field_test.go raw

   1  // Copyright (c) 2013-2016 The btcsuite developers
   2  // Copyright (c) 2013-2016 Dave Collins
   3  // Use of this source code is governed by an ISC
   4  // license that can be found in the LICENSE file.
   5  
   6  package ecc
   7  
   8  import (
   9  	"crypto/rand"
  10  	"encoding/hex"
  11  	"fmt"
  12  	"reflect"
  13  	"testing"
  14  )
  15  
  16  // TestSetInt ensures that setting a field value to various native integers
  17  // works as expected.
  18  func TestSetInt(t *testing.T) {
  19  	tests := []struct {
  20  		in  uint
  21  		raw [10]uint32
  22  	}{
  23  		{5, [10]uint32{5, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
  24  		// 2^26
  25  		{67108864, [10]uint32{67108864, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
  26  		// 2^26 + 1
  27  		{67108865, [10]uint32{67108865, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
  28  		// 2^32 - 1
  29  		{4294967295, [10]uint32{4294967295, 0, 0, 0, 0, 0, 0, 0, 0, 0}},
  30  	}
  31  
  32  	t.Logf("Running %d tests", len(tests))
  33  	for i, test := range tests {
  34  		f := new(fieldVal).SetInt(test.in)
  35  		if !reflect.DeepEqual(f.n, test.raw) {
  36  			t.Errorf("fieldVal.Set #%d wrong result\ngot: %v\n"+
  37  				"want: %v", i, f.n, test.raw)
  38  			continue
  39  		}
  40  	}
  41  }
  42  
  43  // TestZero ensures that zeroing a field value zero works as expected.
  44  func TestZero(t *testing.T) {
  45  	f := new(fieldVal).SetInt(2)
  46  	f.Zero()
  47  	for idx, rawInt := range f.n {
  48  		if rawInt != 0 {
  49  			t.Errorf("internal field integer at index #%d is not "+
  50  				"zero - got %d", idx, rawInt)
  51  		}
  52  	}
  53  }
  54  
  55  // TestIsZero ensures that checking if a field IsZero works as expected.
  56  func TestIsZero(t *testing.T) {
  57  	f := new(fieldVal)
  58  	if !f.IsZero() {
  59  		t.Errorf("new field value is not zero - got %v (rawints %x)", f,
  60  			f.n)
  61  	}
  62  
  63  	f.SetInt(1)
  64  	if f.IsZero() {
  65  		t.Errorf("field claims it's zero when it's not - got %v "+
  66  			"(raw rawints %x)", f, f.n)
  67  	}
  68  
  69  	f.Zero()
  70  	if !f.IsZero() {
  71  		t.Errorf("field claims it's not zero when it is - got %v "+
  72  			"(raw rawints %x)", f, f.n)
  73  	}
  74  }
  75  
  76  // TestStringer ensures the stringer returns the appropriate hex string.
  77  func TestStringer(t *testing.T) {
  78  	tests := []struct {
  79  		in       string
  80  		expected string
  81  	}{
  82  		{"0", "0000000000000000000000000000000000000000000000000000000000000000"},
  83  		{"1", "0000000000000000000000000000000000000000000000000000000000000001"},
  84  		{"a", "000000000000000000000000000000000000000000000000000000000000000a"},
  85  		{"b", "000000000000000000000000000000000000000000000000000000000000000b"},
  86  		{"c", "000000000000000000000000000000000000000000000000000000000000000c"},
  87  		{"d", "000000000000000000000000000000000000000000000000000000000000000d"},
  88  		{"e", "000000000000000000000000000000000000000000000000000000000000000e"},
  89  		{"f", "000000000000000000000000000000000000000000000000000000000000000f"},
  90  		{"f0", "00000000000000000000000000000000000000000000000000000000000000f0"},
  91  		// 2^26-1
  92  		{
  93  			"3ffffff",
  94  			"0000000000000000000000000000000000000000000000000000000003ffffff",
  95  		},
  96  		// 2^32-1
  97  		{
  98  			"ffffffff",
  99  			"00000000000000000000000000000000000000000000000000000000ffffffff",
 100  		},
 101  		// 2^64-1
 102  		{
 103  			"ffffffffffffffff",
 104  			"000000000000000000000000000000000000000000000000ffffffffffffffff",
 105  		},
 106  		// 2^96-1
 107  		{
 108  			"ffffffffffffffffffffffff",
 109  			"0000000000000000000000000000000000000000ffffffffffffffffffffffff",
 110  		},
 111  		// 2^128-1
 112  		{
 113  			"ffffffffffffffffffffffffffffffff",
 114  			"00000000000000000000000000000000ffffffffffffffffffffffffffffffff",
 115  		},
 116  		// 2^160-1
 117  		{
 118  			"ffffffffffffffffffffffffffffffffffffffff",
 119  			"000000000000000000000000ffffffffffffffffffffffffffffffffffffffff",
 120  		},
 121  		// 2^192-1
 122  		{
 123  			"ffffffffffffffffffffffffffffffffffffffffffffffff",
 124  			"0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffff",
 125  		},
 126  		// 2^224-1
 127  		{
 128  			"ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
 129  			"00000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
 130  		},
 131  		// 2^256-4294968273 (the btcec prime, so should result in 0)
 132  		{
 133  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
 134  			"0000000000000000000000000000000000000000000000000000000000000000",
 135  		},
 136  		// 2^256-4294968274 (the secp256k1 prime+1, so should result in 1)
 137  		{
 138  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
 139  			"0000000000000000000000000000000000000000000000000000000000000001",
 140  		},
 141  
 142  		// Invalid hex
 143  		{"g", "0000000000000000000000000000000000000000000000000000000000000000"},
 144  		{"1h", "0000000000000000000000000000000000000000000000000000000000000000"},
 145  		{"i1", "0000000000000000000000000000000000000000000000000000000000000000"},
 146  	}
 147  
 148  	t.Logf("Running %d tests", len(tests))
 149  	for i, test := range tests {
 150  		f := new(fieldVal).SetHex(test.in)
 151  		result := f.String()
 152  		if result != test.expected {
 153  			t.Errorf("fieldVal.String #%d wrong result\ngot: %v\n"+
 154  				"want: %v", i, result, test.expected)
 155  			continue
 156  		}
 157  	}
 158  }
 159  
 160  // TestNormalize ensures that normalizing the internal field words works as
 161  // expected.
