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1 package org.bouncycastle.math.ec.custom.sec;
2 
3 import java.math.BigInteger;
4 
5 import org.bouncycastle.math.ec.ECFieldElement;
6 import org.bouncycastle.math.raw.Mod;
7 import org.bouncycastle.math.raw.Nat224;
8 import org.bouncycastle.util.Arrays;
9 
10 public class SecP224K1FieldElement extends ECFieldElement
11 {
12     public static final BigInteger Q = SecP224K1Curve.q;
13 
14     // Calculated as ECConstants.TWO.modPow(Q.shiftRight(2), Q)
15     private static final int[] PRECOMP_POW2 = new int[]{ 0x33bfd202, 0xdcfad133, 0x2287624a, 0xc3811ba8,
16         0xa85558fc, 0x1eaef5d7, 0x8edf154c };
17 
18     protected int[] x;
19 
SecP224K1FieldElement(BigInteger x)20     public SecP224K1FieldElement(BigInteger x)
21     {
22         if (x == null || x.signum() < 0 || x.compareTo(Q) >= 0)
23         {
24             throw new IllegalArgumentException("x value invalid for SecP224K1FieldElement");
25         }
26 
27         this.x = SecP224K1Field.fromBigInteger(x);
28     }
29 
SecP224K1FieldElement()30     public SecP224K1FieldElement()
31     {
32         this.x = Nat224.create();
33     }
34 
SecP224K1FieldElement(int[] x)35     protected SecP224K1FieldElement(int[] x)
36     {
37         this.x = x;
38     }
39 
isZero()40     public boolean isZero()
41     {
42         return Nat224.isZero(x);
43     }
44 
isOne()45     public boolean isOne()
46     {
47         return Nat224.isOne(x);
48     }
49 
testBitZero()50     public boolean testBitZero()
51     {
52         return Nat224.getBit(x, 0) == 1;
53     }
54 
toBigInteger()55     public BigInteger toBigInteger()
56     {
57         return Nat224.toBigInteger(x);
58     }
59 
getFieldName()60     public String getFieldName()
61     {
62         return "SecP224K1Field";
63     }
64 
getFieldSize()65     public int getFieldSize()
66     {
67         return Q.bitLength();
68     }
69 
add(ECFieldElement b)70     public ECFieldElement add(ECFieldElement b)
71     {
72         int[] z = Nat224.create();
73         SecP224K1Field.add(x, ((SecP224K1FieldElement)b).x, z);
74         return new SecP224K1FieldElement(z);
75     }
76 
addOne()77     public ECFieldElement addOne()
78     {
79         int[] z = Nat224.create();
80         SecP224K1Field.addOne(x, z);
81         return new SecP224K1FieldElement(z);
82     }
83 
subtract(ECFieldElement b)84     public ECFieldElement subtract(ECFieldElement b)
85     {
86         int[] z = Nat224.create();
87         SecP224K1Field.subtract(x, ((SecP224K1FieldElement)b).x, z);
88         return new SecP224K1FieldElement(z);
89     }
90 
multiply(ECFieldElement b)91     public ECFieldElement multiply(ECFieldElement b)
92     {
93         int[] z = Nat224.create();
94         SecP224K1Field.multiply(x, ((SecP224K1FieldElement)b).x, z);
95         return new SecP224K1FieldElement(z);
96     }
97 
divide(ECFieldElement b)98     public ECFieldElement divide(ECFieldElement b)
99     {
100 //        return multiply(b.invert());
101         int[] z = Nat224.create();
102         Mod.invert(SecP224K1Field.P, ((SecP224K1FieldElement)b).x, z);
103         SecP224K1Field.multiply(z, x, z);
104         return new SecP224K1FieldElement(z);
105     }
106 
negate()107     public ECFieldElement negate()
108     {
109         int[] z = Nat224.create();
110         SecP224K1Field.negate(x, z);
111         return new SecP224K1FieldElement(z);
112     }
113 
square()114     public ECFieldElement square()
115     {
116         int[] z = Nat224.create();
117         SecP224K1Field.square(x, z);
118         return new SecP224K1FieldElement(z);
119     }
120 
invert()121     public ECFieldElement invert()
122     {
123 //        return new SecP224K1FieldElement(toBigInteger().modInverse(Q));
124         int[] z = Nat224.create();
125         Mod.invert(SecP224K1Field.P, x, z);
126         return new SecP224K1FieldElement(z);
127     }
128 
129     // D.1.4 91
130     /**
131      * return a sqrt root - the routine verifies that the calculation returns the right value - if
132      * none exists it returns null.
