys any sensitive data held within the EC_POINT and then frees its memory. | |
8fdc3734 | 59 | if B<point> is NULL nothing is done. |
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60 | |
61 | EC_POINT_copy copies the point B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD. | |
62 | ||
63 | EC_POINT_dup creates a new EC_POINT object and copies the content from B<src> to the newly created | |
64 | EC_POINT object. | |
65 | ||
66 | EC_POINT_method_of obtains the EC_METHOD associated with B<point>. | |
67 | ||
68 | A valid point on a curve is the special point at infinity. A point is set to be at infinity by calling EC_POINT_set_to_infinity. | |
69 | ||
70 | The affine co-ordinates for a point describe a point in terms of its x and y position. The functions | |
71 | EC_POINT_set_affine_coordinates_GFp and EC_POINT_set_affine_coordinates_GF2m set the B<x> and B<y> co-ordinates for the point | |
72 | B<p> defined over the curve given in B<group>. | |
73 | ||
74 | As well as the affine co-ordinates, a point can alternatively be described in terms of its Jacobian | |
75 | projective co-ordinates (for Fp curves only). Jacobian projective co-ordinates are expressed as three values x, y and z. Working in | |
76 | this co-ordinate system provides more efficient point multiplication operations. | |
77 | A mapping exists between Jacobian projective co-ordinates and affine co-ordinates. A Jacobian projective co-ordinate (x, y, z) can be written as an affine co-ordinate as (x/(z^2), y/(z^3)). Conversion to Jacobian projective to affine co-ordinates is simple. The co-ordinate (x, y) is | |
78 | mapped to (x, y, 1). To set or get the projective co-ordinates use EC_POINT_set_Jprojective_coordinates_GFp and | |
79 | EC_POINT_get_Jprojective_coordinates_GFp respectively. | |
80 | ||
81 | Points can also be described in terms of their compressed co-ordinates. For a point (x, y), for any given value for x such that the point is | |
82 | on the curve there will only ever be two possible values for y. Therefore a point can be set using the EC_POINT_set_compressed_coordinates_GFp | |
83 | and EC_POINT_set_compressed_coordinates_GF2m functions where B<x> is the x co-ordinate and B<y_bit> is a value 0 or 1 to identify which of | |
84 | the two possible values for y should be used. | |
85 | ||
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86 | In addition EC_POINTs can be converted to and from various external |
87 | representations. Supported representations are octet strings, BIGNUMs and | |
88 | hexadecimal. Octet strings are stored in a buffer along with an associated | |
89 | buffer length. A point held in a BIGNUM is calculated by converting the point to | |
90 | an octet string and then converting that octet string into a BIGNUM integer. | |
91 | Points in hexadecimal format are stored in a NULL terminated character string | |
92 | where each character is one of the printable values 0-9 or A-F (or a-f). | |
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93 | |
94 | The functions EC_POINT_point2oct, EC_POINT_oct2point, EC_POINT_point2bn, EC_POINT_bn2point, EC_POINT_point2hex and EC_POINT_hex2point convert | |
95 | from and to EC_POINTs for the formats: octet string, BIGNUM and hexadecimal respectively. | |
96 | ||
97 | The function EC_POINT_point2oct must be supplied with a buffer long enough to store the octet string. The return value provides the number of | |
98 | octets stored. Calling the function with a NULL buffer will not perform the conversion but will still return the required buffer length. | |
99 | ||
100 | The function EC_POINT_point2hex will allocate sufficient memory to store the hexadecimal string. It is the caller's responsibility to free | |
101 | this memory with a subsequent call to OPENSSL_free(). | |
102 | ||
103 | =head1 RETURN VALUES | |
104 | ||
105 | EC_POINT_new and EC_POINT_dup return the newly allocated EC_POINT or NULL on error. | |
106 | ||
107 | The following functions return 1 on success or 0 on error: EC_POINT_copy, EC_POINT_set_to_infinity, EC_POINT_set_Jprojective_coordinates_GFp, | |
108 | EC_POINT_get_Jprojective_coordinates_GFp, EC_POINT_set_affine_coordinates_GFp, EC_POINT_get_affine_coordinates_GFp, | |
109 | EC_POINT_set_compressed_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m, EC_POINT_get_affine_coordinates_GF2m, | |
110 | EC_POINT_set_compressed_coordinates_GF2m and EC_POINT_oct2point. | |
111 | ||
112 | EC_POINT_method_of returns the EC_METHOD associated with the supplied EC_POINT. | |
113 | ||
114 | EC_POINT_point2oct returns the length of the required buffer, or 0 on error. | |
115 | ||
116 | EC_POINT_point2bn returns the pointer to the BIGNUM supplied, or NULL on error. | |
117 | ||
118 | EC_POINT_bn2point returns the pointer to the EC_POINT supplied, or NULL on error. | |
119 | ||
120 | EC_POINT_point2hex returns a pointer to the hex string, or NULL on error. | |
121 | ||
122 | EC_POINT_hex2point returns the pointer to the EC_POINT supplied, or NULL on error. | |
123 | ||
124 | =head1 SEE ALSO | |
125 | ||
9b86974e RS |
126 | L<crypto(3)>, L<ec(3)>, L<EC_GROUP_new(3)>, L<EC_GROUP_copy(3)>, |
127 | L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, | |
128 | L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> | |
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129 | |
130 | =cut |