 162  func TestNormalize(t *testing.T) {
 163  	tests := []struct {
 164  		raw        [10]uint32 // Intentionally denormalized value
 165  		normalized [10]uint32 // Normalized form of the raw value
 166  	}{
 167  		{
 168  			[10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 169  			[10]uint32{0x00000005, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 170  		},
 171  		// 2^26
 172  		{
 173  			[10]uint32{0x04000000, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
 174  			[10]uint32{0x00000000, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
 175  		},
 176  		// 2^26 + 1
 177  		{
 178  			[10]uint32{0x04000001, 0x0, 0, 0, 0, 0, 0, 0, 0, 0},
 179  			[10]uint32{0x00000001, 0x1, 0, 0, 0, 0, 0, 0, 0, 0},
 180  		},
 181  		// 2^32 - 1
 182  		{
 183  			[10]uint32{0xffffffff, 0x00, 0, 0, 0, 0, 0, 0, 0, 0},
 184  			[10]uint32{0x03ffffff, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
 185  		},
 186  		// 2^32
 187  		{
 188  			[10]uint32{0x04000000, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
 189  			[10]uint32{0x00000000, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
 190  		},
 191  		// 2^32 + 1
 192  		{
 193  			[10]uint32{0x04000001, 0x3f, 0, 0, 0, 0, 0, 0, 0, 0},
 194  			[10]uint32{0x00000001, 0x40, 0, 0, 0, 0, 0, 0, 0, 0},
 195  		},
 196  		// 2^64 - 1
 197  		{
 198  			[10]uint32{0xffffffff, 0xffffffc0, 0xfc0, 0, 0, 0, 0, 0, 0, 0},
 199  			[10]uint32{0x03ffffff, 0x03ffffff, 0xfff, 0, 0, 0, 0, 0, 0, 0},
 200  		},
 201  		// 2^64
 202  		{
 203  			[10]uint32{0x04000000, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
 204  			[10]uint32{0x00000000, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
 205  		},
 206  		// 2^64 + 1
 207  		{
 208  			[10]uint32{0x04000001, 0x03ffffff, 0x0fff, 0, 0, 0, 0, 0, 0, 0},
 209  			[10]uint32{0x00000001, 0x00000000, 0x1000, 0, 0, 0, 0, 0, 0, 0},
 210  		},
 211  		// 2^96 - 1
 212  		{
 213  			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0x3ffc0, 0, 0, 0, 0, 0, 0},
 214  			[10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
 215  		},
 216  		// 2^96
 217  		{
 218  			[10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x3ffff, 0, 0, 0, 0, 0, 0},
 219  			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x40000, 0, 0, 0, 0, 0, 0},
 220  		},
 221  		// 2^128 - 1
 222  		{
 223  			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffc0, 0, 0, 0, 0, 0},
 224  			[10]uint32{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0xffffff, 0, 0, 0, 0, 0},
 225  		},
 226  		// 2^128
 227  		{
 228  			[10]uint32{0x04000000, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x0ffffff, 0, 0, 0, 0, 0},
 229  			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x1000000, 0, 0, 0, 0, 0},
 230  		},
 231  		// 2^256 - 4294968273 (secp256k1 prime)
 232  		{
 233  			[10]uint32{0xfffffc2f, 0xffffff80, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
 234  			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
 235  		},
 236  		// Prime larger than P where both first and second words are larger
 237  		// than P's first and second words
 238  		{
 239  			[10]uint32{0xfffffc30, 0xffffff86, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
 240  			[10]uint32{0x00000001, 0x00000006, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
 241  		},
 242  		// Prime larger than P where only the second word is larger
 243  		// than P's second words.
 244  		{
 245  			[10]uint32{0xfffffc2a, 0xffffff87, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
 246  			[10]uint32{0x03fffffb, 0x00000006, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
 247  		},
 248  		// 2^256 - 1
 249  		{
 250  			[10]uint32{0xffffffff, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0xffffffc0, 0x3fffc0},
 251  			[10]uint32{0x000003d0, 0x00000040, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000},
 252  		},
 253  		// Prime with field representation such that the initial
 254  		// reduction does not result in a carry to bit 256.
 255  		//
 256  		// 2^256 - 4294968273 (secp256k1 prime)
 257  		{
 258  			[10]uint32{0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
 259  			[10]uint32{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},
 260  		},
 261  		// Prime larger than P that reduces to a value which is still
 262  		// larger than P when it has a magnitude of 1 due to its first
 263  		// word and does not result in a carry to bit 256.
 264  		//
 265  		// 2^256 - 4294968272 (secp256k1 prime + 1)
 266  		{
 267  			[10]uint32{0x03fffc30, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
 268  			[10]uint32{0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},
 269  		},
 270  		// Prime larger than P that reduces to a value which is still
 271  		// larger than P when it has a magnitude of 1 due to its second
 272  		// word and does not result in a carry to bit 256.
 273  		//
 274  		// 2^256 - 4227859409 (secp256k1 prime + 0x4000000)
 275  		{
 276  			[10]uint32{0x03fffc2f, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff},
 277  			[10]uint32{0x00000000, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},
 278  		},
 279  		// Prime larger than P that reduces to a value which is still
 280  		// larger than P when it has a magnitude of 1 due to a carry to
 281  		// bit 256, but would not be without the carry.  These values
 282  		// come from the fact that P is 2^256 - 4294968273 and 977 is
 283  		// the low order word in the internal field representation.
