[Go] Try SHA-512 implementation
Tags: go
Published: 2022-06-12 02:04:14

## Intro
I want to try authentications in Go.

Because I have tried in ASP.NET Core Identity before, I read its source code.

* [【.NET 5】【ASP.NET Core Identity】SignIn with custom user](https://dev.to/masanori_msl/net-5-asp-net-core-identity-signin-with-custom-user-56fe)

I thought I should know about password hashing first.
According to the "PasswordHasher.cs", it use HMAC-SHA512 by default.

* [Hash passwords in ASP.NET Core - Microsoft Docs](https://docs.microsoft.com/en-us/aspnet/core/security/data-protection/consumer-apis/password-hashing?view=aspnetcore-6.0)
* [aspnetcore/PasswordHasher.cs - dotnet/aspnetcore - GitHub](https://github.com/dotnet/AspNetCore/blob/main/src/Identity/Extensions.Core/src/PasswordHasher.cs)

So this time I decided to learn about SHA-512.

Although Go has [sha512 package](https://pkg.go.dev/crypto/sha512), but I will try implementing it by myself.

## Examples
#### main.go
```go
package main

import (
	"crypto/sha512"
	"log"
)

func main() {
	result := Hash("hello")
	result2 := sha512.Sum512([]byte("hello"))

	log.Println(result)
	log.Printf("%x", result2)
}
```
#### sha512Hasher.go
```go
package main

import (
	"fmt"
)

const (
	messageBlockSize = 128
)
/* eighty constant 64-bit words, K0, K1, ... K79 */
var K = []uint64{
	0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc,
	0x3956c25bf348b538, 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118,
	0xd807aa98a3030242, 0x12835b0145706fbe, 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2,
	0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235, 0xc19bf174cf692694,
	0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,
	0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,
	0x983e5152ee66dfab, 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4,
	0xc6e00bf33da88fc2, 0xd5a79147930aa725, 0x06ca6351e003826f, 0x142929670a0e6e70,
	0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed, 0x53380d139d95b3df,
	0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b,
	0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30,
	0xd192e819d6ef5218, 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8,
	0x19a4c116b8d2d0c8, 0x1e376c085141ab53, 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8,
	0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,
	0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec,
	0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b,
	0xca273eceea26619c, 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178,
	0x06f067aa72176fba, 0x0a637dc5a2c898a6, 0x113f9804bef90dae, 0x1b710b35131c471b,
	0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c,
	0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817,
}

func Hash(original string) string {
	inputValues := []byte(original)
	formattedMessage := formatInput(inputValues)
	computed := compute(formattedMessage)
	return computed
}

func formatInput(values []byte) []byte {
	// Calculate as binary 8-digit numbers
	L := len(values) * 8
	mod := len(values) % messageBlockSize
	padcount := messageBlockSize - mod
    /* 896 < L < 1024 */
	if mod > messageBlockSize-8 {
		padcount += messageBlockSize
	}
	results := make([]byte, len(values)+padcount)
	copy(results, values)
	// add 10000000
	results[len(values)] = 128
	// set L into the end of the message
	for i := 1; i <= 8; i++ {
		results[len(results)-i] = byte(L)
		L = L >> 8
	}
	return results
}
/*
* For t = 0 to 15
*     Wt = M(i)t
*/
func initFirst16Words(words []byte) []uint64 {
	W := make([]uint64, 16)
	for t := 0; t < 16; t++ {
		t8 := t * 8
		W[t] = uint64(words[t8])<<56 |
			uint64(words[t8+1])<<48 |
			uint64(words[t8+2])<<40 |
			uint64(words[t8+3])<<32 |
			uint64(words[t8+4])<<24 |
			uint64(words[t8+5])<<16 |
			uint64(words[t8+6])<<8 |
			uint64(words[t8+7])
	}
	return W
}

func generateMessageBlock(words []byte) [][]byte {
	var M [][]byte
	for i := 0; i < len(words); i += messageBlockSize {
		M = append(M, words[i:i+messageBlockSize])
	}
	return M
}

/* SHR^n(x) = x>>n */
func SHR(bits, word uint64) uint64 {
	return word >> bits
}

/* ROTR^n(x) = (x>>n) OR (x<<(w-n)) */
func ROTR(bits, word uint64) uint64 {
	return (word >> bits) | (word << (64 - bits))
}

/* CH( x, y, z) = (x AND y) XOR ( (NOT x) AND z) */
func CH(x, y, z uint64) uint64 {
	return (x & y) ^ ((^x) & z)
}

/* MAJ( x, y, z) = (x AND y) XOR (x AND z) XOR (y AND z) */
func MAJ(x, y, z uint64) uint64 {
	return (x & y) ^ (x & z) ^ (y & z)
}

/* BSIG0(x) = ROTR^28(x) XOR ROTR^34(x) XOR ROTR^39(x) */
func BSIG0(x uint64) uint64 {
	return ROTR(28, x) ^ ROTR(34, x) ^ ROTR(39, x)
}

/* BSIG1(x) = ROTR^14(x) XOR ROTR^18(x) XOR ROTR^41(x) */
func BSIG1(x uint64) uint64 {
	return ROTR(14, x) ^ ROTR(18, x) ^ ROTR(41, x)
}

/* SSIG0(x) = ROTR^1(x) XOR ROTR^8(x) XOR SHR^7(x) */
func SSIG0(x uint64) uint64 {
	return ROTR(1, x) ^ ROTR(8, x) ^ SHR(7, x)
}

/* SSIG1(x) = ROTR^19(x) XOR ROTR^61(x) XOR SHR^6(x) */
func SSIG1(x uint64) uint64 {
	return ROTR(19, x) ^ ROTR(61, x) ^ SHR(6, x)
}
func compute(messages []byte) string {
	/* initial H(0) hash values */
	H := [8]uint64{
		0x6a09e667f3bcc908,
		0xbb67ae8584caa73b,
		0x3c6ef372fe94f82b,
		0xa54ff53a5f1d36f1,
		0x510e527fade682d1,
		0x9b05688c2b3e6c1f,
		0x1f83d9abfb41bd6b,
		0x5be0cd19137e2179,
	}

	for _, block := range generateMessageBlock(messages) {
		// init W[0]～W[15]
		words := initFirst16Words(block)
		for t := 16; t <= 79; t++ {
			words = append(words, SSIG1(words[t-2])+words[t-7]+SSIG0(words[t-15])+words[t-16])
		}
		a := H[0]
		b := H[1]
		c := H[2]
		d := H[3]
		e := H[4]
		f := H[5]
		g := H[6]
		h := H[7]

		for t, w := range words {
			T1 := h + BSIG1(e) + CH(e, f, g) + K[t] + w
			T2 := BSIG0(a) + MAJ(a, b, c)
			h = g
			g = f
			f = e
			e = d + T1
			d = c
			c = b
			b = a
			a = T1 + T2
		}

		H[0] = a + H[0]
		H[1] = b + H[1]
		H[2] = c + H[2]
		H[3] = d + H[3]
		H[4] = e + H[4]
		H[5] = f + H[5]
		H[6] = g + H[6]
		H[7] = h + H[7]
	}
	// get H[N]
	result := ""
	for _, h := range H {
		// Fill with 0s and align to 16 digits
		result += fmt.Sprintf("%016x", h)
	}
	return result
}
```

