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// Copyright © 2021 siddharth ravikumar <s@ricketyspace.net>
// SPDX-License-Identifier: ISC
package lib
import (
"crypto/rand"
"errors"
"math/big"
)
// Represents an RSA key pair.
type RSAPair struct {
Public *RSAPub
Private *RSAPrivate
}
type RSAPub struct {
e *big.Int
n *big.Int
}
type RSAPrivate struct {
d *big.Int
n *big.Int
}
// Copy b to a.
func biCopy(a, b *big.Int) *big.Int {
a.SetBytes(b.Bytes())
if b.Sign() == -1 {
a.Mul(a, big.NewInt(-1))
}
return a
}
func InvMod(a, n *big.Int) (*big.Int, error) {
// Initialize.
t0 := big.NewInt(0)
t1 := big.NewInt(1)
r0 := biCopy(big.NewInt(0), n)
r1 := biCopy(big.NewInt(0), a)
for r1.Cmp(big.NewInt(0)) != 0 {
q := big.NewInt(0)
q.Div(r0, r1)
tt := big.NewInt(0)
tt = tt.Mul(q, t1)
tt = tt.Sub(t0, tt)
biCopy(t0, t1)
biCopy(t1, tt)
tr := big.NewInt(0)
tr = tr.Mul(q, r1)
tr = tr.Sub(r0, tr)
biCopy(r0, r1)
biCopy(r1, tr)
}
if r0.Cmp(big.NewInt(1)) > 0 {
return nil, CPError{"not invertible"}
}
if t0.Cmp(big.NewInt(0)) < 0 {
t0.Add(t0, n)
}
return t0, nil
}
// RSAGenKey generates a rsa key pair with N equal to size bits.
func RSAGenKey(size int) (*RSAPair, error) {
// Initialize.
e := big.NewInt(3)
d := big.NewInt(0)
n := big.NewInt(0)
// Compute n and d.
for {
// Generate prime p.
p, err := rand.Prime(rand.Reader, size/2)
if err != nil {
return nil, CPError{"unable to generate p"}
}
// Generate prime q.
q, err := rand.Prime(rand.Reader, size/2)
if err != nil {
return nil, CPError{"unable to generate q"}
}
// Calculate n.
n = big.NewInt(0).Mul(p, q)
// Calculate totient.
p1 := big.NewInt(0).Sub(p, big.NewInt(1)) // p-1
q1 := big.NewInt(0).Sub(q, big.NewInt(1)) // q-1
et := big.NewInt(0).Mul(p1, q1) // Totient `et`.
// Calculate private key `d`.
d, err = InvMod(e, et)
if err != nil {
continue // Inverse does not does. Try again.
}
break
}
if n.Cmp(big.NewInt(0)) <= 0 {
return nil, CPError{"unable to compute n"}
}
if d.Cmp(big.NewInt(0)) <= 0 {
return nil, CPError{"unable to compute d"}
}
// Make pub key.
pub := new(RSAPub)
pub.e = e
pub.n = biCopy(big.NewInt(0), n)
// Make private key.
prv := new(RSAPrivate)
prv.d = d
prv.n = biCopy(big.NewInt(0), n)
// Make key pair.
pair := new(RSAPair)
pair.Public = pub
pair.Private = prv
return pair, nil
}
func (r *RSAPub) Encrypt(msg []byte) []byte {
// Convert message to big int.
m := big.NewInt(0).SetBytes(msg)
// Encrypt.
c := big.NewInt(0).Exp(m, r.e, r.n)
return c.Bytes()
}
func (r *RSAPub) E() *big.Int {
return r.e
}
func (r *RSAPub) N() *big.Int {
return r.n
}
func (r *RSAPrivate) Decrypt(cipher []byte) []byte {
// Convert cipher to big int.
c := big.NewInt(0).SetBytes(cipher)
// Decrypt.
m := big.NewInt(0).Exp(c, r.d, r.n)
return m.Bytes()
}
// Sign generates a signature for the give data d according to RFC2313
// sections 8 and 10.
//
// https://datatracker.ietf.org/doc/html/rfc2313
func (r *RSAPrivate) Sign(msg []byte) (ed []byte, err error) {
// Hash message using md4.
var (
dgst Md4 = Md4{}
d []byte // Data to sign.
)
dgst.Init([]uint32{})
dgst.Message(msg)
d = dgst.Hash()
var (
kn int = r.n.BitLen() / 8 // Size of N in bytes.
dn int = len(d) // Length of d.
pn int = kn - 3 - dn // Number of padding characters.
eb []byte // Encryption block.
x *big.Int // Encryption block as an integer.
y *big.Int // Signature as an integer.
)
if dn > kn-11 {
err = errors.New("rsa: data len > k-11")
return
}
// Build encryption block.
eb = []byte{0x00, 0x01}
for i := 0; i < pn; i++ {
eb = append(eb, 0xFF)
}
eb = append(eb, 0x00)
eb = append(eb, d...)
// Convert to big int.
x = new(big.Int).SetBytes(eb)
// Sign.
y = big.NewInt(0).Exp(x, r.d, r.n)
ed = y.Bytes()
return
}
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