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1.Dd $Mdocdate: November 5 2016 $
2.Dt EC 3
3.Os
4.Sh NAME
5.Nm ec
6.Nd Elliptic Curve functions
7.Sh SYNOPSIS
8.In openssl/ec.h
9.In openssl/bn.h
10.Ft const EC_METHOD *
11.Fn EC_GFp_simple_method void
12.Ft const EC_METHOD *
13.Fn EC_GFp_mont_method void
14.Ft const EC_METHOD *
15.Fn EC_GFp_nist_method void
16.Ft const EC_METHOD *
17.Fn EC_GFp_nistp224_method void
18.Ft const EC_METHOD *
19.Fn EC_GFp_nistp256_method void
20.Ft const EC_METHOD *
21.Fn EC_GFp_nistp521_method void
22.Ft const EC_METHOD *
23.Fn EC_GF2m_simple_method void
24.Ft EC_GROUP *
25.Fo EC_GROUP_new
26.Fa "const EC_METHOD *meth"
27.Fc
28.Ft void
29.Fo EC_GROUP_free
30.Fa "EC_GROUP *group"
31.Fc
32.Ft void
33.Fo EC_GROUP_clear_free
34.Fa "EC_GROUP *group"
35.Fc
36.Ft int
37.Fo EC_GROUP_copy
38.Fa "EC_GROUP *dst"
39.Fa "const EC_GROUP *src"
40.Fc
41.Ft EC_GROUP *
42.Fo EC_GROUP_dup
43.Fa "const EC_GROUP *src"
44.Fc
45.Ft const EC_METHOD *
46.Fo EC_GROUP_method_of
47.Fa "const EC_GROUP *group"
48.Fc
49.Ft int
50.Fo EC_METHOD_get_field_type
51.Fa "const EC_METHOD *meth"
52.Fc
53.Ft int
54.Fo EC_GROUP_set_generator
55.Fa "EC_GROUP *group"
56.Fa "const EC_POINT *generator"
57.Fa "const BIGNUM *order"
58.Fa "const BIGNUM *cofactor"
59.Fc
60.Ft const EC_POINT *
61.Fo EC_GROUP_get0_generator
62.Fa "const EC_GROUP *group"
63.Fc
64.Ft int
65.Fo EC_GROUP_get_order
66.Fa "const EC_GROUP *group"
67.Fa "BIGNUM *order"
68.Fa "BN_CTX *ctx"
69.Fc
70.Ft int
71.Fo EC_GROUP_get_cofactor
72.Fa "const EC_GROUP *group"
73.Fa "BIGNUM *cofactor"
74.Fa "BN_CTX *ctx"
75.Fc
76.Ft void
77.Fo EC_GROUP_set_curve_name
78.Fa "EC_GROUP *group"
79.Fa "int nid"
80.Fc
81.Ft int
82.Fo EC_GROUP_get_curve_name
83.Fa "const EC_GROUP *group"
84.Fc
85.Ft void
86.Fo EC_GROUP_set_asn1_flag
87.Fa "EC_GROUP *group"
88.Fa "int flag"
89.Fc
90.Ft int
91.Fo EC_GROUP_get_asn1_flag
92.Fa "const EC_GROUP *group"
93.Fc
94.Ft void
95.Fo EC_GROUP_set_point_conversion_form
96.Fa "EC_GROUP *group"
97.Fa "point_conversion_form_t form"
98.Fc
99.Ft point_conversion_form_t
100.Fo EC_GROUP_get_point_conversion_form
101.Fa "const EC_GROUP *"
102.Fc
103.Ft unsigned char *
104.Fo EC_GROUP_get0_seed
105.Fa "const EC_GROUP *x"
106.Fc
107.Ft size_t
108.Fo EC_GROUP_get_seed_len
109.Fa "const EC_GROUP *"
110.Fc
111.Ft size_t
112.Fo EC_GROUP_set_seed
113.Fa "EC_GROUP *"
114.Fa "const unsigned char *"
115.Fa "size_t len"
116.Fc
117.Ft int
118.Fo EC_GROUP_set_curve_GFp
119.Fa "EC_GROUP *group"
120.Fa "const BIGNUM *p"
121.Fa "const BIGNUM *a"
122.Fa "const BIGNUM *b"
123.Fa "BN_CTX *ctx"
124.Fc
125.Ft int
