mirror of
https://github.com/golang/go
synced 2024-11-12 09:10:21 -07:00
roll back 3985: build is broken
TBR=agl1 CC=golang-dev https://golang.org/cl/154065
This commit is contained in:
Russ Cox
parent
af1fa43a81
commit
ed86d0e70a
@ -1,6 +1,6 @@
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archive/tar.install: bytes.install io.install os.install strconv.install strings.install
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asn1.install: fmt.install os.install reflect.install strconv.install strings.install time.install
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big.install: rand.install
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big.install:
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bignum.install: fmt.install
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bufio.install: io.install os.install strconv.install utf8.install
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bytes.install: os.install unicode.install utf8.install
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@ -19,8 +19,8 @@ crypto/rc4.install: os.install strconv.install
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crypto/rsa.install: big.install bytes.install crypto/subtle.install hash.install io.install os.install
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crypto/sha1.install: hash.install os.install
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crypto/subtle.install:
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crypto/tls.install: bufio.install bytes.install container/list.install crypto/hmac.install crypto/md5.install crypto/rc4.install crypto/rsa.install crypto/sha1.install crypto/subtle.install crypto/x509.install fmt.install hash.install io.install net.install os.install strings.install time.install
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crypto/x509.install: asn1.install big.install container/vector.install crypto/rsa.install os.install time.install
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crypto/tls.install: bufio.install bytes.install container/list.install crypto/hmac.install crypto/md5.install crypto/rc4.install crypto/rsa.install crypto/sha1.install crypto/subtle.install fmt.install hash.install io.install net.install os.install strings.install time.install
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crypto/x509.install: asn1.install big.install crypto/rsa.install os.install
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debug/dwarf.install: encoding/binary.install os.install strconv.install
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debug/macho.install: bytes.install debug/dwarf.install encoding/binary.install fmt.install io.install os.install strconv.install
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debug/elf.install: bytes.install debug/dwarf.install encoding/binary.install fmt.install io.install os.install strconv.install
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@ -43,7 +43,7 @@ fmt.install: io.install os.install reflect.install strconv.install utf8.install
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go/ast.install: fmt.install go/token.install unicode.install utf8.install
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go/doc.install: container/vector.install go/ast.install go/token.install io.install regexp.install sort.install strings.install template.install
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go/parser.install: bytes.install container/vector.install fmt.install go/ast.install go/scanner.install go/token.install io.install os.install path.install strings.install
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go/printer.install: bytes.install fmt.install go/ast.install go/token.install io.install os.install reflect.install runtime.install strings.install tabwriter.install
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go/printer.install: bytes.install container/vector.install fmt.install go/ast.install go/token.install io.install os.install reflect.install runtime.install strings.install tabwriter.install
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go/scanner.install: bytes.install container/vector.install fmt.install go/token.install io.install os.install sort.install strconv.install unicode.install utf8.install
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go/token.install: fmt.install strconv.install
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gob.install: bytes.install fmt.install io.install math.install os.install reflect.install sync.install
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@ -119,6 +119,40 @@ func (z *Int) Mod(x, y *Int) (r *Int) {
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func div(q, r, x, y *Int) {
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if len(y.abs) == 0 {
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panic("Divide by zero undefined")
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}
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if cmpNN(x.abs, y.abs) < 0 {
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q.neg = false;
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q.abs = nil;
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r.neg = y.neg;
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src := x.abs;
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dst := x.abs;
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if r == x {
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dst = nil
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}
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r.abs = makeN(dst, len(src), false);
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for i, v := range src {
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r.abs[i] = v
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}
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return;
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}
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if len(y.abs) == 1 {
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var rprime Word;
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q.abs, rprime = divNW(q.abs, x.abs, y.abs[0]);
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if rprime > 0 {
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r.abs = makeN(r.abs, 1, false);
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r.abs[0] = rprime;
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r.neg = x.neg;
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}
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q.neg = len(q.abs) > 0 && x.neg != y.neg;
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return;
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}
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q.neg = x.neg != y.neg;
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r.neg = x.neg;
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q.abs, r.abs = divNN(q.abs, r.abs, x.abs, y.abs);
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@ -134,13 +168,15 @@ func (z *Int) Neg(x *Int) *Int {
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}
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// Cmp compares x and y. The result is
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// TODO(gri) Should this be x.Cmp(y) instead?
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// CmpInt compares x and y. The result is
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//
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// -1 if x < y
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// 0 if x == y
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// +1 if x > y
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//
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func (x *Int) Cmp(y *Int) (r int) {
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func CmpInt(x, y *Int) (r int) {
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// x cmp y == x cmp y
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// x cmp (-y) == x
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// (-x) cmp y == y
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@ -271,7 +307,7 @@ func (z *Int) Len() int {
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return 0
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}
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return len(z.abs)*_W - int(leadingZeros(z.abs[len(z.abs)-1]));
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return len(z.abs)*int(_W) - int(leadingZeros(z.abs[len(z.abs)-1]));
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}
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@ -284,12 +320,52 @@ func (z *Int) Exp(x, y, m *Int) *Int {
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return z;
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}
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var mWords []Word;
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if m != nil {
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mWords = m.abs
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z.Set(x);
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v := y.abs[len(y.abs)-1];
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// It's invalid for the most significant word to be zero, therefore we
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// will find a one bit.
