Scrypt is a slow-by-design hash function or more accurately, a KDF function. Its purpose is to take some input data, and create a fingerprint of that data, but to do it very slowly. A common use-case is to take a password and create an n-bit private key, which is much longer and more secure. Here at Qvault we use a similar KDF for securing user passwords.

For example, let’s pretend your password is password1234. By using Scrypt, we can extend that deterministically into a 256-bit key:

**password1234 **->

AwEEDA4HCwQFAA8DAwwHDQwPDwUOBwoOCQACAgUJBQ0JAAYNBAMCDQ4JCQgLDwcGDQMDDgMKAQsNBAkLAwsACA==

That long 256-bit key can now be used as a private key to encrypt and decrypt data. For example, it could be the key in an AES-256 cipher.

## Why not use the password to encrypt directly?

Most encryption algorithms, including AES-256, require that a key of sufficient length is used. By hashing the password, we can derive a longer, more secure, fixed-size key.

Furthermore, using a KDF like Scrypt provides additional benefits over a traditional hash function like SHA-2:

- Computationally expensive and slow
- Memory intensive (potentially several gigabytes of RAM is used to execute the hash)

Often times brute-force attackers will try to break encryption by guessing passwords over and over until they get it right. AES-256 and SHA-2 are fast, so an attacker would be able to guess many passwords per second. By using a slow hashing function like Scrypt to derive a key, we can force the attacker to waste more resources trying to break in.

## Scrypt Step-by-Step

Scrypt can be visualized by some psuedo-code:

```
func Scrypt(
passphrase, // string of characters to be hashed
salt, // random salt
costFactor, // CPU/Memory cost, must be power of 2
blockSizeFactor,
parallelizationFactor, // (1..232-1 * hLen/MFlen)
desiredKeyLen // Desired key length in bytes
) derivedKey {
// we'll get to theis
}
```

Let’s go through the steps of converting those inputs into the desired `derivedKey`

### 1 – Define Blocksize

`const blockSize = 128 * blockSizeFactor`

### 2 – Generate Initial Salt

Scrypt uses PBKDF2 as a child key-derivation function. We use it to generate an initial salt. PBKDF2 has the following signature:

```
func PBKDF2(
prf,
password,
salt,
numIterations,
desiredKeyLen
) derivedKey {}
```

We use it as follows:

`const initialSalt = PBKDF2(HMAC-SHA256, passphrase, salt, 1, blockSize * parallelizationFactor)`

### 3 – Mix Salt

Next, we mix the salt. We split `initialSalt`

into `splitSalt`

, which is a 2D array of bytes. Each sub-array contains 1024 bytes

```
splitSalt := [][1024]byte(initialSalt)
for i, block := range splitSalt {
newBlock := roMix(block, costFactor)
splitSalt[i] = newBlock
}
```

where `roMix`

is:

```
func roMix(block, iterations){
v := []
x := block
for i := 0; i < iterations; i++ {
v[i] = x
x = blockMix(x)
}
for i := 0; i < iterations; i++ {
j := integerify(x) % iterations
x = blockMix(x ^ v[j])
}
return x
}
```

Where `integerify`

is defined by RFC-7914 and `blockMix`

is:

```
func blockMix(block){
r := len(block) / 128
// split block into an array of 2r 64-byte chunks
chunks := get2r64ByteChunks()
x := chunks[len(chunks)-1]
y := []
for i := 0; i < len(chunks); i++{
x = salsa20-8(x ^ chunks[i])
y[i] = x
}
return [y[0], y[2], ...y[2r-2], y[1], y[3], ...y[2r-1]]
}
```

Where `salsa20-8`

is the 8-round version of the algorithm defined here.

### 4 – Finalize Salt

Now `splitSalt`

has been mixed in such a computationally exhausting way that we will call it an `expensiveSalt`

. Expensive salt will be a single array of bytes, so we need to concatenate all the subarrays in `splitSalt`

.

`expensiveSalt := append([], splitSalt...)`

### 5 – Return Final KDF

`return PBKDF2(HMAC-SHA256, passphrase, expensiveSalt, 1, desiredKeyLen)`

The final pseudocode for our top level function is as follows:

```
func Scrypt(
passphrase, // string of characters to be hashed
salt, // random salt
costFactor, // CPU/Memory cost, must be power of 2
blockSizeFactor,
parallelizationFactor, // (1..232-1 * hLen/MFlen)
desiredKeyLen // Desired key length in bytes
) derivedKey {
const blockSize = 128 * blockSizeFactor
const initialSalt = PBKDF2(HMAC-SHA256, passphrase, salt, 1, blockSize * parallelizationFactor)
splitSalt := [][1024]byte(initialSalt)
for i, block := range splitSalt {
newBlock := roMix(block, costFactor)
splitSalt[i] = newBlock
}
expensiveSalt := append([], splitSalt...)
return PBKDF2(HMAC-SHA256, passphrase, expensiveSalt, 1, desiredKeyLen)
}
```

Or, if you prefer, the pseudocode as defined by Wikipedia:

```
Function scrypt
Inputs:
Passphrase: Bytes string of characters to be hashed
Salt: Bytes random salt
CostFactor (N): Integer CPU/memory cost parameter - Must be a power of 2 (e.g. 1024)
BlockSizeFactor (r): Integer blocksize parameter (8 is commonly used)
ParallelizationFactor (p): Integer Parallelization parameter. (1..232-1 * hLen/MFlen)
DesiredKeyLen: Integer Desired key length in bytes
Output:
DerivedKey: Bytes array of bytes, DesiredKeyLen long
Step 1. Generate expensive salt
blockSize ← 128*BlockSizeFactor //Length (in bytes) of the SMix mixing function output (e.g. 128*8 = 1024 bytes)
Use PBKDF2 to generate initial 128*BlockSizeFactor*p bytes of data (e.g. 128*8*3 = 3072 bytes)
Treat the result as an array of p elements, each entry being blocksize bytes (e.g. 3 elements, each 1024 bytes)
[B0...Bp−1] ← PBKDF2HMAC-SHA256(Passphrase, Salt, 1, blockSize*ParallelizationFactor)
Mix each block in B Costfactor times using ROMix function (each block can be mixed in parallel)
for i ← 0 to p-1 do
Bi ← ROMix(Bi, CostFactor)
All the elements of B is our new "expensive" salt
expensiveSalt ← B0∥B1∥B2∥ ... ∥Bp-1 //where ∥ is concatenation
Step 2. Use PBKDF2 to generate the desired number of bytes, but using the expensive salt we just generated
return PBKDF2HMAC-SHA256(Passphrase, expensiveSalt, 1, DesiredKeyLen);
```

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