 284  		//
 285  		// 2^256 * 5 - ((4294968273 - (977+1)) * 4)
 286  		{
 287  			[10]uint32{0x03ffffff, 0x03fffeff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x0013fffff},
 288  			[10]uint32{0x00001314, 0x00000040, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x000000000},
 289  		},
 290  		// Prime larger than P that reduces to a value which is still
 291  		// larger than P when it has a magnitude of 1 due to both a
 292  		// carry to bit 256 and the first word.
 293  		{
 294  			[10]uint32{0x03fffc30, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x07ffffff, 0x003fffff},
 295  			[10]uint32{0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001},
 296  		},
 297  		// Prime larger than P that reduces to a value which is still
 298  		// larger than P when it has a magnitude of 1 due to both a
 299  		// carry to bit 256 and the second word.
 300  		//
 301  		{
 302  			[10]uint32{0x03fffc2f, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x3ffffff, 0x07ffffff, 0x003fffff},
 303  			[10]uint32{0x00000000, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x0000000, 0x00000000, 0x00000001},
 304  		},
 305  		// Prime larger than P that reduces to a value which is still
 306  		// larger than P when it has a magnitude of 1 due to a carry to
 307  		// bit 256 and the first and second words.
 308  		//
 309  		{
 310  			[10]uint32{0x03fffc30, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x07ffffff, 0x003fffff},
 311  			[10]uint32{0x00000001, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001},
 312  		},
 313  	}
 314  
 315  	t.Logf("Running %d tests", len(tests))
 316  	for i, test := range tests {
 317  		f := new(fieldVal)
 318  		f.n = test.raw
 319  		f.Normalize()
 320  		if !reflect.DeepEqual(f.n, test.normalized) {
 321  			t.Errorf("fieldVal.Normalize #%d wrong result\n"+
 322  				"got: %x\nwant: %x", i, f.n, test.normalized)
 323  			continue
 324  		}
 325  	}
 326  }
 327  
 328  // TestIsOdd ensures that checking if a field value IsOdd works as expected.
 329  func TestIsOdd(t *testing.T) {
 330  	tests := []struct {
 331  		in       string // hex encoded value
 332  		expected bool   // expected oddness
 333  	}{
 334  		{"0", false},
 335  		{"1", true},
 336  		{"2", false},
 337  		// 2^32 - 1
 338  		{"ffffffff", true},
 339  		// 2^64 - 2
 340  		{"fffffffffffffffe", false},
 341  		// secp256k1 prime
 342  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", true},
 343  	}
 344  
 345  	t.Logf("Running %d tests", len(tests))
 346  	for i, test := range tests {
 347  		f := new(fieldVal).SetHex(test.in)
 348  		result := f.IsOdd()
 349  		if result != test.expected {
 350  			t.Errorf("fieldVal.IsOdd #%d wrong result\n"+
 351  				"got: %v\nwant: %v", i, result, test.expected)
 352  			continue
 353  		}
 354  	}
 355  }
 356  
 357  // TestEquals ensures that checking two field values for equality via Equals
 358  // works as expected.
 359  func TestEquals(t *testing.T) {
 360  	tests := []struct {
 361  		in1      string // hex encoded value
 362  		in2      string // hex encoded value
 363  		expected bool   // expected equality
 364  	}{
 365  		{"0", "0", true},
 366  		{"0", "1", false},
 367  		{"1", "0", false},
 368  		// 2^32 - 1 == 2^32 - 1?
 369  		{"ffffffff", "ffffffff", true},
 370  		// 2^64 - 1 == 2^64 - 2?
 371  		{"ffffffffffffffff", "fffffffffffffffe", false},
 372  		// 0 == prime (mod prime)?
 373  		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", true},
 374  		// 1 == prime+1 (mod prime)?
 375  		{"1", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30", true},
 376  	}
 377  
 378  	t.Logf("Running %d tests", len(tests))
 379  	for i, test := range tests {
 380  		f := new(fieldVal).SetHex(test.in1).Normalize()
 381  		f2 := new(fieldVal).SetHex(test.in2).Normalize()
 382  		result := f.Equals(f2)
 383  		if result != test.expected {
 384  			t.Errorf("fieldVal.Equals #%d wrong result\n"+
 385  				"got: %v\nwant: %v", i, result, test.expected)
 386  			continue
 387  		}
 388  	}
 389  }
 390  
 391  // TestNegate ensures that negating field values via Negate works as expected.
 392  func TestNegate(t *testing.T) {
 393  	tests := []struct {
 394  		in       string // hex encoded value
 395  		expected string // expected hex encoded value
 396  	}{
 397  		// secp256k1 prime (aka 0)
 398  		{"0", "0"},
 399  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
 400  		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
 401  		// secp256k1 prime-1
 402  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1"},
 403  		{"1", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e"},
 404  		// secp256k1 prime-2
 405  		{"2", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d"},
 406  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d", "2"},
 407  		// Random sampling
 408  		{
 409  			"b3d9aac9c5e43910b4385b53c7e78c21d4cd5f8e683c633aed04c233efc2e120",
 410  			"4c2655363a1bc6ef4bc7a4ac381873de2b32a07197c39cc512fb3dcb103d1b0f",
 411  		},
 412  		{
 413  			"f8a85984fee5a12a7c8dd08830d83423c937d77c379e4a958e447a25f407733f",
 414  			"757a67b011a5ed583722f77cf27cbdc36c82883c861b56a71bb85d90bf888f0",
 415  		},
 416  		{
 417  			"45ee6142a7fda884211e93352ed6cb2807800e419533be723a9548823ece8312",
 418  			"ba119ebd5802577bdee16ccad12934d7f87ff1be6acc418dc56ab77cc131791d",
 419  		},
 420  		{
 421  			"53c2a668f07e411a2e473e1c3b6dcb495dec1227af27673761d44afe5b43d22b",
 422  			"ac3d59970f81bee5d1b8c1e3c49234b6a213edd850d898c89e2bb500a4bc2a04",
 423  		},
 424  	}
 425  
 426  	t.Logf("Running %d tests", len(tests))
 427  	for i, test := range tests {
 428  		f := new(fieldVal).SetHex(test.in).Normalize()
 429  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 430  		result := f.Negate(1).Normalize()
 431  		if !result.Equals(expected) {
 432  			t.Errorf("fieldVal.Negate #%d wrong result\n"+
 433  				"got: %v\nwant: %v", i, result, expected)
 434  			continue
 435  		}
 436  	}
 437  }
 438  
 439  // TestAddInt ensures that adding an integer to field values via AddInt works as
 440  // expected.