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shift := leadingZeros(v) + 1;
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v <<= shift;
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const mask = 1 << (_W - 1);
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// We walk through the bits of the exponent one by one. Each time we see
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// a bit, we square, thus doubling the power. If the bit is a one, we
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// also multiply by x, thus adding one to the power.
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w := int(_W) - int(shift);
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for j := 0; j < w; j++ {
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z.Mul(z, z);
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if v&mask != 0 {
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z.Mul(z, x)
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}
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if m != nil {
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z.Mod(z, m)
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}
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v <<= 1;
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}
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for i := len(y.abs) - 2; i >= 0; i-- {
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v = y.abs[i];
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for j := 0; j < int(_W); j++ {
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z.Mul(z, z);
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if v&mask != 0 {
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z.Mul(z, x)
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}
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if m != nil {
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z.Mod(z, m)
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}
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v <<= 1;
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}
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}
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z.abs = expNNN(z.abs, x.abs, y.abs, mWords);
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z.neg = x.neg && y.abs[0]&1 == 1;
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return z;
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}
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@ -351,20 +427,3 @@ func GcdInt(d, x, y, a, b *Int) {
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*d = *A;
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}
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// ProbablyPrime performs n Miller-Rabin tests to check whether z is prime.
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// If it returns true, z is prime with probability 1 - 1/4^n.
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// If it returns false, z is not prime.
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func ProbablyPrime(z *Int, reps int) bool { return !z.neg && probablyPrime(z.abs, reps) }
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// Rsh sets z = x >> s and returns z.
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func (z *Int) Rsh(x *Int, n int) *Int {
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removedWords := n / _W;
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z.abs = makeN(z.abs, len(x.abs)-removedWords, false);
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z.neg = x.neg;
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shiftRight(z.abs, x.abs[removedWords:len(x.abs)], n%_W);
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z.abs = normN(z.abs);
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return z;
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}
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@ -46,7 +46,7 @@ func TestSetZ(t *testing.T) {
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for _, a := range sumZZ {
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var z Int;
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z.Set(a.z);
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if (&z).Cmp(a.z) != 0 {
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if CmpInt(&z, a.z) != 0 {
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t.Errorf("got z = %v; want %v", z, a.z)
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}
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}
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@ -56,7 +56,7 @@ func TestSetZ(t *testing.T) {
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func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) {
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var z Int;
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f(&z, a.x, a.y);
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if (&z).Cmp(a.z) != 0 {
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if CmpInt(&z, a.z) != 0 {
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t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z)
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}
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}
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@ -165,7 +165,7 @@ func TestSetString(t *testing.T) {
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continue
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}
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if n.Cmp(new(Int).New(test.out)) != 0 {
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if CmpInt(n, new(Int).New(test.out)) != 0 {
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t.Errorf("#%d (input '%s') got: %s want: %d\n", i, test.in, n, test.out)
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}
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}
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@ -196,7 +196,7 @@ func TestDivSigns(t *testing.T) {
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expectedQ := new(Int).New(test.q);
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expectedR := new(Int).New(test.r);
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if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
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if CmpInt(q, expectedQ) != 0 || CmpInt(r, expectedR) != 0 {
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t.Errorf("#%d: got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
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}
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}
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@ -251,7 +251,7 @@ func checkDiv(x, y []byte) bool {
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q, r := new(Int).Div(u, v);
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if r.Cmp(v) >= 0 {
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if CmpInt(r, v) >= 0 {
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return false
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}
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@ -259,7 +259,7 @@ func checkDiv(x, y []byte) bool {
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uprime.Mul(uprime, v);
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uprime.Add(uprime, r);
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return uprime.Cmp(u) == 0;
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return CmpInt(uprime, u) == 0;
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}
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@ -276,12 +276,6 @@ var divTests = []divTest{
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"50911",
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"1",
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},
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divTest{
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"11510768301994997771168",
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"1328165573307167369775",
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"8",
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"885443715537658812968",
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},
