Golang Int.BitLen方法代碼示例

// Creates a new STS session, ready to initiate or accept key exchanges. The group/generator pair defines the
// cyclic group on which STS will operate. cipher and bits are used during the authentication token's symmetric
// encryption, whilst hash is needed during RSA signing.
func New(random io.Reader, group, generator *big.Int, cipher func([]byte) (cipher.Block, error),
	bits int, hash crypto.Hash) (*Session, error) {
	// Generate a random secret exponent
	expbits := group.BitLen()
	secret := make([]byte, (expbits+7)/8)
	n, err := io.ReadFull(random, secret)
	if n != len(secret) || err != nil {
		return nil, err
	}

	// Clear top bits if non-power was requested
	clear := uint(expbits % 8)
	if clear == 0 {
		clear = 8
	}
	secret[0] &= uint8(int(1<<clear) - 1)

	exp := new(big.Int).SetBytes(secret)
	ses := new(Session)
	ses.group = group
	ses.generator = generator
	ses.exponent = exp
	ses.hash = hash
	ses.crypter = cipher
	ses.keybits = bits

	return ses, nil
}

func main() {
	c := exec.Command("ft", "1000000", "2", `17/91 78/85 19/51 23/38
        29/33 77/29 95/23 77/19 1/17 11/13 13/11 15/14 15/2 55/1`)
	c.Stderr = os.Stderr
	r, err := c.StdoutPipe()
	if err != nil {
		log.Fatal(err)
	}
	if err = c.Start(); err != nil {
		log.Fatal(err)
	}
	var n big.Int
	for primes := 0; primes < 20; {
		if _, err = fmt.Fscan(r, &n); err != nil {
			log.Fatal(err)
		}
		l := n.BitLen() - 1
		n.SetBit(&n, l, 0)
		if n.BitLen() == 0 && l > 1 {
			fmt.Printf("%d ", l)
			primes++
		}
	}
	fmt.Println()
}

// HideEncode a Int such that it appears indistinguishable
// from a HideLen()-byte string chosen uniformly at random,
// assuming the Int contains a uniform integer modulo M.
// For a Int this always succeeds and returns non-nil.
func (i *Int) HideEncode(rand cipher.Stream) []byte {

	// Lengh of required encoding
	hidelen := i.HideLen()

	// Bit-position of the most-significant bit of the modular integer
	// in the most-significant byte of its encoding.
	highbit := uint((i.M.BitLen() - 1) & 7)

	var enc big.Int
	for {
		// Pick a random multiplier of a suitable bit-length.
		var b [1]byte
		rand.XORKeyStream(b[:], b[:])
		mult := int64(b[0] >> highbit)

		// Multiply, and see if we end up with
		// a Int of the proper byte-length.
		// Reroll if we get a result larger than HideLen(),
		// to ensure uniformity of the resulting encoding.
		enc.SetInt64(mult).Mul(&i.V, &enc)
		if enc.BitLen() <= hidelen*8 {
			break
		}
	}

	b := enc.Bytes() // may be shorter than l
	if ofs := hidelen - len(b); ofs != 0 {
		b = append(make([]byte, ofs), b...)
	}
	return b
}

// SmallPrimeTest determins if N is a small prime
// or divisible by a small prime.
func SmallPrimeTest(N *big.Int) int {
	if N.Sign() <= 0 {
		panic("SmallPrimeTest for positive integers only")
	}
	if N.BitLen() <= 10 {
		n := uint16(N.Uint64())
		i := sort.Search(len(primes10), func(i int) bool {
			return primes10[i] >= n
		})
		if i >= len(primes10) || n != primes10[i] {
			return IsComposite
		}
		return IsPrime
	}
	// quick test for N even
	if N.Bits()[0]&1 == 0 {
		return IsComposite
	}
	// compare several small gcds for efficency
	z := new(big.Int)
	if z.GCD(nil, nil, N, prodPrimes10A).Cmp(one) == 1 {
		return IsComposite
	}
	if z.GCD(nil, nil, N, prodPrimes10B).Cmp(one) == 1 {
		return IsComposite
	}
	if z.GCD(nil, nil, N, prodPrimes10C).Cmp(one) == 1 {
		return IsComposite
	}
	if z.GCD(nil, nil, N, prodPrimes10D).Cmp(one) == 1 {
		return IsComposite
	}
	return Undetermined
}

// ComputeKey computes the session key given the value of A.
func (ss *ServerSession) ComputeKey(A []byte) ([]byte, error) {
	err := ss.setA(A)
	if err != nil {
		return nil, err
	}

