/
ModularSquaring.sol
199 lines (156 loc) · 6.31 KB
/
ModularSquaring.sol
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
pragma solidity ^0.4.7;
contract ModSquaring{
//It is faster to pass in the parameters then to store them in the contract
//mu is precomputed as in http://cacr.uwaterloo.ca/hac/about/chap14.pdf 14.42
function squareMod(uint128[] a,uint128[] p,uint128[] mu) returns (uint128[]){
return reduce(square(a),p,mu);
}
//http://cacr.uwaterloo.ca/hac/about/chap14.pdf 14.42
function reduce(uint128[] x,uint128[] p, uint128[] mu) returns (uint128[]) {
uint k=p.length;
uint128[] memory q2=multiply(x,(k-1),x.length,mu);
uint128[] memory resultArr=new uint128[] (k+1);
multiply(q2,k+1,q2.length,p,resultArr);
subtract(x,k+1,resultArr,resultArr);
if(compare(resultArr,p)>0){
subtract(resultArr,resultArr.length,p,resultArr);
}
return resultArr;
}
//["55118165149374409119441216119413761026", "265061826949299110830368790704498640569", "300521695615681644794695341510018298528", "54530299560789227599107570026971128394", "71733251100534160453953577909295437626", "220411398049372823160336614040244919231", "184696793962099687431081466998393535749", "7322398326798248374870583692637721116"],["8927915239697290504852011324446591464", "187495788097959546505201523618550384481", "40973013603509160184080314943928029279", "172895300241464466985696750100405637966", "61578131693935342232040621215739594614", "251941516561054923699045255914867180567", "211463475223641439340526528779523568258", "214728581139365324922875373285087570001", "273870799808541713772737455294475126899", "279682588608523038486153166561967936179", "57394012307978892662500096995871093432", "155834915080132789790604408201555017510", "82896135016063304504922814160290442132", "212052247433649349713454407107857307483", "119842806979691575985921458468191875116", "284391773475239181811945254931245429520"]
function multiply(uint128[] a,uint128[] b) returns (uint128[]){
uint blength=b.length;
uint128[] memory result=new uint128[](a.length+blength);
for (uint i=0;i<a.length;++i){
uint128 carry=0;
uint128 ai;
assembly{
ai:=mload(add(add(a,0x20),i))
}
for (uint j =0;j<blength;++j){
uint256 temp;
assembly{
let j:=0
loop:
jumpi(loopend, eq(j, blength))
let bj:=mload(add(add(b,0x20),j))
let resultij:=mload(add(add(result,0x20),add(i,j)))
temp:=add(carry,add(mul(ai,bj),resultij))
j := add(j, 1)
jump(loop)
loopend:
}
result[i+j]=uint128(temp);
carry=uint128(temp>>128);
}
result[i+blength]=carry;
}
return result;
}
function multiply(uint128[] a, uint aStart,uint aEnd,uint128[] b) returns (uint128[]){
uint128[] memory result=new uint128[](aEnd-aStart+b.length);
for (uint i=aStart;i<aEnd;++i){
uint128 carry=0;
uint256 ai=uint256(a[i]);
for (uint j =0;j<b.length;++j){
uint resultIndex=i+j-aStart;
uint256 temp=carry+ai*b[j]+result[resultIndex];
result[resultIndex]=uint128(temp);
carry=uint128(temp>>128);
}
result[i+b.length-aStart]=carry;
}
return result;
}
function multiply(uint128[] a, uint aStart,uint aEnd,uint128[] b,uint128[] result) returns (uint128[]){
for (uint i=aStart;i<aEnd;++i){
uint128 carry=0;
uint256 ai;
assembly{
ai:=mload(add(add(a,0x20),i))
}
for (uint j =0;j<b.length;++j){
uint resultIndex=i+j-aStart;
if(resultIndex<result.length){
uint256 temp=carry+ai*b[j]+result[resultIndex];
result[resultIndex]=uint128(temp);
carry=uint128(temp>>128);
}
}
uint finalIndex=i+b.length-aStart;
if(finalIndex<result.length){
result[finalIndex]=carry;
}
}
}
function square(uint128[] a) returns (uint128[]){
uint128[] memory result=new uint128[](a.length*2);
for(uint i=0;i<a.length;++i){
uint256 temp=a[i]*a[i];
}
return multiply(a,a);
}
function compare(uint128[] a, uint128[] b) returns (int8){
uint aLength=a.length;
uint bLength=b.length;
uint maxLength=aLength > bLength? aLength : bLength;
for(uint i =maxLength-1;i>=0;--i){
uint128 aVal=i>=aLength?0:a[i];
uint128 bVal=i>=bLength?0:b[i];
if(aVal>bVal){
return 1;
}
if(bVal > aVal){
return -1;
}
}
return 0;
}
//a>b
function subtract(uint128[] a, uint128[] b) returns (uint128[]){
uint128[] memory result=new uint128[](a.length);
uint8 carry=0;
for(uint i=0;i<a.length;++i){
int bVal=i>=b.length?0:b[i];
int resultBuf=a[i]-bVal-carry;
result[i]=uint128(resultBuf);
if(resultBuf<0){
carry=1;
}else{
carry=0;
}
}
return result;
}
//a>b
function subtract(uint128[] a,uint aLength, uint128[] b) returns (uint128[]){
uint128[] memory result=new uint128[](aLength);
uint8 carry=0;
for(uint i=0;i<aLength;++i){
int bVal=i>=b.length?0:b[i];
int resultBuf=a[i]-bVal-carry;
result[i]=uint128(resultBuf);
if(resultBuf<0){
carry=1;
}else{
carry=0;
}
}
return result;
}
//a>b
function subtract(uint128[] a,uint aLength, uint128[] b,uint128[] result) returns (uint128[]){
uint8 carry=0;
for(uint i=0;i<aLength;++i){
int bVal=i>=b.length?0:b[i];
int resultBuf=a[i]-bVal-carry;
result[i]=uint128(resultBuf);
if(resultBuf<0){
carry=1;
}else{
carry=0;
}
}
return result;
}
}