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}
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@ -299,7 +293,7 @@ func TestDiv(t *testing.T) {
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q, r := new(Int).Div(x, y);
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if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
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if CmpInt(q, expectedQ) != 0 || CmpInt(r, expectedR) != 0 {
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t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
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}
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}
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@ -407,7 +401,7 @@ func TestExp(t *testing.T) {
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}
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z := new(Int).Exp(x, y, m);
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if z.Cmp(out) != 0 {
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if CmpInt(z, out) != 0 {
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t.Errorf("#%d got %s want %s", i, z, out)
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}
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}
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@ -427,7 +421,7 @@ func checkGcd(aBytes, bBytes []byte) bool {
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y.Mul(y, b);
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x.Add(x, y);
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return x.Cmp(d) == 0;
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return CmpInt(x, d) == 0;
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}
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@ -457,95 +451,12 @@ func TestGcd(t *testing.T) {
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GcdInt(d, x, y, a, b);
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if expectedX.Cmp(x) != 0 ||
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expectedY.Cmp(y) != 0 ||
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expectedD.Cmp(d) != 0 {
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if CmpInt(expectedX, x) != 0 ||
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CmpInt(expectedY, y) != 0 ||
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CmpInt(expectedD, d) != 0 {
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t.Errorf("#%d got (%s %s %s) want (%s %s %s)", i, x, y, d, expectedX, expectedY, expectedD)
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}
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}
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quick.Check(checkGcd, nil);
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}
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var primes = []string{
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"2",
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"3",
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"5",
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"7",
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"11",
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"98920366548084643601728869055592650835572950932266967461790948584315647051443",
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"94560208308847015747498523884063394671606671904944666360068158221458669711639",
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// http://primes.utm.edu/lists/small/small3.html
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"449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
|
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"230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
|
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"5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
|
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"203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",
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}
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|
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var composites = []string{
|
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"21284175091214687912771199898307297748211672914763848041968395774954376176754",
|
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"6084766654921918907427900243509372380954290099172559290432744450051395395951",
|
||||
"84594350493221918389213352992032324280367711247940675652888030554255915464401",
|
||||
"82793403787388584738507275144194252681",
|
||||
}
|
||||
|
||||
|
||||
func TestProbablyPrime(t *testing.T) {
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for i, s := range primes {
|
||||
p, _ := new(Int).SetString(s, 10);
|
||||
if !ProbablyPrime(p, 20) {
|
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t.Errorf("#%d prime found to be non-prime", i)
|
||||
}
|
||||
}
|
||||
|
||||
for i, s := range composites {
|
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c, _ := new(Int).SetString(s, 10);
|
||||
if ProbablyPrime(c, 20) {
|
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t.Errorf("#%d composite found to be prime", i)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
type rshTest struct {
|
||||
in string;
|
||||
shift int;
|
||||
out string;
|
||||
}
|
||||
|
||||
|
||||
var rshTests = []rshTest{
|
||||
rshTest{"0", 0, "0"},
|
||||
rshTest{"0", 1, "0"},
|
||||
rshTest{"0", 2, "0"},
|
||||
rshTest{"1", 0, "1"},
|
||||
rshTest{"1", 1, "0"},
|
||||
rshTest{"1", 2, "0"},
|
||||
rshTest{"2", 0, "2"},
|
||||
rshTest{"2", 1, "1"},
|
||||
rshTest{"2", 2, "0"},
|
||||
rshTest{"4294967296", 0, "4294967296"},
|
||||
rshTest{"4294967296", 1, "2147483648"},
|
||||
rshTest{"4294967296", 2, "1073741824"},
|
||||
rshTest{"18446744073709551616", 0, "18446744073709551616"},
|
||||
rshTest{"18446744073709551616", 1, "9223372036854775808"},
|
||||
rshTest{"18446744073709551616", 2, "4611686018427387904"},
|
||||
rshTest{"18446744073709551616", 64, "1"},
|
||||
rshTest{"340282366920938463463374607431768211456", 64, "18446744073709551616"},
|
||||
rshTest{"340282366920938463463374607431768211456", 128, "1"},
|
||||
}
|
||||
|
||||
|
||||
func TestRsh(t *testing.T) {
|
||||
for i, test := range rshTests {
|
||||
in, _ := new(Int).SetString(test.in, 10);
|
||||
expected, _ := new(Int).SetString(test.out, 10);
|
||||
out := new(Int).Rsh(in, test.shift);
|
||||
|
||||
if out.Cmp(expected) != 0 {
|
||||
t.Errorf("#%d got %s want %s", i, out, expected)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
@ -6,7 +6,9 @@
|
||||
// These are the building blocks for the operations on signed integers
|
||||
// and rationals.
|
||||
|
||||
// This package implements multi-precision arithmetic (big numbers).
|
||||
// NOTE: PACKAGE UNDER CONSTRUCTION.
|
||||
//
|
||||
// The big package implements multi-precision arithmetic (big numbers).
|
||||
// The following numeric types are supported:
|
||||
//
|
||||
// - Int signed integers
|
||||
@ -15,13 +17,8 @@
|
||||
// of the operands it may be overwritten (and its memory reused).
|
||||
// To enable chaining of operations, the result is also returned.
|
||||
//
|
||||
// If possible, one should use big over bignum as the latter is headed for
|
||||
// deprecation.
|
||||
//
|
||||
package big
|
||||
|
||||
import "rand"
|
||||
|
||||
// An unsigned integer x of the form
|
||||
//
|
||||
// x = x[n-1]*_B^(n-1) + x[n-2]*_B^(n-2) + ... + x[1]*_B + x[0]
|
||||
@ -260,40 +257,12 @@ func divNW(z, x []Word, y Word) (q []Word, r Word) {
|
||||
}
|
||||
|
||||
|
||||
func divNN(z, z2, u, v []Word) (q, r []Word) {
|
||||
if len(v) == 0 {
|
||||
panic("Divide by zero undefined")
|
||||
}
|
||||
|
||||
if cmpNN(u, v) < 0 {
|
||||
q = makeN(z, 0, false);
|
||||
r = setN(z2, u);
|
||||
return;
|
||||
}
|
||||
|
||||
if len(v) == 1 {
|
||||
var rprime Word;
|
||||
q, rprime = divNW(z, u, v[0]);
|
||||
if rprime > 0 {
|
||||
r = makeN(z2, 1, false);
|
||||
r[0] = rprime;
|
||||
} else {
|
||||
r = makeN(z2, 0, false)
|
||||
}
|
||||
return;
|
||||
}
|
||||
|
||||
q, r = divLargeNN(z, z2, u, v);
|
||||
return;
|
||||
}
|
||||
|
||||
|
||||
// q = (uIn-r)/v, with 0 <= r < y
|
||||
// See Knuth, Volume 2, section 4.3.1, Algorithm D.
