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// Copyright 2011 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Package ecdsa implements the Elliptic Curve Digital Signature Algorithm, as
// defined in FIPS 186-3.
package ecdsa

// References:
//   [NSA]: Suite B implementor's guide to FIPS 186-3,
//     http://www.nsa.gov/ia/_files/ecdsa.pdf
//   [SECG]: SECG, SEC1
//     http://www.secg.org/download/aid-780/sec1-v2.pdf

import (
        "crypto/elliptic"
        "io"
        "math/big"
)

// PublicKey represents an ECDSA public key.
type PublicKey struct {
        elliptic.Curve
        X, Y *big.Int
}

// PrivateKey represents a ECDSA private key.
type PrivateKey struct {
        PublicKey
        D *big.Int
}

var one = new(big.Int).SetInt64(1)

// randFieldElement returns a random element of the field underlying the given
// curve using the procedure given in [NSA] A.2.1.
func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
        params := c.Params()
        b := make([]byte, params.BitSize/8+8)
        _, err = io.ReadFull(rand, b)
        if err != nil {
                return
        }

        k = new(big.Int).SetBytes(b)
        n := new(big.Int).Sub(params.N, one)
        k.Mod(k, n)
        k.Add(k, one)
        return
}

// GenerateKey generates a public&private key pair.
func GenerateKey(c elliptic.Curve, rand io.Reader) (priv *PrivateKey, err error) {
        k, err := randFieldElement(c, rand)
        if err != nil {
                return
        }

        priv = new(PrivateKey)
        priv.PublicKey.Curve = c
        priv.D = k
        priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
        return
}

// hashToInt converts a hash value to an integer. There is some disagreement
// about how this is done. [NSA] suggests that this is done in the obvious
// manner, but [SECG] truncates the hash to the bit-length of the curve order
// first. We follow [SECG] because that's what OpenSSL does.
func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
        orderBits := c.Params().N.BitLen()
        orderBytes := (orderBits + 7) / 8
        if len(hash) > orderBytes {
                hash = hash[:orderBytes]
        }

        ret := new(big.Int).SetBytes(hash)
        excess := orderBytes*8 - orderBits
        if excess > 0 {
                ret.Rsh(ret, uint(excess))
        }
        return ret
}

// Sign signs an arbitrary length hash (which should be the result of hashing a
// larger message) using the private key, priv. It returns the signature as a
// pair of integers. The security of the private key depends on the entropy of
// rand.
func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
        // See [NSA] 3.4.1
        c := priv.PublicKey.Curve
        N := c.Params().N

        var k, kInv *big.Int
        for {
                for {
                        k, err = randFieldElement(c, rand)
                        if err != nil {
                                r = nil
                                return
                        }

                        kInv = new(big.Int).ModInverse(k, N)
                        r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
                        r.Mod(r, N)
                        if r.Sign() != 0 {
                                break
                        }
                }

                e := hashToInt(hash, c)
                s = new(big.Int).Mul(priv.D, r)
                s.Add(s, e)
                s.Mul(s, kInv)
                s.Mod(s, N)
                if s.Sign() != 0 {
                        break
                }
        }

        return
}

// Verify verifies the signature in r, s of hash using the public key, pub. It
// returns true iff the signature is valid.
func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
        // See [NSA] 3.4.2
        c := pub.Curve
        N := c.Params().N

        if r.Sign() == 0 || s.Sign() == 0 {
                return false
        }
        if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
                return false
        }
        e := hashToInt(hash, c)
        w := new(big.Int).ModInverse(s, N)

        u1 := e.Mul(e, w)
        u2 := w.Mul(r, w)

        x1, y1 := c.ScalarBaseMult(u1.Bytes())
        x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
        if x1.Cmp(x2) == 0 {
                return false
        }
        x, _ := c.Add(x1, y1, x2, y2)
        x.Mod(x, N)
        return x.Cmp(r) == 0
}