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
232
233
234
235
236
237
238
239
240
|
'''
EXAMPLES (handwritten):
# p256 - amd128
{
"modulus" : "2^256-2^224+2^192+2^96-1",
"base" : "128",
"sz" : "2",
"bitwidth" : "128",
"montgomery" : "true",
"operations" : ["fenz", "feadd", "femul", "feopp", "fesub"],
"compiler" : "gcc -fno-peephole2 `#GCC BUG 81300` -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes -Wno-incompatible-pointer-types -fno-strict-aliasing"
}
# p256 - amd64
{
"modulus" : "2^256-2^224+2^192+2^96-1",
"base" : "64",
"sz" : "4",
"bitwidth" : "64",
"montgomery" : "true",
"operations" : ["fenz", "feadd", "femul", "feopp", "fesub"],
"compiler" : "gcc -fno-peephole2 `#GCC BUG 81300` -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes -Wno-incompatible-pointer-types -fno-strict-aliasing"
}
# p448 - c64
{
"modulus" : "2^448-2^224-1",
"base" : "56",
"goldilocks" : "true",
"sz" : "8",
"bitwidth" : "64",
"carry_chains" : [[3, 7],
[0, 4, 1, 5, 2, 6, 3, 7],
[4, 0]],
"coef_div_modulus" : "2",
"operations" : ["femul"]
}
# curve25519 - c64
{
"modulus" : "2^255-19",
"base" : "51",
"sz" : "5",
"bitwidth" : "64",
"carry_chains" : "default",
"coef_div_modulus" : "2",
"operations" : ["femul", "fesquare", "freeze"],
"compiler" : "gcc -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes",
}
# curve25519 - c32
{
"modulus" : "2^255-19",
"base" : "25.5",
"sz" : "10",
"bitwidth" : "32",
"carry_chains" : "default",
"coef_div_modulus" : "2",
"operations" : ["femul", "fesquare", "freeze"],
"compiler" : "gcc -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes",
}
'''
import math,json,sys,os
# for montgomery
COMPILER_MONT = "gcc -fno-peephole2 `#GCC BUG 81300` -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes -Wno-incompatible-pointer-types -fno-strict-aliasing"
# for solinas
COMPILER_SOLI = "gcc -march=native -mtune=native -std=gnu11 -O3 -flto -fomit-frame-pointer -fwrapv -Wno-attributes"
CUR_PATH = os.path.dirname(os.path.realpath(__file__))
JSON_DIRECTORY = os.path.join(CUR_PATH, "src/Specific/CurveParameters")
REMAKE_CURVES = os.path.join(JSON_DIRECTORY, 'remake_curves.sh')
# given a string representing one term or "tap" in a prime, returns a pair of
# integers representing the weight and coefficient of that tap
# "2 ^ y" -> [1, y]
# "x * 2 ^ y" -> [x, y]
# "x * y" -> [x*y,0]
# "x" -> [x,0]
def parse_term(t) :
if "*" not in t and "^" not in t:
return [int(t),0]
if "*" in t:
a,b = t.split("*")
if "^" not in b:
return [int(a) * int(b),0]
else:
a,b = (1,t)
b,e = b.split("^")
if int(b) != 2:
raise Exception("Could not parse term, power with base other than 2: %s" %t)
return [int(a),int(e)]
# expects prime to be a string and expressed as sum/difference of products of
# two with small coefficients (e.g. '2^448 - 2^224 - 1', '2^255 - 19')
def parse_prime(prime):
terms = prime.replace("-", "+ -1 *").split("+")
return list(map(parse_term, terms))
# check that the parsed prime makes sense
def sanity_check(p):