126.Fo EC_GROUP_get_curve_GFp
127.Fa "const EC_GROUP *group"
128.Fa "BIGNUM *p"
129.Fa "BIGNUM *a"
130.Fa "BIGNUM *b"
131.Fa "BN_CTX *ctx"
132.Fc
133.Ft int
134.Fo EC_GROUP_set_curve_GF2m
135.Fa "EC_GROUP *group"
136.Fa "const BIGNUM *p"
137.Fa "const BIGNUM *a"
138.Fa "const BIGNUM *b"
139.Fa "BN_CTX *ctx"
140.Fc
141.Ft int
142.Fo EC_GROUP_get_curve_GF2m
143.Fa "const EC_GROUP *group"
144.Fa "BIGNUM *p"
145.Fa "BIGNUM *a"
146.Fa "BIGNUM *b"
147.Fa "BN_CTX *ctx"
148.Fc
149.Ft int
150.Fo EC_GROUP_get_degree
151.Fa "const EC_GROUP *group"
152.Fc
153.Ft int
154.Fo EC_GROUP_check
155.Fa "const EC_GROUP *group"
156.Fa "BN_CTX *ctx"
157.Fc
158.Ft int
159.Fo EC_GROUP_check_discriminant
160.Fa "const EC_GROUP *group"
161.Fa "BN_CTX *ctx"
162.Fc
163.Ft int
164.Fo EC_GROUP_cmp
165.Fa "const EC_GROUP *a"
166.Fa "const EC_GROUP *b"
167.Fa "BN_CTX *ctx"
168.Fc
169.Ft EC_GROUP *
170.Fo EC_GROUP_new_curve_GFp
171.Fa "const BIGNUM *p"
172.Fa "const BIGNUM *a"
173.Fa "const BIGNUM *b"
174.Fa "BN_CTX *ctx"
175.Fc
176.Ft EC_GROUP *
177.Fo EC_GROUP_new_curve_GF2m
178.Fa "const BIGNUM *p"
179.Fa "const BIGNUM *a"
180.Fa "const BIGNUM *b"
181.Fa "BN_CTX *ctx"
182.Fc
183.Ft EC_GROUP *
184.Fo EC_GROUP_new_by_curve_name
185.Fa "int nid"
186.Fc
187.Ft size_t
188.Fo EC_get_builtin_curves
189.Fa "EC_builtin_curve *r"
190.Fa "size_t nitems"
191.Fc
192.Ft EC_POINT *
193.Fo EC_POINT_new
194.Fa "const EC_GROUP *group"
195.Fc
196.Ft void
197.Fo EC_POINT_free
198.Fa "EC_POINT *point"
199.Fc
200.Ft void
201.Fo EC_POINT_clear_free
202.Fa "EC_POINT *point"
203.Fc
204.Ft int
205.Fo EC_POINT_copy
206.Fa "EC_POINT *dst"
207.Fa "const EC_POINT *src"
208.Fc
209.Ft EC_POINT *
210.Fo EC_POINT_dup
211.Fa "const EC_POINT *src"
212.Fa "const EC_GROUP *group"
213.Fc
214.Ft const EC_METHOD *
215.Fo EC_POINT_method_of
216.Fa "const EC_POINT *point"
217.Fc
218.Ft int
219.Fo EC_POINT_set_to_infinity
220.Fa "const EC_GROUP *group"
221.Fa "EC_POINT *point"
222.Fc
223.Ft int
224.Fo EC_POINT_set_Jprojective_coordinates_GFp
225.Fa "const EC_GROUP *group"
226.Fa "EC_POINT *p"
227.Fa "const BIGNUM *x"
228.Fa "const BIGNUM *y"
229.Fa "const BIGNUM *z"
230.Fa "BN_CTX *ctx"
231.Fc
232.Ft int
233.Fo EC_POINT_get_Jprojective_coordinates_GFp
234.Fa "const EC_GROUP *group"
235.Fa "const EC_POINT *p"
236.Fa "BIGNUM *x"
237.Fa "BIGNUM *y"
238.Fa "BIGNUM *z"
239.Fa "BN_CTX *ctx"
240.Fc
241.Ft int
242.Fo EC_POINT_set_affine_coordinates_GFp
243.Fa "const EC_GROUP *group"
244.Fa "EC_POINT *p"
245.Fa "const BIGNUM *x"
246.Fa "const BIGNUM *y"
247.Fa "BN_CTX *ctx"
248.Fc
249.Ft int
250.Fo EC_POINT_get_affine_coordinates_GFp
