Full Domain Hash

A Full Domain Hash (FDH) is a useful cryptographic construction that extends the size of a hash digest to an arbitrary length. For example, SHA256 can be expanded to 1024 bits instead of the usual 256 bits.

We construct an FDH by computing a number of cycles where cycles=(target length)/(digest length) + 1 We then compute FDH(M) = HASH(M||0)||HASH(M||1)||...||HASH(M||cycles−1), where HASH is any hash function defined in package crypto, || denotes concatenation, and numerical values are binary (\x01, \x02 etc).

FDHs are usually used with an RSA signature scheme where the target length is the size of the key. See https://en.wikipedia.org/wiki/Full_Domain_Hash

Example

import (
	"crypto"
	_ "crypto/sha256"
	"github.com/cryptoballot/fdh"
	"fmt"
	"encoding/hex"
)

var message = []byte("ATTACK AT DAWN")

func main() {
	h := fdh.New(crypto.SHA256, 2048)
	h.Write(message)
	digest := h.Sum(nil)
	
	// We now have a SHA256 digest that has been extended from 256 bits to 2048 bits.
	fmt.Println(hex.EncodeToString(digest))
}

As a shortcut you can also use the Sum function.

import (
	"crypto"
	_ "crypto/md5"
	"github.com/cryptoballot/fdh"
	"log"
)

var message = []byte("ATTACK AT DAWN")

func main() {
	digest := fdh.Sum(crypto.MD5, 1024, message)
	// ... do something with digest ...
}

Bash equivalent

# Expand SHA256 hash of "ATTACK AT DAWN" to 1024 bits
echo -n -e 'ATTACK AT DAWN\x00' | shasum -a 256 | cut -d ' ' -f 1 | tr -d '\n' &&\
echo -n -e 'ATTACK AT DAWN\x01' | shasum -a 256 | cut -d ' ' -f 1 | tr -d '\n' &&\
echo -n -e 'ATTACK AT DAWN\x02' | shasum -a 256 | cut -d ' ' -f 1 | tr -d '\n' &&\
echo -n -e 'ATTACK AT DAWN\x03' | shasum -a 256 | cut -d ' ' -f 1