if not all([
# are there at least 2 terms?
len(p) > 1,
# do all terms have 2 elements?
all(map(lambda t:len(t) == 2, p)),
# are terms are in order (most to least significant)?
p == list(sorted(p,reverse=True,key=lambda t:t[1])),
# does the least significant term have weight 2^0=1?
p[-1][1] == 0,
# are all the exponents positive and the coefficients nonzero?
all(map(lambda t:t[0] != 0 and t[1] >= 0, p)),
# is second-most-significant term negative?
p[1][0] < 0,
# are any exponents repeated?
len(set(map(lambda t:t[1], p))) == len(p)]) :
raise Exception("Parsed prime %s has unexpected format" %p)
def num_bits(p):
return p[0][1]
def get_params_montgomery(prime, bitwidth):
p = parse_prime(prime)
sanity_check(p)
sz = int(math.ceil(num_bits(p) / bitwidth))
return {
"modulus" : prime,
"base" : str(bitwidth),
"sz" : str(sz),
"montgomery" : True,
"operations" : ["fenz", "feadd", "femul", "feopp", "fesub"],
"compiler" : COMPILER_MONT
}
# given a parsed prime, pick a number of (unsaturated) limbs
def get_num_limbs(p, bitwidth):
# we want to leave enough bits unused to do a full solinas reduction
# without carrying; the number of bits necessary is the sum of the bits in
# the negative coefficients of p (other than the most significant digit)
unused_bits = sum(map(lambda t: math.ceil(math.log(-t[0], 2)) if t[0] < 0 else 0, p[1:]))
# print(p,unused_bits)
min_limbs = int(math.ceil(num_bits(p) / (bitwidth - unused_bits))) + 1
choices = []
for n in range(min_limbs, 5 * min_limbs): # don't search past 5x as many limbs as saturated representation; that's just wasteful
# check that the number of 'extra' bits needed fits in this number of limbs
min_bits = int(num_bits(p) / n)
extra = num_bits(p) % n
if extra == 0 or n % extra == 0:
choices.append((n, num_bits(p) / n))
break
if len(choices) == 0:
raise Exception("Unable to pick a number of limbs for prime %s and bitwidth %s in range %s-%s limbs" %(p,bitwidth,min_limbs,5*min_limbs))
# print (p,choices)
return choices[0][0]
def is_goldilocks(p):
return p[0][1] == 2 * p[1][1]
def get_params_solinas(prime, bitwidth):
p = parse_prime(prime)
sanity_check(p)
sz = get_num_limbs(p, bitwidth)
base = num_bits(p) / sz
output = {
"modulus": prime,
"base" : str(base),
"sz" : str(sz),
"bitwidth" : bitwidth,
"carry_chains" : "default",
"coef_div_modulus" : str(2),
"operations" : ["femul", "fesquare", "freeze"],
"compiler" : COMPILER_SOLI
}
if is_goldilocks(p):
output["goldilocks"] = True
return output
def update_remake_curves(filename):
with open(REMAKE_CURVES, 'r') as f:
lines = f.readlines()
new_line = '${MAKE} "$@" %s ../%s/\n' % (filename, filename[:-len('.json')])
if new_line in lines: return
if any(filename in line for line in lines):
lines = [(line if filename not in line else new_line)
for line in lines]
else:
lines.append(new_line)
with open(REMAKE_CURVES, 'w') as f:
f.write(''.join(lines))
def format_json(params):
return json.dumps(params, indent=4, separators=(',', ': '), sort_keys=True) + '\n'
def write_output(name, params):
prime = params["modulus"]
filename = (name + "_" + prime + ".json").replace("^","e").replace(" ","").replace("-","m").replace("+","p").replace("*","x")
g = open(os.path.join(JSON_DIRECTORY, filename), "w")
g.write(format_json(params))
g.close()
update_remake_curves(filename)
USAGE = "python generate_parameters.py input_file"
if __name__ == "__main__":
if len(sys.argv) < 2:
print(USAGE)
sys.exit()
f = open(sys.argv[1])
for line in f:
# skip comments and empty lines
if line.strip().startswith("#") or len(line.strip()) == 0:
continue
prime = line.strip().split("#")[0] # remove trailing comments and trailing/leading whitespace
try:
write_output("montgomery32", get_params_montgomery(prime, 32))
except Exception as e:
print(e)
try:
write_output("montgomery64", get_params_montgomery(prime, 64))
except Exception as e:
print(e)
try:
write_output("solinas32", get_params_solinas(prime, 32))
except Exception as e:
print(e)
try:
write_output("solinas64", get_params_solinas(prime, 64))
except Exception as e:
print(e)
f.close()
|