 441  func TestAddInt(t *testing.T) {
 442  	tests := []struct {
 443  		in1      string // hex encoded value
 444  		in2      uint   // unsigned integer to add to the value above
 445  		expected string // expected hex encoded value
 446  	}{
 447  		{"0", 1, "1"},
 448  		{"1", 0, "1"},
 449  		{"1", 1, "2"},
 450  		// secp256k1 prime-1 + 1
 451  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", 1, "0"},
 452  		// secp256k1 prime + 1
 453  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 1, "1"},
 454  		// Random samples.
 455  		{
 456  			"ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d6c1",
 457  			0x10f,
 458  			"ff95ad9315aff04ab4af0ce673620c7145dc85d03bab5ba4b09ca2c4dec2d7d0",
 459  		},
 460  		{
 461  			"44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41deea9cecf",
 462  			0x2cf11d41,
 463  			"44bdae6b772e7987941f1ba314e6a5b7804a4c12c00961b57d20f41e1b9aec10",
 464  		},
 465  		{
 466  			"88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f7105122c9c",
 467  			0x4829aa2d,
 468  			"88c3ecae67b591935fb1f6a9499c35315ffad766adca665c50b55f714d3bd6c9",
 469  		},
 470  		{
 471  			"8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee09a015e2a6",
 472  			0xa21265a5,
 473  			"8523e9edf360ca32a95aae4e57fcde5a542b471d08a974d94ea0ee0a4228484b",
 474  		},
 475  	}
 476  
 477  	t.Logf("Running %d tests", len(tests))
 478  	for i, test := range tests {
 479  		f := new(fieldVal).SetHex(test.in1).Normalize()
 480  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 481  		result := f.AddInt(test.in2).Normalize()
 482  		if !result.Equals(expected) {
 483  			t.Errorf("fieldVal.AddInt #%d wrong result\n"+
 484  				"got: %v\nwant: %v", i, result, expected)
 485  			continue
 486  		}
 487  	}
 488  }
 489  
 490  // TestAdd ensures that adding two field values together via Add works as
 491  // expected.
 492  func TestAdd(t *testing.T) {
 493  	tests := []struct {
 494  		in1      string // first hex encoded value
 495  		in2      string // second hex encoded value to add
 496  		expected string // expected hex encoded value
 497  	}{
 498  		{"0", "1", "1"},
 499  		{"1", "0", "1"},
 500  		{"1", "1", "2"},
 501  		// secp256k1 prime-1 + 1
 502  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
 503  		// secp256k1 prime + 1
 504  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
 505  		// Random samples.
 506  		{
 507  			"2b2012f975404e5065b4292fb8bed0a5d315eacf24c74d8b27e73bcc5430edcc",
 508  			"2c3cefa4e4753e8aeec6ac4c12d99da4d78accefda3b7885d4c6bab46c86db92",
 509  			"575d029e59b58cdb547ad57bcb986e4aaaa0b7beff02c610fcadf680c0b7c95e",
 510  		},
 511  		{
 512  			"8131e8722fe59bb189692b96c9f38de92885730f1dd39ab025daffb94c97f79c",
 513  			"ff5454b765f0aab5f0977dcc629becc84cabeb9def48e79c6aadb2622c490fa9",
 514  			"80863d2995d646677a00a9632c8f7ab175315ead0d1c824c9088b21c78e10b16",
 515  		},
 516  		{
 517  			"c7c95e93d0892b2b2cdd77e80eb646ea61be7a30ac7e097e9f843af73fad5c22",
 518  			"3afe6f91a74dfc1c7f15c34907ee981656c37236d946767dd53ccad9190e437c",
 519  			"02c7ce2577d72747abf33b3116a4df00b881ec6785c47ffc74c105d158bba36f",
 520  		},
 521  		{
 522  			"fd1c26f6a23381e5d785ba889494ec059369b888ad8431cd67d8c934b580dbe1",
 523  			"a475aa5a31dcca90ef5b53c097d9133d6b7117474b41e7877bb199590fc0489c",
 524  			"a191d150d4104c76c6e10e492c6dff42fedacfcff8c61954e38a628ec541284e",
 525  		},
 526  	}
 527  
 528  	t.Logf("Running %d tests", len(tests))
 529  	for i, test := range tests {
 530  		f := new(fieldVal).SetHex(test.in1).Normalize()
 531  		f2 := new(fieldVal).SetHex(test.in2).Normalize()
 532  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 533  		result := f.Add(f2).Normalize()
 534  		if !result.Equals(expected) {
 535  			t.Errorf("fieldVal.Add #%d wrong result\n"+
 536  				"got: %v\nwant: %v", i, result, expected)
 537  			continue
 538  		}
 539  	}
 540  }
 541  
 542  // TestAdd2 ensures that adding two field values together via Add2 works as
 543  // expected.
 544  func TestAdd2(t *testing.T) {
 545  	tests := []struct {
 546  		in1      string // first hex encoded value
 547  		in2      string // second hex encoded value to add
 548  		expected string // expected hex encoded value
 549  	}{
 550  		{"0", "1", "1"},
 551  		{"1", "0", "1"},
 552  		{"1", "1", "2"},
 553  		// secp256k1 prime-1 + 1
 554  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1", "0"},
 555  		// secp256k1 prime + 1
 556  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "1", "1"},
 557  		// close but over the secp256k1 prime
 558  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffff000000000", "f1ffff000", "1ffff3d1"},
 559  		// Random samples.