|
||||
// Preconditions:
|
||||
// len(v) >= 2
|
||||
// len(uIn) >= len(v)
|
||||
func divLargeNN(z, z2, uIn, v []Word) (q, r []Word) {
|
||||
// len(uIn) >= 1 + len(vIn)
|
||||
func divNN(z, z2, uIn, v []Word) (q, r []Word) {
|
||||
n := len(v);
|
||||
m := len(uIn) - len(v);
|
||||
|
||||
@ -305,7 +274,7 @@ func divLargeNN(z, z2, uIn, v []Word) (q, r []Word) {
|
||||
shift := leadingZeroBits(v[n-1]);
|
||||
shiftLeft(v, v, shift);
|
||||
shiftLeft(u, uIn, shift);
|
||||
u[len(uIn)] = uIn[len(uIn)-1] >> (_W - uint(shift));
|
||||
u[len(uIn)] = uIn[len(uIn)-1] >> (uint(_W) - uint(shift));
|
||||
|
||||
// D2.
|
||||
for j := m; j >= 0; j-- {
|
||||
@ -366,7 +335,7 @@ func log2(x Word) int {
|
||||
func log2N(x []Word) int {
|
||||
m := len(x);
|
||||
if m > 0 {
|
||||
return (m-1)*_W + log2(x[m-1])
|
||||
return (m-1)*int(_W) + log2(x[m-1])
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
@ -470,7 +439,7 @@ func leadingZeroBits(x Word) int {
|
||||
c := 0;
|
||||
if x < 1<<(_W/2) {
|
||||
x <<= _W / 2;
|
||||
c = _W / 2;
|
||||
c = int(_W / 2);
|
||||
}
|
||||
|
||||
for i := 0; x != 0; i++ {
|
||||
@ -480,47 +449,7 @@ func leadingZeroBits(x Word) int {
|
||||
x <<= 1;
|
||||
}
|
||||
|
||||
return _W;
|
||||
}
|
||||
|
||||
const deBruijn32 = 0x077CB531
|
||||
|
||||
var deBruijn32Lookup = []byte{
|
||||
0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
|
||||
31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
|
||||
}
|
||||
|
||||
const deBruijn64 = 0x03f79d71b4ca8b09
|
||||
|
||||
var deBruijn64Lookup = []byte{
|
||||
0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
|
||||
62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
|
||||
63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
|
||||
54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
|
||||
}
|
||||
|
||||
// trailingZeroBits returns the number of consecutive zero bits on the right
|
||||
// side of the given Word.
|
||||
// See Knuth, volume 4, section 7.3.1
|
||||
func trailingZeroBits(x Word) int {
|
||||
// x & -x leaves only the right-most bit set in the word. Let k be the
|
||||
// index of that bit. Since only a single bit is set, the value is two
|
||||
// to the power of k. Multipling by a power of two is equivalent to
|
||||
// left shifting, in this case by k bits. The de Bruijn constant is
|
||||
// such that all six bit, consecutive substrings are distinct.
|
||||
// Therefore, if we have a left shifted version of this constant we can
|
||||
// find by how many bits it was shifted by looking at which six bit
|
||||
// substring ended up at the top of the word.
|
||||
switch _W {
|
||||
case 32:
|
||||
return int(deBruijn32Lookup[((x&-x)*deBruijn32)>>27])
|
||||
case 64:
|
||||
return int(deBruijn64Lookup[((x&-x)*(deBruijn64&_M))>>58])
|
||||
default:
|
||||
panic("Unknown word size")
|
||||
}
|
||||
|
||||
return 0;
|
||||
return int(_W);
|
||||
}
|
||||
|
||||
|
||||
@ -529,7 +458,7 @@ func shiftLeft(dst, src []Word, n int) {
|
||||
return
|
||||
}
|
||||
|
||||
ñ := _W - uint(n);
|
||||
ñ := uint(_W) - uint(n);
|
||||
for i := len(src) - 1; i >= 1; i-- {
|
||||
dst[i] = src[i] << uint(n);
|
||||
dst[i] |= src[i-1] >> ñ;
|
||||
@ -543,7 +472,7 @@ func shiftRight(dst, src []Word, n int) {
|
||||
return
|
||||
}
|
||||
|
||||
ñ := _W - uint(n);
|
||||
ñ := uint(_W) - uint(n);
|
||||
for i := 0; i < len(src)-1; i++ {
|
||||
dst[i] = src[i] >> uint(n);
|
||||
dst[i] |= src[i+1] << ñ;
|
||||
@ -554,221 +483,3 @@ func shiftRight(dst, src []Word, n int) {
|
||||
|
||||
// greaterThan returns true iff (x1<<_W + x2) > (y1<<_W + y2)
|
||||
func greaterThan(x1, x2, y1, y2 Word) bool { return x1 > y1 || x1 == y1 && x2 > y2 }
|
||||
|
||||
|
||||
// modNW returns x % d.
|
||||
func modNW(x []Word, d Word) (r Word) {
|
||||
// TODO(agl): we don't actually need to store the q value.
|
||||
q := makeN(nil, len(x), false);
|
||||
return divWVW(&q[0], 0, &x[0], d, len(x));
|
||||
}
|
||||
|
||||
|
||||
// powersOfTwoDecompose finds q and k such that q * 1<<k = n and q is odd.
|
||||
func powersOfTwoDecompose(n []Word) (q []Word, k Word) {
|
||||
if len(n) == 0 {
|
||||
return n, 0
|
||||
}
|
||||
|
||||
zeroWords := 0;
|
||||
for n[zeroWords] == 0 {
|
||||
zeroWords++
|
||||
}
|
||||
// One of the words must be non-zero by invariant, therefore
|
||||
// zeroWords < len(n).