## 0 padding
To get final result, I wrote like below.

```go
...
    // get H[N]
	result := ""
	for _, h := range H {
		result += fmt.Sprintf("%x", h)
	}
	return result
}
```

But it wasn't as same as the result of crypto/sha512.

```
// the result of my code
9b71d224bd62f3785d96d46ad3ea3d73319bfbc2890caadae2dff72519673ca72323c3d99ba5c11d7c7acc6e14b8c5dac4663475c2e5c3adef46f73bcdec043

// the result of crypto/sha512
9b71d224bd62f3785d96d46ad3ea3d73319bfbc2890caadae2dff72519673ca72323c3d99ba5c11d7c7acc6e14b8c5da0c4663475c2e5c3adef46f73bcdec043
```

Because one of the H[N] started from "0" and it was omitted.

```
9b71d224bd62f378
5d96d46ad3ea3d73
319bfbc2890caada
e2dff72519673ca7
2323c3d99ba5c11d
7c7acc6e14b8c5da
c4663475c2e5c3a
def46f73bcdec043
```

So I fill with 0s like below.

```go
...
	// get H[N]
	result := ""
	for _, h := range H {
		log.Printf("%x", h)
		// Fill with 0s and align to 16 digits
		result += fmt.Sprintf("%016x", h)
	}
	return result
}
```

## Resources

* [RFC6234 - US Secure Hash Algorithms(SHA and SHA-based HMAC and HKDF)](https://datatracker.ietf.org/doc/html/rfc6234)
* [FIPS140-3 Secure Hash Standard (SHS)](http://csrc.nist.gov/publications/fips/)
* [sha512 package - crypto/sha512 - Go packages](https://pkg.go.dev/crypto/sha512)
* [【Go】暗号化やハッシュ化について考えるついでにSHA256を実装する - タウン情報誌 AIR函館](https://www.air-h.jp/articles/emopro/%E3%80%90go%E3%80%91%E6%9A%97%E5%8F%B7%E5%8C%96%E3%82%84%E3%83%8F%E3%83%83%E3%82%B7%E3%83%A5%E5%8C%96%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%80%83%E3%81%88%E3%82%8B%E3%81%A4%E3%81%84%E3%81%A7%E3%81%AB/)
* [ハッシュ関数 SHA-256 のGoによる実装 - Goプログラミングの森](https://program.sakaiboz.com/golang/algorithm/sha-256/)