 560  		{
 561  			"ad82b8d1cc136e23e9fd77fe2c7db1fe5a2ecbfcbde59ab3529758334f862d28",
 562  			"4d6a4e95d6d61f4f46b528bebe152d408fd741157a28f415639347a84f6f574b",
 563  			"faed0767a2e98d7330b2a0bcea92df3eea060d12380e8ec8b62a9fdb9ef58473",
 564  		},
 565  		{
 566  			"f3f43a2540054a86e1df98547ec1c0e157b193e5350fb4a3c3ea214b228ac5e7",
 567  			"25706572592690ea3ddc951a1b48b504a4c83dc253756e1b96d56fdfb3199522",
 568  			"19649f97992bdb711fbc2d6e9a0a75e5fc79d1a7888522bf5abf912bd5a45eda",
 569  		},
 570  		{
 571  			"6915bb94eef13ff1bb9b2633d997e13b9b1157c713363cc0e891416d6734f5b8",
 572  			"11f90d6ac6fe1c4e8900b1c85fb575c251ec31b9bc34b35ada0aea1c21eded22",
 573  			"7b0ec8ffb5ef5c40449bd7fc394d56fdecfd8980cf6af01bc29c2b898922e2da",
 574  		},
 575  		{
 576  			"48b0c9eae622eed9335b747968544eb3e75cb2dc8128388f948aa30f88cabde4",
 577  			"0989882b52f85f9d524a3a3061a0e01f46d597839d2ba637320f4b9510c8d2d5",
 578  			"523a5216391b4e7685a5aea9c9f52ed32e324a601e53dec6c699eea4999390b9",
 579  		},
 580  	}
 581  
 582  	t.Logf("Running %d tests", len(tests))
 583  	for i, test := range tests {
 584  		f := new(fieldVal).SetHex(test.in1).Normalize()
 585  		f2 := new(fieldVal).SetHex(test.in2).Normalize()
 586  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 587  		result := f.Add2(f, f2).Normalize()
 588  		if !result.Equals(expected) {
 589  			t.Errorf("fieldVal.Add2 #%d wrong result\n"+
 590  				"got: %v\nwant: %v", i, result, expected)
 591  			continue
 592  		}
 593  	}
 594  }
 595  
 596  // TestMulInt ensures that adding an integer to field values via MulInt works as
 597  // expected.
 598  func TestMulInt(t *testing.T) {
 599  	tests := []struct {
 600  		in1      string // hex encoded value
 601  		in2      uint   // unsigned integer to multiply with value above
 602  		expected string // expected hex encoded value
 603  	}{
 604  		{"0", 0, "0"},
 605  		{"1", 0, "0"},
 606  		{"0", 1, "0"},
 607  		{"1", 1, "1"},
 608  		// secp256k1 prime-1 * 2
 609  		{
 610  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 611  			2,
 612  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
 613  		},
 614  		// secp256k1 prime * 3
 615  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 3, "0"},
 616  		// secp256k1 prime-1 * 8
 617  		{
 618  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 619  			8,
 620  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
 621  		},
 622  		// Random samples for first value.  The second value is limited
 623  		// to 8 since that is the maximum int used in the elliptic curve
 624  		// calculations.
 625  		{
 626  			"b75674dc9180d306c692163ac5e089f7cef166af99645c0c23568ab6d967288a",
 627  			6,
 628  			"4c06bd2b6904f228a76c8560a3433bced9a8681d985a2848d407404d186b0280",
 629  		},
 630  		{
 631  			"54873298ac2b5ba8591c125ae54931f5ea72040aee07b208d6135476fb5b9c0e",
 632  			3,
 633  			"fd9597ca048212f90b543710afdb95e1bf560c20ca17161a8239fd64f212d42a",
 634  		},
 635  		{
 636  			"7c30fbd363a74c17e1198f56b090b59bbb6c8755a74927a6cba7a54843506401",
 637  			5,
 638  			"6cf4eb20f2447c77657fccb172d38c0aa91ea4ac446dc641fa463a6b5091fba7",
 639  		},
 640  		{
 641  			"fb4529be3e027a3d1587d8a500b72f2d312e3577340ef5175f96d113be4c2ceb",
 642  			8,
 643  			"da294df1f013d1e8ac3ec52805b979698971abb9a077a8bafcb688a4f261820f",
 644  		},
 645  	}
 646  
 647  	t.Logf("Running %d tests", len(tests))
 648  	for i, test := range tests {
 649  		f := new(fieldVal).SetHex(test.in1).Normalize()
 650  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 651  		result := f.MulInt(test.in2).Normalize()
 652  		if !result.Equals(expected) {
 653  			t.Errorf("fieldVal.MulInt #%d wrong result\n"+
 654  				"got: %v\nwant: %v", i, result, expected)
 655  			continue
 656  		}
 657  	}
 658  }
 659  
 660  // TestMul ensures that multiplying two field valuess via Mul works as expected.
 661  func TestMul(t *testing.T) {
 662  	tests := []struct {
 663  		in1      string // first hex encoded value
 664  		in2      string // second hex encoded value to multiply with
 665  		expected string // expected hex encoded value
 666  	}{
 667  		{"0", "0", "0"},
 668  		{"1", "0", "0"},
 669  		{"0", "1", "0"},
 670  		{"1", "1", "1"},
 671  		// slightly over prime
 672  		{
 673  			"ffffffffffffffffffffffffffffffffffffffffffffffffffffffff1ffff",
 674  			"1000",
 675  			"1ffff3d1",
 676  		},
 677  		// secp256k1 prime-1 * 2
 678  		{
 679  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 680  			"2",
 681  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
 682  		},
 683  		// secp256k1 prime * 3
 684  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "3", "0"},
 685  		// secp256k1 prime-1 * 8
 686  		{
 687  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 688  			"8",
 689  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc27",
 690  		},
 691  		// Random samples.