251.Fa "const EC_GROUP *group"
252.Fa "const EC_POINT *p"
253.Fa "BIGNUM *x"
254.Fa "BIGNUM *y"
255.Fa "BN_CTX *ctx"
256.Fc
257.Ft int
258.Fo EC_POINT_set_compressed_coordinates_GFp
259.Fa "const EC_GROUP *group"
260.Fa "EC_POINT *p"
261.Fa "const BIGNUM *x"
262.Fa "int y_bit"
263.Fa "BN_CTX *ctx"
264.Fc
265.Ft int
266.Fo EC_POINT_set_affine_coordinates_GF2m
267.Fa "const EC_GROUP *group"
268.Fa "EC_POINT *p"
269.Fa "const BIGNUM *x"
270.Fa "const BIGNUM *y"
271.Fa "BN_CTX *ctx"
272.Fc
273.Ft int
274.Fo EC_POINT_get_affine_coordinates_GF2m
275.Fa "const EC_GROUP *group"
276.Fa "const EC_POINT *p"
277.Fa "BIGNUM *x"
278.Fa "BIGNUM *y"
279.Fa "BN_CTX *ctx"
280.Fc
281.Ft int
282.Fo EC_POINT_set_compressed_coordinates_GF2m
283.Fa "const EC_GROUP *group"
284.Fa "EC_POINT *p"
285.Fa "const BIGNUM *x"
286.Fa "int y_bit"
287.Fa "BN_CTX *ctx"
288.Fc
289.Ft size_t
290.Fo EC_POINT_point2oct
291.Fa "const EC_GROUP *group"
292.Fa "const EC_POINT *p"
293.Fa "point_conversion_form_t form"
294.Fa "unsigned char *buf"
295.Fa "size_t len"
296.Fa "BN_CTX *ctx"
297.Fc
298.Ft int
299.Fo EC_POINT_oct2point
300.Fa "const EC_GROUP *group"
301.Fa "EC_POINT *p"
302.Fa "const unsigned char *buf"
303.Fa "size_t len"
304.Fa "BN_CTX *ctx"
305.Fc
306.Ft BIGNUM *
307.Fo EC_POINT_point2bn
308.Fa "const EC_GROUP *"
309.Fa "const EC_POINT *"
310.Fa "point_conversion_form_t form"
311.Fa "BIGNUM *"
312.Fa "BN_CTX *"
313.Fc
314.Ft EC_POINT *
315.Fo EC_POINT_bn2point
316.Fa "const EC_GROUP *"
317.Fa "const BIGNUM *"
318.Fa "EC_POINT *"
319.Fa "BN_CTX *"
320.Fc
321.Ft char *
322.Fo EC_POINT_point2hex
323.Fa "const EC_GROUP *"
324.Fa "const EC_POINT *"
325.Fa "point_conversion_form_t form"
326.Fa "BN_CTX *"
327.Fc
328.Ft EC_POINT *
329.Fo EC_POINT_hex2point
330.Fa "const EC_GROUP *"
331.Fa "const char *"
332.Fa "EC_POINT *"
333.Fa "BN_CTX *"
334.Fc
335.Ft int
336.Fo EC_POINT_add
337.Fa "const EC_GROUP *group"
338.Fa "EC_POINT *r"
339.Fa "const EC_POINT *a"
340.Fa "const EC_POINT *b"
341.Fa "BN_CTX *ctx"
342.Fc
343.Ft int
344.Fo EC_POINT_dbl
345.Fa "const EC_GROUP *group"
346.Fa "EC_POINT *r"
347.Fa "const EC_POINT *a"
348.Fa "BN_CTX *ctx"
349.Fc
350.Ft int
351.Fo EC_POINT_invert
352.Fa "const EC_GROUP *group"
353.Fa "EC_POINT *a"
354.Fa "BN_CTX *ctx"
355.Fc
356.Ft int
357.Fo EC_POINT_is_at_infinity
358.Fa "const EC_GROUP *group"
359.Fa "const EC_POINT *p"
360.Fc
361.Ft int
362.Fo EC_POINT_is_on_curve
363.Fa "const EC_GROUP *group"
364.Fa "const EC_POINT *point"
365.Fa "BN_CTX *ctx"
366.Fc
367.Ft int
368.Fo EC_POINT_cmp
369.Fa "const EC_GROUP *group"
370.Fa "const EC_POINT *a"
371.Fa "const EC_POINT *b"