|
||||
x := trailingZeroBits(n[zeroWords]);
|
||||
|
||||
q = makeN(nil, len(n)-zeroWords, false);
|
||||
shiftRight(q, n[zeroWords:len(n)], x);
|
||||
|
||||
k = Word(_W*zeroWords + x);
|
||||
return;
|
||||
}
|
||||
|
||||
|
||||
// randomN creates a random integer in [0..limit), using the space in z if
|
||||
// possible. n is the bit length of limit.
|
||||
func randomN(z []Word, rand *rand.Rand, limit []Word, n int) []Word {
|
||||
bitLengthOfMSW := uint(n % _W);
|
||||
mask := Word((1 << bitLengthOfMSW) - 1);
|
||||
z = makeN(z, len(limit), false);
|
||||
|
||||
for {
|
||||
for i := range z {
|
||||
switch _W {
|
||||
case 32:
|
||||
z[i] = Word(rand.Uint32())
|
||||
case 64:
|
||||
z[i] = Word(rand.Uint32()) | Word(rand.Uint32())<<32
|
||||
}
|
||||
}
|
||||
|
||||
z[len(limit)-1] &= mask;
|
||||
|
||||
if cmpNN(z, limit) < 0 {
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
return z;
|
||||
}
|
||||
|
||||
|
||||
// If m != nil, expNNN calculates x**y mod m. Otherwise it calculates x**y. It
|
||||
// reuses the storage of z if possible.
|
||||
func expNNN(z, x, y, m []Word) []Word {
|
||||
if len(y) == 0 {
|
||||
z = makeN(z, 1, false);
|
||||
z[0] = 1;
|
||||
return z;
|
||||
}
|
||||
|
||||
if m != nil {
|
||||
// We likely end up being as long as the modulus.
|
||||
z = makeN(z, len(m), false)
|
||||
}
|
||||
z = setN(z, x);
|
||||
v := y[len(y)-1];
|
||||
// It's invalid for the most significant word to be zero, therefore we
|
||||
// will find a one bit.
|
||||
shift := leadingZeros(v) + 1;
|
||||
v <<= shift;
|
||||
var q []Word;
|
||||
|
||||
const mask = 1 << (_W - 1);
|
||||
|
||||
// We walk through the bits of the exponent one by one. Each time we
|
||||
// see a bit, we square, thus doubling the power. If the bit is a one,
|
||||
// we also multiply by x, thus adding one to the power.
|
||||
|
||||
w := _W - int(shift);
|
||||
for j := 0; j < w; j++ {
|
||||
z = mulNN(z, z, z);
|
||||
|
||||
if v&mask != 0 {
|
||||
z = mulNN(z, z, x)
|
||||
}
|
||||
|
||||
if m != nil {
|
||||
q, z = divNN(q, z, z, m)
|
||||
}
|
||||
|
||||
v <<= 1;
|
||||
}
|
||||
|
||||
for i := len(y) - 2; i >= 0; i-- {
|
||||
v = y[i];
|
||||
|
||||
for j := 0; j < _W; j++ {
|
||||
z = mulNN(z, z, z);
|
||||
|
||||
if v&mask != 0 {
|
||||
z = mulNN(z, z, x)
|
||||
}
|
||||
|
||||
if m != nil {
|
||||
q, z = divNN(q, z, z, m)
|
||||
}
|
||||
|
||||
v <<= 1;
|
||||
}
|
||||
}
|
||||
|
||||
return z;
|
||||
}
|
||||
|
||||
|
||||
// lenN returns the bit length of z.
|
||||
func lenN(z []Word) int {
|
||||
if len(z) == 0 {
|
||||
return 0
|
||||
}
|
||||
|
||||
return (len(z)-1)*_W + (_W - leadingZeroBits(z[len(z)-1]));
|
||||
}
|
||||
|
||||
|
||||
const (
|
||||
primesProduct32 = 0xC0CFD797; // Π {p ∈ primes, 2 < p <= 29}
|
||||
primesProduct64 = 0xE221F97C30E94E1D; // Π {p ∈ primes, 2 < p <= 53}
|
||||
)
|
||||
|
||||
var bigOne = []Word{1}
|
||||
var bigTwo = []Word{2}
|
||||
|
||||
// ProbablyPrime performs n Miller-Rabin tests to check whether n is prime.
|
||||
// If it returns true, n is prime with probability 1 - 1/4^n.
|
||||
// If it returns false, n is not prime.
|
||||
func probablyPrime(n []Word, reps int) bool {
|
||||
if len(n) == 0 {
|
||||
return false
|
||||
}
|
||||
|
||||
if len(n) == 1 {
|
||||
if n[0]%2 == 0 {
|
||||
return n[0] == 2
|
||||
}
|
||||
|
||||
// We have to exclude these cases because we reject all
|
||||
// multiples of these numbers below.