 692  		{
 693  			"cfb81753d5ef499a98ecc04c62cb7768c2e4f1740032946db1c12e405248137e",
 694  			"58f355ad27b4d75fb7db0442452e732c436c1f7c5a7c4e214fa9cc031426a7d3",
 695  			"1018cd2d7c2535235b71e18db9cd98027386328d2fa6a14b36ec663c4c87282b",
 696  		},
 697  		{
 698  			"26e9d61d1cdf3920e9928e85fa3df3e7556ef9ab1d14ec56d8b4fc8ed37235bf",
 699  			"2dfc4bbe537afee979c644f8c97b31e58be5296d6dbc460091eae630c98511cf",
 700  			"da85f48da2dc371e223a1ae63bd30b7e7ee45ae9b189ac43ff357e9ef8cf107a",
 701  		},
 702  		{
 703  			"5db64ed5afb71646c8b231585d5b2bf7e628590154e0854c4c29920b999ff351",
 704  			"279cfae5eea5d09ade8e6a7409182f9de40981bc31c84c3d3dfe1d933f152e9a",
 705  			"2c78fbae91792dd0b157abe3054920049b1879a7cc9d98cfda927d83be411b37",
 706  		},
 707  		{
 708  			"b66dfc1f96820b07d2bdbd559c19319a3a73c97ceb7b3d662f4fe75ecb6819e6",
 709  			"bf774aba43e3e49eb63a6e18037d1118152568f1a3ac4ec8b89aeb6ff8008ae1",
 710  			"c4f016558ca8e950c21c3f7fc15f640293a979c7b01754ee7f8b3340d4902ebb",
 711  		},
 712  	}
 713  
 714  	t.Logf("Running %d tests", len(tests))
 715  	for i, test := range tests {
 716  		f := new(fieldVal).SetHex(test.in1).Normalize()
 717  		f2 := new(fieldVal).SetHex(test.in2).Normalize()
 718  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 719  		result := f.Mul(f2).Normalize()
 720  		if !result.Equals(expected) {
 721  			t.Errorf("fieldVal.Mul #%d wrong result\n"+
 722  				"got: %v\nwant: %v", i, result, expected)
 723  			continue
 724  		}
 725  	}
 726  }
 727  
 728  // TestSquare ensures that squaring field values via Square works as expected.
 729  func TestSquare(t *testing.T) {
 730  	tests := []struct {
 731  		in       string // hex encoded value
 732  		expected string // expected hex encoded value
 733  	}{
 734  		// secp256k1 prime (aka 0)
 735  		{"0", "0"},
 736  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
 737  		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
 738  		// secp256k1 prime-1
 739  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e", "1"},
 740  		// secp256k1 prime-2
 741  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d", "4"},
 742  		// Random sampling
 743  		{
 744  			"b0ba920360ea8436a216128047aab9766d8faf468895eb5090fc8241ec758896",
 745  			"133896b0b69fda8ce9f648b9a3af38f345290c9eea3cbd35bafcadf7c34653d3",
 746  		},
 747  		{
 748  			"c55d0d730b1d0285a1599995938b042a756e6e8857d390165ffab480af61cbd5",
 749  			"cd81758b3f5877cbe7e5b0a10cebfa73bcbf0957ca6453e63ee8954ab7780bee",
 750  		},
 751  		{
 752  			"e89c1f9a70d93651a1ba4bca5b78658f00de65a66014a25544d3365b0ab82324",
 753  			"39ffc7a43e5dbef78fd5d0354fb82c6d34f5a08735e34df29da14665b43aa1f",
 754  		},
 755  		{
 756  			"7dc26186079d22bcbe1614aa20ae627e62d72f9be7ad1e99cac0feb438956f05",
 757  			"bf86bcfc4edb3d81f916853adfda80c07c57745b008b60f560b1912f95bce8ae",
 758  		},
 759  	}
 760  
 761  	t.Logf("Running %d tests", len(tests))
 762  	for i, test := range tests {
 763  		f := new(fieldVal).SetHex(test.in).Normalize()
 764  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 765  		result := f.Square().Normalize()
 766  		if !result.Equals(expected) {
 767  			t.Errorf("fieldVal.Square #%d wrong result\n"+
 768  				"got: %v\nwant: %v", i, result, expected)
 769  			continue
 770  		}
 771  	}
 772  }
 773  
 774  // TestInverse ensures that finding the multiplicative inverse via Inverse works
 775  // as expected.
 776  func TestInverse(t *testing.T) {
 777  	tests := []struct {
 778  		in       string // hex encoded value
 779  		expected string // expected hex encoded value
 780  	}{
 781  		// secp256k1 prime (aka 0)
 782  		{"0", "0"},
 783  		{"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", "0"},
 784  		{"0", "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"},
 785  		// secp256k1 prime-1
 786  		{
 787  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 788  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 789  		},
 790  		// secp256k1 prime-2
 791  		{
 792  			"fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2d",
 793  			"7fffffffffffffffffffffffffffffffffffffffffffffffffffffff7ffffe17",
 794  		},
 795  		// Random sampling
 796  		{
 797  			"16fb970147a9acc73654d4be233cc48b875ce20a2122d24f073d29bd28805aca",
 798  			"987aeb257b063df0c6d1334051c47092b6d8766c4bf10c463786d93f5bc54354",
 799  		},
 800  		{
 801  			"69d1323ce9f1f7b3bd3c7320b0d6311408e30281e273e39a0d8c7ee1c8257919",
 802  			"49340981fa9b8d3dad72de470b34f547ed9179c3953797d0943af67806f4bb6",
 803  		},
 804  		{
 805  			"e0debf988ae098ecda07d0b57713e97c6d213db19753e8c95aa12a2fc1cc5272",
 806  			"64f58077b68af5b656b413ea366863f7b2819f8d27375d9c4d9804135ca220c2",
 807  		},
 808  		{
 809  			"dcd394f91f74c2ba16aad74a22bb0ed47fe857774b8f2d6c09e28bfb14642878",
 810  			"fb848ec64d0be572a63c38fe83df5e7f3d032f60bf8c969ef67d36bf4ada22a9",
 811  		},
 812  	}
 813  
 814  	t.Logf("Running %d tests", len(tests))
 815  	for i, test := range tests {
 816  		f := new(fieldVal).SetHex(test.in).Normalize()
 817  		expected := new(fieldVal).SetHex(test.expected).Normalize()
 818  		result := f.Inverse().Normalize()
 819  		if !result.Equals(expected) {
 820  			t.Errorf("fieldVal.Inverse #%d wrong result\n"+
 821  				"got: %v\nwant: %v", i, result, expected)
 822  			continue
 823  		}
 824  	}
 825  }
 826  
 827  // randFieldVal returns a random, normalized element in the field.