372.Fa "BN_CTX *ctx"
373.Fc
374.Ft int
375.Fo EC_POINT_make_affine
376.Fa "const EC_GROUP *group"
377.Fa "EC_POINT *point"
378.Fa "BN_CTX *ctx"
379.Fc
380.Ft int
381.Fo EC_POINTs_make_affine
382.Fa "const EC_GROUP *group"
383.Fa "size_t num"
384.Fa "EC_POINT *points[]"
385.Fa "BN_CTX *ctx"
386.Fc
387.Ft int
388.Fo EC_POINTs_mul
389.Fa "const EC_GROUP *group"
390.Fa "EC_POINT *r"
391.Fa "const BIGNUM *n"
392.Fa "size_t num"
393.Fa "const EC_POINT *p[]"
394.Fa "const BIGNUM *m[]"
395.Fa "BN_CTX *ctx"
396.Fc
397.Ft int
398.Fo EC_POINT_mul
399.Fa "const EC_GROUP *group"
400.Fa "EC_POINT *r"
401.Fa "const BIGNUM *n"
402.Fa "const EC_POINT *q"
403.Fa "const BIGNUM *m"
404.Fa "BN_CTX *ctx"
405.Fc
406.Ft int
407.Fo EC_GROUP_precompute_mult
408.Fa "EC_GROUP *group"
409.Fa "BN_CTX *ctx"
410.Fc
411.Ft int
412.Fo EC_GROUP_have_precompute_mult
413.Fa "const EC_GROUP *group"
414.Fc
415.Ft int
416.Fo EC_GROUP_get_basis_type
417.Fa "const EC_GROUP *"
418.Fc
419.Ft int
420.Fo EC_GROUP_get_trinomial_basis
421.Fa "const EC_GROUP *"
422.Fa "unsigned int *k"
423.Fc
424.Ft int
425.Fo EC_GROUP_get_pentanomial_basis
426.Fa "const EC_GROUP *"
427.Fa "unsigned int *k1"
428.Fa "unsigned int *k2"
429.Fa "unsigned int *k3"
430.Fc
431.Ft EC_GROUP *
432.Fo d2i_ECPKParameters
433.Fa "EC_GROUP **"
434.Fa "const unsigned char **in"
435.Fa "long len"
436.Fc
437.Ft int
438.Fo i2d_ECPKParameters
439.Fa "const EC_GROUP *"
440.Fa "unsigned char **out"
441.Fc
442.Fd #define d2i_ECPKParameters_bio(bp,x)\
443 ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
444.Fd #define i2d_ECPKParameters_bio(bp,x)\
445 ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
446.Fd #define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL,\
447 (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
448.Fd #define i2d_ECPKParameters_fp(fp,x)\
449 ASN1_i2d_fp(i2d_ECPKParameters,(fp), (unsigned char *)(x))
450.Ft int
451.Fo ECPKParameters_print
452.Fa "BIO *bp"
453.Fa "const EC_GROUP *x"
454.Fa "int off"
455.Fc
456.Ft int
457.Fo ECPKParameters_print_fp
458.Fa "FILE *fp"
459.Fa "const EC_GROUP *x"
460.Fa "int off"
461.Fc
462.Ft EC_KEY *
463.Fn EC_KEY_new void
464.Ft int
465.Fo EC_KEY_get_flags
466.Fa "const EC_KEY *key"
467.Fc
468.Ft void
469.Fo EC_KEY_set_flags
470.Fa "EC_KEY *key"
471.Fa "int flags"
472.Fc
473.Ft void
474.Fo EC_KEY_clear_flags
475.Fa "EC_KEY *key"
476.Fa "int flags"
477.Fc
478.Ft EC_KEY *
479.Fo EC_KEY_new_by_curve_name
480.Fa "int nid"
481.Fc
482.Ft void
483.Fo EC_KEY_free
484.Fa "EC_KEY *key"
485.Fc
486.Ft EC_KEY *
487.Fo EC_KEY_copy
488.Fa "EC_KEY *dst"
489.Fa "const EC_KEY *src"
490.Fc