|
||||
if n[0] == 3 || n[0] == 5 || n[0] == 7 || n[0] == 11 ||
|
||||
n[0] == 13 || n[0] == 17 || n[0] == 19 || n[0] == 23 ||
|
||||
n[0] == 29 || n[0] == 31 || n[0] == 37 || n[0] == 41 ||
|
||||
n[0] == 43 || n[0] == 47 || n[0] == 53 {
|
||||
return true
|
||||
}
|
||||
}
|
||||
|
||||
var r Word;
|
||||
switch _W {
|
||||
case 32:
|
||||
r = modNW(n, primesProduct32)
|
||||
case 64:
|
||||
r = modNW(n, primesProduct64&_M)
|
||||
default:
|
||||
panic("Unknown word size")
|
||||
}
|
||||
|
||||
if r%3 == 0 || r%5 == 0 || r%7 == 0 || r%11 == 0 ||
|
||||
r%13 == 0 || r%17 == 0 || r%19 == 0 || r%23 == 0 || r%29 == 0 {
|
||||
return false
|
||||
}
|
||||
|
||||
if _W == 64 && (r%31 == 0 || r%37 == 0 || r%41 == 0 ||
|
||||
r%43 == 0 || r%47 == 0 || r%53 == 0) {
|
||||
return false
|
||||
}
|
||||
|
||||
nm1 := subNN(nil, n, bigOne);
|
||||
// 1<<k * q = nm1;
|
||||
q, k := powersOfTwoDecompose(nm1);
|
||||
|
||||
nm3 := subNN(nil, nm1, bigTwo);
|
||||
rand := rand.New(rand.NewSource(int64(n[0])));
|
||||
|
||||
var x, y, quotient []Word;
|
||||
nm3Len := lenN(nm3);
|
||||
|
||||
NextRandom:
|
||||
for i := 0; i < reps; i++ {
|
||||
x = randomN(x, rand, nm3, nm3Len);
|
||||
addNN(x, x, bigTwo);
|
||||
y = expNNN(y, x, q, n);
|
||||
if cmpNN(y, bigOne) == 0 || cmpNN(y, nm1) == 0 {
|
||||
continue
|
||||
}
|
||||
for j := Word(1); j < k; j++ {
|
||||
y = mulNN(y, y, y);
|
||||
quotient, y = divNN(quotient, y, y, n);
|
||||
if cmpNN(y, nm1) == 0 {
|
||||
continue NextRandom
|
||||
}
|
||||
if cmpNN(y, bigOne) == 0 {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
@ -120,7 +120,7 @@ func TestStringN(t *testing.T) {
|
||||
|
||||
func TestLeadingZeroBits(t *testing.T) {
|
||||
var x Word = 1 << (_W - 1);
|
||||
for i := 0; i <= _W; i++ {
|
||||
for i := 0; i <= int(_W); i++ {
|
||||
if leadingZeroBits(x) != i {
|
||||
t.Errorf("failed at %x: got %d want %d", x, leadingZeroBits(x), i)
|
||||
}
|
||||
@ -185,97 +185,3 @@ func TestShiftRight(t *testing.T) {
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
type modNWTest struct {
|
||||
in string;
|
||||
dividend string;
|
||||
out string;
|
||||
}
|
||||
|
||||
|
||||
var modNWTests32 = []modNWTest{
|
||||
modNWTest{"23492635982634928349238759823742", "252341", "220170"},
|
||||
}
|
||||
|
||||
|
||||
var modNWTests64 = []modNWTest{
|
||||
modNWTest{"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
|
||||
}
|
||||
|
||||
|
||||
func runModNWTests(t *testing.T, tests []modNWTest) {
|
||||
for i, test := range tests {
|
||||
in, _ := new(Int).SetString(test.in, 10);
|
||||
d, _ := new(Int).SetString(test.dividend, 10);
|
||||
out, _ := new(Int).SetString(test.out, 10);
|
||||
|
||||
r := modNW(in.abs, d.abs[0]);
|
||||
if r != out.abs[0] {
|
||||
t.Errorf("#%d failed: got %s want %s\n", i, r, out)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
func TestModNW(t *testing.T) {
|
||||
if _W >= 32 {
|
||||
runModNWTests(t, modNWTests32)
|
||||
}
|
||||
if _W >= 64 {
|
||||
runModNWTests(t, modNWTests32)
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
func TestTrailingZeroBits(t *testing.T) {
|
||||
var x Word;
|
||||
x--;
|
||||
for i := 0; i < _W; i++ {
|
||||
if trailingZeroBits(x) != i {
|
||||
t.Errorf("Failed at step %d: x: %x got: %d\n", i, x, trailingZeroBits(x))
|
||||
}
|
||||
x <<= 1;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
type expNNNTest struct {
|
||||
x, y, m string;
|
||||
out string;
|
||||
}
|
||||
|
||||
|
||||
var expNNNTests = []expNNNTest{
|
||||
expNNNTest{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
|
||||
expNNNTest{"0x8000000000000000", "2", "6719", "4944"},
|
||||
expNNNTest{"0x8000000000000000", "3", "6719", "5447"},
|
||||
expNNNTest{"0x8000000000000000", "1000", "6719", "1603"},
|
||||
expNNNTest{"0x8000000000000000", "1000000", "6719", "3199"},
|
||||
expNNNTest{
|
||||
"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
|
||||
"298472983472983471903246121093472394872319615612417471234712061",
|
||||
"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
|
||||
"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
|
||||
},
|
||||
}
|
||||
|
||||
|
||||
func TestExpNNN(t *testing.T) {
|
||||
for i, test := range expNNNTests {
|
||||
x, _, _ := scanN(nil, test.x, 0);
|
||||
y, _, _ := scanN(nil, test.y, 0);
|
||||
out, _, _ := scanN(nil, test.out, 0);
|
||||
|
||||
var m []Word;
|
||||
|
||||
if len(test.m) > 0 {
|
||||
m, _, _ = scanN(nil, test.m, 0)
|
||||
}
|
||||
|
||||
z := expNNN(nil, x, y, m);
|
||||
if cmpNN(z, out) != 0 {
|
||||
t.Errorf("#%d got %v want %v", i, z, out)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
@ -9,10 +9,6 @@
|
||||
// - Integer signed integers
|
||||
// - Rational rational numbers
|
||||
//
|
||||
// This package has been designed for ease of use but the functions it provides
|
||||
// are likely to be quite slow. It may be deprecated eventually. Use package
|
||||
// big instead, if possible.
