Constant-Time JavaScript

Constant-time algorithms written in TypeScript.

Important: This Github repository is the companion to Soatok's Guide to Side-Channel Attacks. Do not use this in production, especially if you don't have the budget for a cryptography audit.

Documentation

This is just a quick outline of what each function does.

compare(a, b) - Compare two Uint8Array objects.
- Explanation
- Returns -1 if a < b
- Returns 1 if a > b
- Returns 0 if a === b
- Throws an Error if a.length !== b.length
compare_ints(a, b) - Compare two integers.
- Explanation
- Returns -1 if a < b
- Returns 1 if a > b
- Returns 0 if a === b
equals(a, b) - Are these Uint8Array objects equal?
- Explanation
- Returns true if they are equal.
- Returns false if they are not equal.
- Throws an Error if a.length !== b.length
hmac_equals(a, b) - Are these Uint8Array objects equal? (Using HMAC to compare.)
- Explanation
- Returns true if they are equal.
- Returns false if they are not equal.
- Throws an Error if a.length !== b.length
intdiv(N, D) - Divide N into D, discarding remainder.
- Explanation
- Returns an integer.
modulo(N, D) - Divide N into D, return the remainder.
- Explanation
- Returns an integer.
resize(buf, size) - Return a resized Uint8Array object (to side-step memory access leakage)
select(x, a, b) - Read it as a ternary. If x is true, returns a. Otherwise, returns b.
- Explanation
- x must be a boolean
- a must be a Uint8Array
- b must be a Uint8Array
- Throws an Error if a.length !== b.length
select_ints(x, a, b) - Read it as a ternary. If x is even, returns a. Otherwise, returns b. (You should pass 1 or 0 for x).
- Explanation
- x must be a boolean
- a must be a number
- b must be a number
trim_zeroes_left(buf)
- Explanation
- buf must be a Uint8Array
- Returns a Uint8Array
trim_zeroes_right(buf)
- Explanation
- buf must be a Uint8Array
- Returns a Uint8Array

BigNumber

Our BigNumber implementation aims to be constant-time for the magnitude of the numbers (i.e. number of limbs or bytes, regardless of how many bits are significant).

Unless otherwise stated, all of our APIs expect Uint8Array objects (Buffer extends from Uint8Array and should work too, but we return Uint8Array objects, not Buffer objects).

Unless otherwise stated, all Uint8Array objects are big-endian byte order.

Unless otherwise stated, all Uint8Array objects assume unsigned integer behavior.

Unless otherwise stated, all of the bignum methods are immutable (meaning: they return a new Uint8Array object rather than mutating the input arrays).

bignum.add()

Returns a + b. Overflow is discarded.

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.add(a, b);

bignum.and()

Returns a & b (bitwise AND).

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.and(a, b);

bignum.count_trailing_zero_bits()

Counts the number of 0 bits beneath the most significant 1 bit.

Returns a BigInt (the native JS type), since the number of bits may exceed 2^32 for an array that is less than 2^32 elements long.

/** 
 * @var {Uint8Array} a
 */
const c: bigint = bignum.count_trailing_zero_bits(a, b);

bignum.divide()

Calculate a / b, discarding the remainder.

/**
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.divide(a, b);

bignum.gcd()

Calculate the Greatest Common Denominator of two integers.

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.gcd(a, b);

bignum.is_nonzero()

Returns true if this number is not equal to zero?

/**
 * @var {Uint8Array} x
 */
const check: boolean = bignum.is_nonzero(x);

bignum.lsb()

Returns the least significant bit of a big number. (If 0, this is a multiple of two.)

/**
 * @var {Uint8Array} x
 */
const least: number = bignum.lsb(x);

bignum.lshift1()

Mutates the input array.

Left-shift by 1. This is used internally in some algorithms.

/** 
 * @var {Uint8Array} a
 */
lshift1(a);
// `a` is now double its previous value

bignum.modulo()

Calculate a mod b.