 828  func randFieldVal(t *testing.T) fieldVal {
 829  	var b [32]byte
 830  	if _, err := rand.Read(b[:]); err != nil {
 831  		t.Fatalf("unable to create random element: %v", err)
 832  	}
 833  
 834  	var x fieldVal
 835  	return *x.SetBytes(&b).Normalize()
 836  }
 837  
 838  type sqrtTest struct {
 839  	name     string
 840  	in       string
 841  	expected string
 842  }
 843  
 844  // TestSqrt asserts that a fieldVal properly computes the square root modulo the
 845  // sep256k1 prime.
 846  func TestSqrt(t *testing.T) {
 847  	var tests []sqrtTest
 848  
 849  	// No valid root exists for the negative of a square.
 850  	for i := uint(9); i > 0; i-- {
 851  		var (
 852  			x fieldVal
 853  			s fieldVal // x^2 mod p
 854  			n fieldVal // -x^2 mod p
 855  		)
 856  
 857  		x.SetInt(i)
 858  		s.SquareVal(&x).Normalize()
 859  		n.NegateVal(&s, 1).Normalize()
 860  
 861  		tests = append(tests, sqrtTest{
 862  			name: fmt.Sprintf("-%d", i),
 863  			in:   fmt.Sprintf("%x", *n.Bytes()),
 864  		})
 865  	}
 866  
 867  	// A root should exist for true squares.
 868  	for i := uint(0); i < 10; i++ {
 869  		var (
 870  			x fieldVal
 871  			s fieldVal // x^2 mod p
 872  		)
 873  
 874  		x.SetInt(i)
 875  		s.SquareVal(&x).Normalize()
 876  
 877  		tests = append(tests, sqrtTest{
 878  			name:     fmt.Sprintf("%d", i),
 879  			in:       fmt.Sprintf("%x", *s.Bytes()),
 880  			expected: fmt.Sprintf("%x", *x.Bytes()),
 881  		})
 882  	}
 883  
 884  	// Compute a non-square element, by negating if it has a root.
 885  	ns := randFieldVal(t)
 886  	if new(fieldVal).SqrtVal(&ns).Square().Equals(&ns) {
 887  		ns.Negate(1).Normalize()
 888  	}
 889  
 890  	// For large random field values, test that:
 891  	//  1) its square has a valid root.
 892  	//  2) the negative of its square has no root.
 893  	//  3) the product of its square with a non-square has no root.
 894  	for i := 0; i < 10; i++ {
 895  		var (
 896  			x fieldVal
 897  			s fieldVal // x^2 mod p
 898  			n fieldVal // -x^2 mod p
 899  			m fieldVal // ns*x^2 mod p
 900  		)
 901  
 902  		x = randFieldVal(t)
 903  		s.SquareVal(&x).Normalize()
 904  		n.NegateVal(&s, 1).Normalize()
 905  		m.Mul2(&s, &ns).Normalize()
 906  
 907  		// A root should exist for true squares.
 908  		tests = append(tests, sqrtTest{
 909  			name:     fmt.Sprintf("%x", *s.Bytes()),
 910  			in:       fmt.Sprintf("%x", *s.Bytes()),
 911  			expected: fmt.Sprintf("%x", *x.Bytes()),
 912  		})
 913  
 914  		// No valid root exists for the negative of a square.
 915  		tests = append(tests, sqrtTest{
 916  			name: fmt.Sprintf("-%x", *s.Bytes()),
 917  			in:   fmt.Sprintf("%x", *n.Bytes()),
 918  		})
 919  
 920  		// No root should be computed for product of a square and
 921  		// non-square.
 922  		tests = append(tests, sqrtTest{
 923  			name: fmt.Sprintf("ns*%x", *s.Bytes()),
 924  			in:   fmt.Sprintf("%x", *m.Bytes()),
 925  		})
 926  	}
 927  
 928  	for _, test := range tests {
 929  		t.Run(test.name, func(t *testing.T) {
 930  			testSqrt(t, test)
 931  		})
 932  	}
 933  }
 934  
 935  func testSqrt(t *testing.T, test sqrtTest) {
 936  	var (
 937  		f       fieldVal
 938  		root    fieldVal
 939  		rootNeg fieldVal
 940  	)
 941  
 942  	f.SetHex(test.in).Normalize()
 943  
 944  	// Compute sqrt(f) and its negative.
 945  	root.SqrtVal(&f).Normalize()
 946  	rootNeg.NegateVal(&root, 1).Normalize()
 947  
 948  	switch {
 949  
 950  	// If we expect a square root, verify that either the computed square
 951  	// root is +/- the expected value.
 952  	case len(test.expected) > 0:
 953  		var expected fieldVal
 954  		expected.SetHex(test.expected).Normalize()
 955  		if !root.Equals(&expected) && !rootNeg.Equals(&expected) {
 956  			t.Fatalf("fieldVal.Sqrt incorrect root\n"+
 957  				"got:     %v\ngot_neg: %v\nwant:    %v",
 958  				root, rootNeg, expected)
 959  		}
 960  
 961  	// Otherwise, we expect this input not to have a square root.
 962  	default:
 963  		if root.Square().Equals(&f) || rootNeg.Square().Equals(&f) {
 964  			t.Fatalf("fieldVal.Sqrt root should not exist\n"+
 965  				"got:     %v\ngot_neg: %v", root, rootNeg)
 966  		}
 967  	}
 968  }
 969  
 970  // TestFieldSetBytes ensures that setting a field value to a 256-bit big-endian
 971  // unsigned integer via both the slice and array methods works as expected for
 972  // edge cases.  Random cases are tested via the various other tests.