|
||||
//
|
||||
package bignum
|
||||
|
||||
import (
|
||||
|
||||
@ -19,11 +19,15 @@ import (
|
||||
var bigZero = big.NewInt(0)
|
||||
var bigOne = big.NewInt(1)
|
||||
|
||||
/*
|
||||
|
||||
TODO(agl): Enable once big implements ProbablyPrime.
|
||||
|
||||
// randomSafePrime returns a number, p, of the given size, such that p and
|
||||
// (p-1)/2 are both prime with high probability.
|
||||
func randomSafePrime(rand io.Reader, bits int) (p *big.Int, err os.Error) {
|
||||
if bits < 1 {
|
||||
err = os.EINVAL
|
||||
err = os.EINVAL;
|
||||
}
|
||||
|
||||
bytes := make([]byte, (bits+7)/8);
|
||||
@ -33,7 +37,7 @@ func randomSafePrime(rand io.Reader, bits int) (p *big.Int, err os.Error) {
|
||||
for {
|
||||
_, err = io.ReadFull(rand, bytes);
|
||||
if err != nil {
|
||||
return
|
||||
return;
|
||||
}
|
||||
|
||||
// Don't let the value be too small.
|
||||
@ -42,10 +46,10 @@ func randomSafePrime(rand io.Reader, bits int) (p *big.Int, err os.Error) {
|
||||
bytes[len(bytes)-1] |= 1;
|
||||
|
||||
p.SetBytes(bytes);
|
||||
if big.ProbablyPrime(p, 20) {
|
||||
if p.ProbablyPrime(20) {
|
||||
p2.Rsh(p, 1); // p2 = (p - 1)/2
|
||||
if big.ProbablyPrime(p2, 20) {
|
||||
return
|
||||
if p2.ProbablyPrime(20) {
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -53,6 +57,8 @@ func randomSafePrime(rand io.Reader, bits int) (p *big.Int, err os.Error) {
|
||||
return;
|
||||
}
|
||||
|
||||
*/
|
||||
|
||||
// randomNumber returns a uniform random value in [0, max).
|
||||
func randomNumber(rand io.Reader, max *big.Int) (n *big.Int, err os.Error) {
|
||||
k := (max.Len() + 7) / 8;
|
||||
@ -78,7 +84,7 @@ func randomNumber(rand io.Reader, max *big.Int) (n *big.Int, err os.Error) {
|
||||
bytes[0] &= uint8(int(1<<r) - 1);
|
||||
|
||||
n.SetBytes(bytes);
|
||||
if n.Cmp(max) < 0 {
|
||||
if big.CmpInt(n, max) < 0 {
|
||||
return
|
||||
}
|
||||
}
|
||||
@ -103,20 +109,20 @@ type PrivateKey struct {
|
||||
// It returns nil if the key is valid, or else an os.Error describing a problem.
|
||||
|
||||
func (priv PrivateKey) Validate() os.Error {
|
||||
// Check that p and q are prime. Note that this is just a sanity
|
||||
// check. Since the random witnesses chosen by ProbablyPrime are
|
||||
// deterministic, given the candidate number, it's easy for an attack
|
||||
// to generate composites that pass this test.
|
||||
if !big.ProbablyPrime(priv.P, 20) {
|
||||
return os.ErrorString("P is composite")
|
||||
}
|
||||
if !big.ProbablyPrime(priv.Q, 20) {
|
||||
return os.ErrorString("Q is composite")
|
||||
}
|
||||
/*
|
||||
TODO(agl): Enable once big implements ProbablyPrime.
|
||||
|
||||
// Check that p and q are prime.
|
||||
if !priv.P.ProbablyPrime(20) {
|
||||
return os.ErrorString("P is composite");
|
||||
}
|
||||
if !priv.Q.ProbablyPrime(20) {
|
||||
return os.ErrorString("Q is composite");
|
||||
}
|
||||
*/
|
||||
// Check that p*q == n.
|
||||
modulus := new(big.Int).Mul(priv.P, priv.Q);
|
||||
if modulus.Cmp(priv.N) != 0 {
|
||||
if big.CmpInt(modulus, priv.N) != 0 {
|
||||
return os.ErrorString("invalid modulus")
|
||||
}
|
||||
// Check that e and totient(p, q) are coprime.
|
||||
@ -128,18 +134,20 @@ func (priv PrivateKey) Validate() os.Error {
|
||||
x := new(big.Int);
|
||||
y := new(big.Int);
|
||||
big.GcdInt(gcd, x, y, totient, e);
|
||||
if gcd.Cmp(bigOne) != 0 {
|
||||
if big.CmpInt(gcd, bigOne) != 0 {
|
||||
return os.ErrorString("invalid public exponent E")
|
||||
}
|
||||
// Check that de ≡ 1 (mod totient(p, q))
|
||||
de := new(big.Int).Mul(priv.D, e);
|
||||
de.Mod(de, totient);
|
||||
if de.Cmp(bigOne) != 0 {
|
||||
if big.CmpInt(de, bigOne) != 0 {
|
||||
return os.ErrorString("invalid private exponent D")
|
||||
}
|
||||
return nil;
|
||||
}
|
||||
|
||||
/*
|
||||
|
||||
// GenerateKeyPair generates an RSA keypair of the given bit size.