/**
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.modulo(a, b);

bignum.modInverse()

Calculate the modular inverse of two integers.

Throws if gcd(a, b) is not equal to 1.

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
let one_over_a: Uint8Array;
try {
    one_over_a = bignum.modInverse(a, b);
} catch (e) {
    // Handle exception when 1/a is not defined (mod b).
}

bignum.modPow()

Modular exponentiation.

/**
 * @var {Uint8Array} base
 * @var {Uint8Array} exp
 * @var {Uint8Array} mod
 */
const out: Uint8Array = bignum.modPow(base, exp, mod);

bignum.msb()

Returns the most significant bit of a big number.

/**
 * @var {Uint8Array} x
 */
const most: number = bignum.msb(x);

bignum.multiply()

Multiply two big numbers, return the product.

The output size will be larger than the inputs.

/**
 * @var {Uint8Array} x
 * @var {Uint8Array} y
 */
const z: Uint8Array = bignum.multiply(x, y);

bignum.normalize()

Resize an Uint8Array to the desired length.

The default behavior is to treat the number as signed (thereby filling in the left with 0xFF bytes if the most significant bit of the input Uint8Array is set).

Pass true to the optional third argument to always zero-fill this padding value.

/** 
 * @var {Uint8Array} a
 * @var {number} len
 */
const c: Uint8Array = bignum.normalize(a, len);

bignum.or()

Returns a | b (bitwise OR).

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.or(a, b);

bignum.pow()

Exponentiation.

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} n
 */
const c: Uint8Array = bignum.pow(a, n);

bignum.rshift1()

Mutates the input array.

Right-shift by 1. This is used internally in some algorithms.

/** 
 * @var {Uint8Array} a
 */
rshift1(a);
// `a` is half double its previous value

The default behavior is congruent to JavaScript's >> operator. For an unsigned right shift (>>>), pass true as the second argument:

rshift1(a, true);

bignum.shift_left()

Shift left by an arbitrary amount.

/**
 * @var {Uint8Array} x
 */
const y: Uint8Array = bignum.shift_left(x, 3n);
// y :=  8 * x

bignum.shift_right()

Shift right by an arbitrary amount.

/**
 * @var {Uint8Array} x
 */
const y: Uint8Array = bignum.shift_right(x, 3n);
// y := x / 8

bignum.sub()

Returns a - b. Use msb() to check if the output is negative.

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.sub(a, b);

bignum.xor()

Returns a ^ b (bitwise XOR).

/** 
 * @var {Uint8Array} a
 * @var {Uint8Array} b
 */
const c: Uint8Array = bignum.xor(a, b);

Limitations

Potentially Dangerous on 32-bit Applications

32-bit v8 (and, presumably, a lot of other 32-bit implementations) do things wrong, and our implementation might be variable-time on it.

Specifically, the most significant bit of a 32-bit integer distinguishes values from pointers. As a result, accessing the highest bit of a 32-bit number in 32-bit JavaScript engines (such as v8) is potentially variable-time.

To mitigate this risk, the int32 class was created which wraps operates on 16-bit limbs (wrapping Uint16Array).

Frequently Asked Questions

But Why Though?

For science!

This is a proof-of-concept library, that will eventually implement all of the algorithms described in the accompanying blog post.

The main purpose of this library is to demonstrate the concepts in a programming language widely accessible outside of the cryptography orthodoxy (which today is largely C and sometimes Python, and hopefully soon Rust).

Can I use this in a project?

Hold off until v1.0.0 is tagged before you even think about relying on it for anything. APIs might break until then.

What's with the blue {fox, wolf}?

My fursona is a dhole, not a wolf.

You should remove your fursona from this so my manager might take it seriously.

I don't owe you anything. I don't owe your manager anything.

Besides, if anyone is bigoted against a predominantly LGBTQIA+ community, they're precisely the sort of person whose career I don't want to help.

In sum:

timurkartaev / constant-time-js Goto Github PK

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