/
element.go
231 lines (201 loc) · 6.55 KB
/
element.go
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
package primefield
import (
"math/bits"
"math/rand"
"regexp"
"strconv"
"github.com/ReneBoedker/algobra/errors"
"github.com/ReneBoedker/algobra/finitefield/ff"
)
// Ensure that Element implements the ff.Element interface
var _ ff.Element = &Element{}
// Element is the implementation of a finite field element.
type Element struct {
field *Field
val uint
err error
}
// Zero returns the additive identity in f.
func (f *Field) Zero() ff.Element {
return &Element{field: f, val: 0}
}
// One returns the multiplicative identity in f.
func (f *Field) One() ff.Element {
return &Element{field: f, val: 1}
}
// RandElement returns a pseudo-random element in f.
//
// This function uses the default source from the math/rand package. The seed is
// set automatically when loading the primefield package, but a new seed can be
// set by calling rand.Seed().
//
// The pseudo-random generator used is not cryptographically safe.
func (f *Field) RandElement() ff.Element {
if bits.UintSize == 32 {
return f.ElementFromUnsigned(uint(rand.Uint32()))
}
return f.ElementFromUnsigned(uint(rand.Uint64()))
}
// Element defines a new element over f with value val, which must be either
// uint, int, or string.
//
// If type of val is unsupported, the function returns an Input-error.
func (f *Field) Element(val interface{}) (ff.Element, error) {
const op = "Defining element"
switch v := val.(type) {
case uint:
return f.element(v), nil
case int:
return f.ElementFromSigned(v), nil
case string:
return f.ElementFromString(v)
default:
return nil, errors.New(
op, errors.Input,
"Cannot define element in %v from type %T", f, v,
)
}
}
// element defines a new element over f with value val.
//
// The returned element will automatically be reduced modulo the characteristic.
func (f *Field) element(val uint) *Element {
return &Element{field: f, val: val % f.char}
}
// ElementFromUnsigned defines a new element over f with value val.
//
// The returned element will automatically be reduced modulo the characteristic.
func (f *Field) ElementFromUnsigned(val uint) ff.Element {
return f.element(val)
}
// ElementFromSigned defines a new element over f with value val.
//
// The returned element will be reduced modulo the characteristic automatically.
// Negative values are reduced to a positive remainder (as opposed to the
// %-operator in Go).
func (f *Field) ElementFromSigned(val int) ff.Element {
val %= int(f.char)
if val < 0 {
val += int(f.char)
}
return f.element(uint(val))
}
// ElementFromString defines a new element over f from the given string.
//
// A Parsing-error is returned if the string cannot be parsed.
func (f *Field) ElementFromString(val string) (ff.Element, error) {
const op = "Defining element from string"
match := regexp.MustCompile(`(-)?([0-9]+)`).FindStringSubmatch(val)
// Check that the pattern matches the full string
if len(match[0]) != len(val) {
return nil, errors.New(
op, errors.Parsing,
"Pattern match %q is not the full input string %q", match[0], val,
)
}
switch {
case len(match[1]) == 1:
// The input contains a minus
tmp, err := strconv.ParseInt(match[0], 10, 0)
if err != nil {
return nil, errors.New(
op, errors.Parsing,
"Failed to convert input with error %q", err,
)
}
return f.ElementFromSigned(int(tmp)), nil
default:
// The input does not contain a minus
tmp, err := strconv.ParseUint(match[0], 10, 0)
if err != nil {
return nil, errors.New(
op, errors.Parsing,
"Failed to convert input with error %q", err,
)
}
return f.ElementFromUnsigned(uint(tmp)), nil
}
}
// Copy returns a copy of a.
func (a *Element) Copy() ff.Element {
return &Element{
field: a.field,
val: a.val,
err: a.err,
}
}
// Err returns the error status of a.
func (a *Element) Err() error {
return a.err
}
// Uint returns the value of a represented as an unsigned integer.
func (a *Element) Uint() uint {
return a.val
}
// SetUnsigned sets the value of a to the element corresponding to val. It then
// returns a.
//
// The value is automatically reduced modulo the characteristic.
func (a *Element) SetUnsigned(val uint) ff.Element {
a.val = val % a.field.Char()
return a
}
// Equal tests equality of elements a and b.
func (a *Element) Equal(b ff.Element) bool {
bb, ok := b.(*Element)
if !ok {
return false
}
if a.field == bb.field && a.val == bb.val {
return true
}
return false
}
// IsZero returns a boolean describing whether a is the additive identity.
func (a *Element) IsZero() bool {
return (a.val == 0)
}
// IsNonzero returns a boolean describing whether a is a nonzero element.
func (a *Element) IsNonzero() bool {
return (a.val != 0)
}
// IsOne returns a boolean describing whether a is the multiplicative identity.
func (a *Element) IsOne() bool {
return (a.val == 1)
}
// String returns the string representation of a.
func (a *Element) String() string {
return strconv.FormatUint(uint64(a.val), 10)
}
// NTerms returns the number of terms in the representation of a. For prime
// fields, this is always 1.
func (a *Element) NTerms() uint {
return 1
}
/* Copyright 2019 René Bødker Christensen
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/