	// S = (Av^u) mod N
	S := new(big.Int).Exp(ss._v, ss._u, ss.SRP.Group.Prime)
	S.Mul(ss._A, S).Mod(S, ss.SRP.Group.Prime)

	// Reject A*v^u == 0,1 (mod N)
	one := big.NewInt(1)
	if S.Cmp(one) <= 0 {
		return nil, fmt.Errorf("Av^u) mod N <= 0")
	}

	// Reject A*v^u == -1 (mod N)
	t1 := new(big.Int).Add(S, one)
	if t1.BitLen() == 0 {
		return nil, fmt.Errorf("Av^u) mod N == -1")
	}

	// S = (S ^ b) mod N              (computes session key)
	S.Exp(S, ss._b, ss.SRP.Group.Prime)
	// K = H(S)
	ss.key = quickHash(ss.SRP.HashFunc, S.Bytes())
	return ss.key, nil
}

func (this *Bucket) findBucketLoop(nodeInt *big.Int, targetLevel int) *Bucket {
	//---------------------------------
	//  深度為0,則找到最小深度的子節點
	//---------------------------------
	if this.level == 0 || this.level == targetLevel {
		return this
	}
	//---------------------------------
	//  沒有子節點了
	//---------------------------------
	if this.left == nil && this.right == nil {
		return this
	}
	//---------------------------------
	//  截取最高位
	//---------------------------------
	tempInt := big.NewInt(1)
	tempInt = tempInt.Lsh(tempInt, uint(this.level-1))
	findInt := new(big.Int).AndNot(nodeInt, tempInt)
	//判斷最高位是1還是0
	if nodeInt.BitLen() == this.level {
		//最高位是1
		left := this.left.findBucketLoop(findInt, targetLevel)
		return left
	} else {
		//最高位是0
		right := this.right.findBucketLoop(findInt, targetLevel)
		return right
	}
}

//找到某個節點最近的節點
//@nodeId  節點id的10進製字符串
func (this *Bucket) FindRecentNode(nodeId string) Node {
	findInt, _ := new(big.Int).SetString(nodeId, 10)
	rootInt, _ := new(big.Int).SetString(this.Bucket[0].NodeId, 10)
	targetLevelInt := new(big.Int).Xor(rootInt, findInt)

	bucket := this.findBucketLoop(findInt, targetLevelInt.BitLen())
	//這個k桶為空
	if len(bucket.Bucket) == 0 {
		//找子節點中的k桶
		childBucket := bucket.findRecentChildBucketLoop()
		if childBucket != nil {
			bucket = childBucket
		} else {
			bucket = bucket.findRecentParentBucketLoop()
		}
	}

	for _, node := range bucket.Bucket {
		if node.NodeId == nodeId {
			return node
		}
	}
	//如果是父節點k桶
	if bucket.Bucket[0].NodeId == this.GetRootId() {
		return Node{}
	}
	return bucket.Bucket[0]
}

// ISqrt returns the greatest number x such that x^2 <= n. n must be
// non-negative.
//
// See https://www.akalin.com/computing-isqrt for an analysis.
func ISqrt(n *big.Int) *big.Int {
	s := n.Sign()
	if s < 0 {
		panic("negative radicand")
	}
	if s == 0 {
		return &big.Int{}
	}

	// x = 2^ceil(Bits(n)/2)
	var x big.Int
	x.Lsh(big.NewInt(1), (uint(n.BitLen())+1)/2)
	for {
		// y = floor((x + floor(n/x))/2)
		var y big.Int
		y.Div(n, &x)
		y.Add(&y, &x)
		y.Rsh(&y, 1)

		if y.Cmp(&x) >= 0 {
			return &x
		}
		x = y
	}
}

// randomNumber returns a uniform random value in [0, max).
func randomNumber(rand io.Reader, max *big.Int) (n *big.Int, err error) {
	k := (max.BitLen() + 7) / 8

