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// Copyright © 2021 siddharth ravikumar <s@ricketyspace.net>
// SPDX-License-Identifier: ISC
package lib
import (
"crypto/rand"
"math/big"
)
type GCDResult struct {
Gcd *big.Int
X *big.Int // Bézout coefficient 'x'
Y *big.Int // Bézout coefficient 'y'
}
// 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
}
// Extended Euclidian.
func egcd(a, b *big.Int) GCDResult {
// Initialize.
s0 := big.NewInt(1)
s1 := big.NewInt(0)
r0 := biCopy(big.NewInt(0), a)
r1 := biCopy(big.NewInt(0), b)
for r1.Cmp(big.NewInt(0)) != 0 {
q := big.NewInt(0)
q.Div(r0, r1)
tr := big.NewInt(0)
tr = tr.Mul(q, r1)
tr = tr.Sub(r0, tr)
biCopy(r0, r1)
biCopy(r1, tr)
tr = big.NewInt(0)
tr = tr.Mul(q, s1)
tr = tr.Sub(s0, tr)
biCopy(s0, s1)
biCopy(s1, tr)
}
x := biCopy(big.NewInt(0), s0)
y := big.NewInt(0)
if b.Cmp(big.NewInt(0)) != 0 {
y = y.Mul(s0, a)
y = y.Sub(r0, y)
y = y.Div(y, b)
}
return GCDResult{
Gcd: biCopy(big.NewInt(0), r0),
X: x,
Y: y,
}
}
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
}
func RSAGenKey() (*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, 1024)
if err != nil {
return nil, CPError{"unable to generate p"}
}
// Generate prime q.
q, err := rand.Prime(rand.Reader, 1024)
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
}
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