491.Ft EC_KEY *
492.Fo EC_KEY_dup
493.Fa "const EC_KEY *src"
494.Fc
495.Ft int
496.Fo EC_KEY_up_ref
497.Fa "EC_KEY *key"
498.Fc
499.Ft const EC_GROUP *
500.Fo EC_KEY_get0_group
501.Fa "const EC_KEY *key"
502.Fc
503.Ft int
504.Fo EC_KEY_set_group
505.Fa "EC_KEY *key"
506.Fa "const EC_GROUP *group"
507.Fc
508.Ft const BIGNUM *
509.Fo EC_KEY_get0_private_key
510.Fa "const EC_KEY *key"
511.Fc
512.Ft int
513.Fo EC_KEY_set_private_key
514.Fa "EC_KEY *key"
515.Fa "const BIGNUM *prv"
516.Fc
517.Ft const EC_POINT *
518.Fo EC_KEY_get0_public_key
519.Fa "const EC_KEY *key"
520.Fc
521.Ft int
522.Fo EC_KEY_set_public_key
523.Fa "EC_KEY *key"
524.Fa "const EC_POINT *pub"
525.Fc
526.Ft unsigned
527.Fo EC_KEY_get_enc_flags
528.Fa "const EC_KEY *key"
529.Fc
530.Ft void
531.Fo EC_KEY_set_enc_flags
532.Fa "EC_KEY *eckey"
533.Fa "unsigned int flags"
534.Fc
535.Ft point_conversion_form_t
536.Fo EC_KEY_get_conv_form
537.Fa "const EC_KEY *key"
538.Fc
539.Ft void
540.Fo EC_KEY_set_conv_form
541.Fa "EC_KEY *eckey"
542.Fa "point_conversion_form_t cform"
543.Fc
544.Ft void *
545.Fo EC_KEY_get_key_method_data
546.Fa "EC_KEY *key"
547.Fa "void *(*dup_func)(void *)"
548.Fa "void (*free_func)(void *)"
549.Fa "void (*clear_free_func)(void *)"
550.Fc
551.Ft void
552.Fo EC_KEY_insert_key_method_data
553.Fa "EC_KEY *key"
554.Fa "void *data"
555.Fa "void *(*dup_func)(void *)"
556.Fa "void (*free_func)(void *)"
557.Fa "void (*clear_free_func)(void *)"
558.Fc
559.Ft void
560.Fo EC_KEY_set_asn1_flag
561.Fa "EC_KEY *eckey"
562.Fa "int asn1_flag"
563.Fc
564.Ft int
565.Fo EC_KEY_precompute_mult
566.Fa "EC_KEY *key"
567.Fa "BN_CTX *ctx"
568.Fc
569.Ft int
570.Fo EC_KEY_generate_key
571.Fa "EC_KEY *key"
572.Fc
573.Ft int
574.Fo EC_KEY_check_key
575.Fa "const EC_KEY *key"
576.Fc
577.Ft int
578.Fo EC_KEY_set_public_key_affine_coordinates
579.Fa "EC_KEY *key"
580.Fa "BIGNUM *x"
581.Fa "BIGNUM *y"
582.Fc
583.Ft EC_KEY *
584.Fo d2i_ECPrivateKey
585.Fa "EC_KEY **key"
586.Fa "const unsigned char **in"
587.Fa "long len"
588.Fc
589.Ft int
590.Fo i2d_ECPrivateKey
591.Fa "EC_KEY *key"
592.Fa "unsigned char **out"
593.Fc
594.Ft EC_KEY *
595.Fo d2i_ECParameters
596.Fa "EC_KEY **key"
597.Fa "const unsigned char **in"
598.Fa "long len"
599.Fc
600.Ft int
601.Fo i2d_ECParameters
602.Fa "EC_KEY *key"
603.Fa "unsigned char **out"
604.Fc
605.Ft EC_KEY *
606.Fo o2i_ECPublicKey
607.Fa "EC_KEY **key"
608.Fa "const unsigned char **in"
609.Fa "long len"
610.Fc
611.Ft int
612.Fo i2o_ECPublicKey
613.Fa "EC_KEY *key"
614.Fa "unsigned char **out"
615.Fc
616.Ft int
617.Fo ECParameters_print
618.Fa "BIO *bp"
619.Fa "const EC_KEY *key"