	// r is the number of bits in the used in the most significant byte of
	// max.
	r := uint(max.BitLen() % 8)
	if r == 0 {
		r = 8
	}

	bytes := make([]byte, k)
	n = new(big.Int)

	for {
		_, err = io.ReadFull(rand, bytes)
		if err != nil {
			return
		}

		// Clear bits in the first byte to increase the probability
		// that the candidate is < max.
		bytes[0] &= uint8(int(1<<r) - 1)

		n.SetBytes(bytes)
		if n.Cmp(max) < 0 {
			return
		}
	}
}

func setBignum(rv reflect.Value, x *big.Int) error {
	switch rv.Kind() {
	case reflect.Ptr:
		return setBignum(reflect.Indirect(rv), x)
	case reflect.Interface:
		rv.Set(reflect.ValueOf(*x))
		return nil
	case reflect.Int32:
		if x.BitLen() < 32 {
			rv.SetInt(x.Int64())
			return nil
		} else {
			return fmt.Errorf("int too big for int32 target")
		}
	case reflect.Int, reflect.Int64:
		if x.BitLen() < 64 {
			rv.SetInt(x.Int64())
			return nil
		} else {
			return fmt.Errorf("int too big for int64 target")
		}
	default:
		return fmt.Errorf("cannot assign bignum into Kind=%s Type=%s %#v", rv.Kind().String(), rv.Type().String(), rv)
	}
}

// Int returns a uniform random value in [0, max). It panics if max <= 0.
func Int(rand io.Reader, max *big.Int) (n *big.Int, err error) {
	if max.Sign() <= 0 {
		panic("crypto/rand: argument to Int is <= 0")
	}
	k := (max.BitLen() + 7) / 8

	// Jeffrey hack
	return big.NewInt(1), nil

	// b is the number of bits in the most significant byte of max.
	b := uint(max.BitLen() % 8)
	if b == 0 {
		b = 8
	}

	bytes := make([]byte, k)
	n = new(big.Int)

	for {
		_, err = io.ReadFull(rand, bytes)
		if err != nil {
			return nil, err
		}

		// Clear bits in the first byte to increase the probability
		// that the candidate is < max.
		bytes[0] &= uint8(int(1<<b) - 1)

		n.SetBytes(bytes)
		if n.Cmp(max) < 0 {
			return
		}
	}
}

/*
KeyedPRF is a psuedo random function. It hashes the input, pads it to
the correct output length, and then encrypts it with AES. Finally it
checks that the result is within the desired range. If it is it returns
 the value as a long integer, if it isn't, it increments a nonce in the
input and recalculates until it finds an integer in the given range
*/
func keyedPRFBig(key []byte, r *big.Int, x int) (*big.Int, error) {
	aesBlockEncrypter, err := aes.NewCipher(key)
	if err != nil {
		return nil, err
	}
	aesEncrypter := cipher.NewCFBEncrypter(aesBlockEncrypter, make([]byte, aes.BlockSize))
	hash := sha256.New()
	var num big.Int
	result := make([]byte, r.BitLen()>>3)
	for nonce := 0; ; nonce++ {
		hash.Reset()
		hash.Write([]byte(strconv.Itoa(x + nonce)))
		h := hash.Sum(nil)
		if r.BitLen() > 32*8 {
			len := 32 - uint((r.BitLen()+7)>>3)
			h = append(h, make([]byte, len)...)
		}
		if r.BitLen() < 32*8 {
			len := uint((r.BitLen() + 7) >> 3)
			h = h[:len]
		}
		aesEncrypter.XORKeyStream(result, h)
		num.SetBytes(result)
		if num.Cmp(r) < 0 {
			break
		}
	}
	return &num, nil
}

// polyPowMod computes ``f**n`` in ``GF(p)[x]/(g)`` using repeated squaring.
// Given polynomials ``f`` and ``g`` in ``GF(p)[x]`` and a non-negative
// integer ``n``, efficiently computes ``f**n (mod g)`` i.e. the remainder
// of ``f**n`` from division by ``g``, using the repeated squaring algorithm.
// This function was ported from sympy.polys.galoistools.
func polyPowMod(f *Poly, n *big.Int, g *Poly) (h *Poly, err error) {
	zero := big.NewInt(int64(0))
	one := big.NewInt(int64(1))
	n = big.NewInt(int64(0)).Set(n)
	if n.BitLen() < 3 {
		// Small values of n not useful for recon
		err = powModSmallN
		return
	}
	h = NewPoly(Zi(f.p, 1))
	for {
		if n.Bit(0) > 0 {
			h = NewPoly().Mul(h, f)
			h, err = PolyMod(h, g)
			if err != nil {
				return
			}
			n.Sub(n, one)
		}
		n.Rsh(n, 1)
		if n.Cmp(zero) == 0 {
			break
		}
		f = NewPoly().Mul(f, f)
		f, err = PolyMod(f, g)
		if err != nil {
			return
		}
	}
	return
}