|
||||
func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
|
||||
priv = new(PrivateKey);
|
||||
@ -160,16 +168,16 @@ func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
|
||||
for {
|
||||
p, err := randomSafePrime(rand, bits/2);
|
||||
if err != nil {
|
||||
return
|
||||
return;
|
||||
}
|
||||
|
||||
q, err := randomSafePrime(rand, bits/2);
|
||||
if err != nil {
|
||||
return
|
||||
return;
|
||||
}
|
||||
|
||||
if p.Cmp(q) == 0 {
|
||||
continue
|
||||
if big.CmpInt(p, q) == 0 {
|
||||
continue;
|
||||
}
|
||||
|
||||
n := new(big.Int).Mul(p, q);
|
||||
@ -183,7 +191,7 @@ func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
|
||||
e := big.NewInt(int64(priv.E));
|
||||
big.GcdInt(g, priv.D, y, e, totient);
|
||||
|
||||
if g.Cmp(bigOne) == 0 {
|
||||
if big.CmpInt(g, bigOne) == 0 {
|
||||
priv.D.Add(priv.D, totient);
|
||||
priv.P = p;
|
||||
priv.Q = q;
|
||||
@ -196,6 +204,8 @@ func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
|
||||
return;
|
||||
}
|
||||
|
||||
*/
|
||||
|
||||
// incCounter increments a four byte, big-endian counter.
|
||||
func incCounter(c *[4]byte) {
|
||||
if c[3]++; c[3] != 0 {
|
||||
@ -295,7 +305,7 @@ func modInverse(a, n *big.Int) (ia *big.Int) {
|
||||
x := new(big.Int);
|
||||
y := new(big.Int);
|
||||
big.GcdInt(g, x, y, a, n);
|
||||
if x.Cmp(bigOne) < 0 {
|
||||
if big.CmpInt(x, bigOne) < 0 {
|
||||
// 0 is not the multiplicative inverse of any element so, if x
|
||||
// < 1, then x is negative.
|
||||
x.Add(x, n)
|
||||
@ -308,7 +318,7 @@ func modInverse(a, n *big.Int) (ia *big.Int) {
|
||||
// random source is given, RSA blinding is used.
|
||||
func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.Error) {
|
||||
// TODO(agl): can we get away with reusing blinds?
|
||||
if c.Cmp(priv.N) > 0 {
|
||||
if big.CmpInt(c, priv.N) > 0 {
|
||||
err = DecryptionError{};
|
||||
return;
|
||||
}
|
||||
@ -325,7 +335,7 @@ func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.E
|
||||
err = err1;
|
||||
return;
|
||||
}
|
||||
if r.Cmp(bigZero) == 0 {
|
||||
if big.CmpInt(r, bigZero) == 0 {
|
||||
r = bigOne
|
||||
}
|
||||
ir = modInverse(r, priv.N);
|
||||
|
||||
@ -12,36 +12,42 @@ import (
|
||||
"testing";
|
||||
)
|
||||
|
||||
/*
|
||||
|
||||
TODO(agl): Enable once big implements ProbablyPrime.
|
||||
|
||||
func TestKeyGeneration(t *testing.T) {
|
||||
urandom, err := os.Open("/dev/urandom", os.O_RDONLY, 0);
|
||||
if err != nil {
|
||||
t.Errorf("failed to open /dev/urandom")
|
||||
t.Errorf("failed to open /dev/urandom");
|
||||
}
|
||||
|
||||
priv, err := GenerateKey(urandom, 16);
|
||||
if err != nil {
|
||||
t.Errorf("failed to generate key")
|
||||
t.Errorf("failed to generate key");
|
||||
}
|
||||
pub := &priv.PublicKey;
|
||||
m := big.NewInt(42);
|
||||
c := encrypt(new(big.Int), pub, m);
|
||||
m2, err := decrypt(nil, priv, c);
|
||||
if err != nil {
|
||||
t.Errorf("error while decrypting: %s", err)
|
||||
t.Errorf("error while decrypting: %s", err);
|
||||
}
|
||||
if m.Cmp(m2) != 0 {
|
||||
t.Errorf("got:%v, want:%v (%s)", m2, m, priv)
|
||||
if big.CmpInt(m, m2) != 0 {
|
||||
t.Errorf("got:%v, want:%v (%s)", m2, m, priv);
|
||||
}
|
||||
|
||||
m3, err := decrypt(urandom, priv, c);
|
||||
if err != nil {
|
||||
t.Errorf("error while decrypting (blind): %s", err)
|
||||
t.Errorf("error while decrypting (blind): %s", err);
|
||||
}
|
||||
if m.Cmp(m3) != 0 {
|
||||
t.Errorf("(blind) got:%v, want:%v", m3, m)
|
||||
if big.CmpInt(m, m3) != 0 {
|
||||
t.Errorf("(blind) got:%v, want:%v", m3, m);
|
||||
}
|
||||
}
|
||||
|
||||
*/
|
||||
|
||||
type testEncryptOAEPMessage struct {
|
||||
in []byte;
|
||||
seed []byte;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user