620.Fc
621.Ft int
622.Fo EC_KEY_print
623.Fa "BIO *bp"
624.Fa "const EC_KEY *key"
625.Fa "int off"
626.Fc
627.Ft int
628.Fo ECParameters_print_fp
629.Fa "FILE *fp"
630.Fa "const EC_KEY *key"
631.Fc
632.Ft int
633.Fo EC_KEY_print_fp
634.Fa "FILE *fp"
635.Fa "const EC_KEY *key"
636.Fa "int off"
637.Fc
638.Ft EC_KEY *
639.Fo ECParameters_dup
640.Fa "EC_KEY *key"
641.Fc
642.Fd #define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid)\
643 EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN,\
644 EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
645.Sh DESCRIPTION
646This library provides an extensive set of functions for performing
647operations on elliptic curves over finite fields.
648In general an elliptic curve is one with an equation of the form:
649.Pp
650.Dl y^2 = x^3 + ax + b
651.Pp
652An
653.Vt EC_GROUP
654structure is used to represent the definition of an elliptic curve.
655Points on a curve are stored using an
656.Vt EC_POINT
657structure.
658An
659.Vt EC_KEY
660is used to hold a private/public key pair, where a private key is simply a
661.Vt BIGNUM
662and a public key is a point on a curve represented by an
663.Vt EC_POINT .
664.Pp
665The library contains a number of alternative implementations of the
666different functions.
667Each implementation is optimised for different scenarios.
668No matter which implementation is being used, the interface remains the
669same.
670The library handles calling the correct implementation when an interface
671function is invoked.
672An implementation is represented by an
673.Vt EC_METHOD
674structure.
675.Pp
676The creation and destruction of
677.Vt EC_GROUP
678objects is described in
679.Xr EC_GROUP_new 3 .
680Functions for manipulating
681.Vt EC_GROUP
682objects are described in
683.Xr EC_GROUP_copy 3 .
684.Pp
685Functions for creating, destroying and manipulating
686.Vt EC_POINT
687objects are explained in
688.Xr EC_POINT_new 3 ,
689whilst functions for performing mathematical operations and tests on
690.Vt EC_POINT Ns s
691are coverd in
692.Xr EC_POINT_add 3 .
693.Pp
694For working with private and public keys refer to
695.Xr EC_KEY_new 3 .
696Implementations are covered in
697.Xr EC_GFp_simple_method 3 .
698.Pp
699For information on encoding and decoding curve parameters to and
700from ASN.1 see
701.Xr d2i_ECPKParameters 3 .
702.Sh SEE ALSO
703.Xr crypto 3 ,
704.Xr d2i_ECPKParameters 3 ,
705.Xr EC_GFp_simple_method 3 ,
706.Xr EC_GROUP_copy 3 ,
707.Xr EC_GROUP_new 3 ,
708.Xr EC_KEY_new 3 ,
709.Xr EC_POINT_add 3 ,
710.Xr EC_POINT_new 3
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