 973  func TestFieldSetBytes(t *testing.T) {
 974  	tests := []struct {
 975  		name     string     // test description
 976  		in       string     // hex encoded test value
 977  		expected [10]uint32 // expected raw ints
 978  	}{{
 979  		name:     "zero",
 980  		in:       "00",
 981  		expected: [10]uint32{0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 982  	}, {
 983  		name: "field prime",
 984  		in:   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
 985  		expected: [10]uint32{
 986  			0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff,
 987  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
 988  		},
 989  	}, {
 990  		name: "field prime - 1",
 991  		in:   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
 992  		expected: [10]uint32{
 993  			0x03fffc2e, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff,
 994  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
 995  		},
 996  	}, {
 997  		name: "field prime + 1 (overflow in word zero)",
 998  		in:   "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc30",
 999  		expected: [10]uint32{
1000  			0x03fffc30, 0x03ffffbf, 0x03ffffff, 0x03ffffff, 0x03ffffff,
1001  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
1002  		},
1003  	}, {
1004  		name: "field prime first 32 bits",
1005  		in:   "fffffc2f",
1006  		expected: [10]uint32{
1007  			0x03fffc2f, 0x00000003f, 0x00000000, 0x00000000, 0x00000000,
1008  			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1009  		},
1010  	}, {
1011  		name: "field prime word zero",
1012  		in:   "03fffc2f",
1013  		expected: [10]uint32{
1014  			0x03fffc2f, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1015  			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1016  		},
1017  	}, {
1018  		name: "field prime first 64 bits",
1019  		in:   "fffffffefffffc2f",
1020  		expected: [10]uint32{
1021  			0x03fffc2f, 0x03ffffbf, 0x00000fff, 0x00000000, 0x00000000,
1022  			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1023  		},
1024  	}, {
1025  		name: "field prime word zero and one",
1026  		in:   "0ffffefffffc2f",
1027  		expected: [10]uint32{
1028  			0x03fffc2f, 0x03ffffbf, 0x00000000, 0x00000000, 0x00000000,
1029  			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1030  		},
1031  	}, {
1032  		name: "field prime first 96 bits",
1033  		in:   "fffffffffffffffefffffc2f",
1034  		expected: [10]uint32{
1035  			0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x0003ffff, 0x00000000,
1036  			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1037  		},
1038  	}, {
1039  		name: "field prime word zero, one, and two",
1040  		in:   "3ffffffffffefffffc2f",
1041  		expected: [10]uint32{
1042  			0x03fffc2f, 0x03ffffbf, 0x03ffffff, 0x00000000, 0x00000000,
1043  			0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
1044  		},
1045  	}, {
1046  		name: "overflow in word one (prime + 1<<26)",
1047  		in:   "ffffffffffffffffffffffffffffffffffffffffffffffffffffffff03fffc2f",
1048  		expected: [10]uint32{
1049  			0x03fffc2f, 0x03ffffc0, 0x03ffffff, 0x03ffffff, 0x03ffffff,
1050  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
1051  		},
1052  	}, {
1053  		name: "(field prime - 1) * 2 NOT mod P, truncated >32 bytes",
1054  		in:   "01fffffffffffffffffffffffffffffffffffffffffffffffffffffffdfffff85c",
1055  		expected: [10]uint32{
1056  			0x01fffff8, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff,
1057  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x00007fff,
1058  		},
1059  	}, {
1060  		name: "2^256 - 1",
1061  		in:   "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
1062  		expected: [10]uint32{
1063  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff,
1064  			0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x003fffff,
1065  		},
1066  	}, {
1067  		name: "alternating bits",
1068  		in:   "a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5",
1069  		expected: [10]uint32{
1070  			0x01a5a5a5, 0x01696969, 0x025a5a5a, 0x02969696, 0x01a5a5a5,
1071  			0x01696969, 0x025a5a5a, 0x02969696, 0x01a5a5a5, 0x00296969,
1072  		},
1073  	}, {
1074  		name: "alternating bits 2",
1075  		in:   "5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a5a",
1076  		expected: [10]uint32{
1077  			0x025a5a5a, 0x02969696, 0x01a5a5a5, 0x01696969, 0x025a5a5a,
1078  			0x02969696, 0x01a5a5a5, 0x01696969, 0x025a5a5a, 0x00169696,
1079  		},
1080  	}}
1081  
1082  	for _, test := range tests {
1083  		inBytes := hexToBytes(test.in)
1084  
1085  		// Ensure setting the bytes via the slice method works as expected.
1086  		var f fieldVal
1087  		f.SetByteSlice(inBytes)
1088  		if !reflect.DeepEqual(f.n, test.expected) {
1089  			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name, f.n,
1090  				test.expected)
1091  			continue
1092  		}
1093  
1094  		// Ensure setting the bytes via the array method works as expected.
1095  		var f2 fieldVal
1096  		var b32 [32]byte
1097  		truncatedInBytes := inBytes
1098  		if len(truncatedInBytes) > 32 {
1099  			truncatedInBytes = truncatedInBytes[:32]
1100  		}
1101  		copy(b32[32-len(truncatedInBytes):], truncatedInBytes)
1102  		f2.SetBytes(&b32)
1103  		if !reflect.DeepEqual(f2.n, test.expected) {
1104  			t.Errorf("%s: unexpected result\ngot: %x\nwant: %x", test.name,
1105  				f2.n, test.expected)
1106  			continue
1107  		}
1108  	}
1109  }
1110  
1111  // hexToBytes converts the passed hex string into bytes and will panic if there
1112  // is an error.  This is only provided for the hard-coded constants so errors in
1113  // the source code can be detected. It will only (and must only) be called with
1114  // hard-coded values.
1115  func hexToBytes(s string) []byte {
1116  	b, err := hex.DecodeString(s)
1117  	if err != nil {
1118  		panic("invalid hex in source file: " + s)
1119  	}
1120  	return b
1121  }
1122