133      */
sqrt()134     public ECFieldElement sqrt()
135     {
136         /*
137          * Q == 8m + 5, so we use Pocklington's method for this case.
138          *
139          * First, raise this element to the exponent 2^221 - 2^29 - 2^9 - 2^8 - 2^6 - 2^4 - 2^1 (i.e. m + 1)
140          *
141          * Breaking up the exponent's binary representation into "repunits", we get:
142          * { 191 1s } { 1 0s } { 19 1s } { 2 0s } { 1 1s } { 1 0s} { 1 1s } { 1 0s} { 3 1s } { 1 0s}
143          *
144          * Therefore we need an addition chain containing 1, 3, 19, 191 (the lengths of the repunits)
145          * We use: [1], 2, [3], 4, 8, 11, [19], 23, 42, 84, 107, [191]
146          */
147 
148         int[] x1 = this.x;
149         if (Nat224.isZero(x1) || Nat224.isOne(x1))
150         {
151             return this;
152         }
153 
154         int[] x2 = Nat224.create();
155         SecP224K1Field.square(x1, x2);
156         SecP224K1Field.multiply(x2, x1, x2);
157         int[] x3 = x2;
158         SecP224K1Field.square(x2, x3);
159         SecP224K1Field.multiply(x3, x1, x3);
160         int[] x4 = Nat224.create();
161         SecP224K1Field.square(x3, x4);
162         SecP224K1Field.multiply(x4, x1, x4);
163         int[] x8 = Nat224.create();
164         SecP224K1Field.squareN(x4, 4, x8);
165         SecP224K1Field.multiply(x8, x4, x8);
166         int[] x11 = Nat224.create();
167         SecP224K1Field.squareN(x8, 3, x11);
168         SecP224K1Field.multiply(x11, x3, x11);
169         int[] x19 = x11;
170         SecP224K1Field.squareN(x11, 8, x19);
171         SecP224K1Field.multiply(x19, x8, x19);
172         int[] x23 = x8;
173         SecP224K1Field.squareN(x19, 4, x23);
174         SecP224K1Field.multiply(x23, x4, x23);
175         int[] x42 = x4;
176         SecP224K1Field.squareN(x23, 19, x42);
177         SecP224K1Field.multiply(x42, x19, x42);
178         int[] x84 = Nat224.create();
179         SecP224K1Field.squareN(x42, 42, x84);
180         SecP224K1Field.multiply(x84, x42, x84);
181         int[] x107 = x42;
182         SecP224K1Field.squareN(x84, 23, x107);
183         SecP224K1Field.multiply(x107, x23, x107);
184         int[] x191 = x23;
185         SecP224K1Field.squareN(x107, 84, x191);
186         SecP224K1Field.multiply(x191, x84, x191);
187 
188         int[] t1 = x191;
189         SecP224K1Field.squareN(t1, 20, t1);
190         SecP224K1Field.multiply(t1, x19, t1);
191         SecP224K1Field.squareN(t1, 3, t1);
192         SecP224K1Field.multiply(t1, x1, t1);
193         SecP224K1Field.squareN(t1, 2, t1);
194         SecP224K1Field.multiply(t1, x1, t1);
195         SecP224K1Field.squareN(t1, 4, t1);
196         SecP224K1Field.multiply(t1, x3, t1);
197         SecP224K1Field.square(t1, t1);
198 
199         int[] t2 = x84;
200         SecP224K1Field.square(t1, t2);
201 
202         if (Nat224.eq(x1, t2))
203         {
204             return new SecP224K1FieldElement(t1);
205         }
206 
207         /*
208          * If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess,
209          * which is ((4x)^(m + 1))/2 mod Q
210          */
211         SecP224K1Field.multiply(t1, PRECOMP_POW2, t1);
212 
213         SecP224K1Field.square(t1, t2);
214 
215         if (Nat224.eq(x1, t2))
216         {
217             return new SecP224K1FieldElement(t1);
218         }
219 
220         return null;
221     }
222 
equals(Object other)223     public boolean equals(Object other)
224     {
225         if (other == this)
226         {
227             return true;
228         }
229 
230         if (!(other instanceof SecP224K1FieldElement))
231         {
232             return false;
233         }
234 
235         SecP224K1FieldElement o = (SecP224K1FieldElement)other;
236         return Nat224.eq(x, o.x);
237     }
238 
hashCode()239     public int hashCode()
240     {
241         return Q.hashCode() ^ Arrays.hashCode(x, 0, 7);
242     }
243 }
244