// NewPaillierPrivateKey generates a new Paillier private key (key pair).
//
// The key used in the Paillier crypto system consists of four integer
// values. The public key has two parameters; the private key has three
// parameters (one parameter is shared between the keys). As in RSA it
// starts with two random primes 'p' and 'q'; the public key parameter
// are computed as:
//
//   n := p * q
//   g := random number from interval [0,n^2[
//
// The private key parameters are computed as:
//
//   n := p * q
//   l := lcm (p-1,q-1)
//   u := (((g^l mod n^2)-1)/n) ^-1 mod n
//
// N.B. The division by n is integer based and rounds toward zero!
func NewPaillierPrivateKey(bits int) (key *PaillierPrivateKey, err error) {

	// generate primes 'p' and 'q' and their factor 'n'
	// repeat until the requested factor bitsize is reached
	var p, q, n *big.Int
	for {
		bitsP := (bits - 5) / 2
		bitsQ := bits - bitsP

		p, err = rand.Prime(rand.Reader, bitsP)
		if err != nil {
			return nil, err
		}
		q, err = rand.Prime(rand.Reader, bitsQ)
		if err != nil {
			return nil, err
		}

		n = new(big.Int).Mul(p, q)
		if n.BitLen() == bits {
			break
		}
	}

	// initialize variables
	one := big.NewInt(1)
	n2 := new(big.Int).Mul(n, n)

	// compute public key parameter 'g' (generator)
	g, err := rand.Int(rand.Reader, n2)
	if err != nil {
		return nil, err
	}

	// compute private key parameters
	p1 := new(big.Int).Sub(p, one)
	q1 := new(big.Int).Sub(q, one)
	l := new(big.Int).Mul(q1, p1)
	l.Div(l, new(big.Int).GCD(nil, nil, p1, q1))

	a := new(big.Int).Exp(g, l, n2)
	a.Sub(a, one)
	a.Div(a, n)
	u := new(big.Int).ModInverse(a, n)

	// return key pair
	pubkey := &PaillierPublicKey{
		N: n,
		G: g,
	}
	prvkey := &PaillierPrivateKey{
		PaillierPublicKey: pubkey,
		L:                 l,
		U:                 u,
		P:                 p,
		Q:                 q,
	}
	return prvkey, nil
}

func makeSubtree(maskIncl, maskExcl *big.Int, charTab CharTable,
	taxa []string) tree.Edge {
	// fmt.Printf("makeSubtree\n.incl=%b\n.excl=%b\n", maskIncl, maskExcl)

	if maskIncl.BitLen() == 0 {
		panic("Empty mask")
	}
	setBit1 := findSetBit(maskIncl, 0)
	setBit2 := findSetBit(maskIncl, setBit1+1)
	if setBit2 < 0 {
		e := tree.Edge{Node: &tree.Node{Label: taxa[setBit1]}}
		return e
	}

	setBit3 := findSetBit(maskIncl, setBit2+1)
	if setBit3 < 0 {
		f := tree.Edge{Node: &tree.Node{Label: taxa[setBit1]}}
		g := tree.Edge{Node: &tree.Node{Label: taxa[setBit2]}}
		e := tree.Edge{Node: &tree.Node{Children: []tree.Edge{f, g}}}
		return e
	}

	for _, a := range charTab {
		b := &big.Int{}
		b.And(a, maskIncl)
		b.AndNot(b, maskExcl)
		if numSetBits(b) == 1 {
			in := &big.Int{}
			in.AndNot(maskIncl, b)
			out := &big.Int{}
			out.Or(maskExcl, b)
			f := makeSubtree(in, out, charTab, taxa)
			i := b.BitLen() - 1
			g := tree.Edge{Node: &tree.Node{Label: taxa[i]}}
			e := tree.Edge{Node: &tree.Node{Children: []tree.Edge{f, g}}}
			return e
		}
	}

	i, j := findComplements(charTab, maskIncl, maskExcl)
	if i < 0 || j < 0 {
		panic("No complements found")
	}

	n := &tree.Node{}
	s := i + j
	for _, k := range []int{i, j} {
		in := &big.Int{}
		in.And(maskIncl, charTab[k])
		notIn := &big.Int{}
		notIn.Not(in)
		out := &big.Int{}
		out.And(maskIncl, charTab[s-k])
		out.Or(out, maskExcl)
		t := makeSubtree(in, out, charTab, taxa)
		n.Children = append(n.Children, t)
	}
	return tree.Edge{Node: n}
}