secrets.js

See it in action at http://passguardian.com

• What is it?
• Examples
• Installation and usage
• API
• Share format
• Note on security
• License
• Changelog
• Possible future enhancements

What is it?

secrets.js is an implementation of Shamir's threshold secret sharing scheme in javascript, for node.js and browsers.

It can be used to split any "secret" (i.e. a password, text file, Bitcoin private key, anything) into n number of "shares" (each the same size in bits as the original secret), requiring that exactly any number t ("threshold") of them be present to reconstruct the original secret.

Examples:

Divide a 512-bit key, expressed in hexadecimal form, into 10 shares, requiring that any 5 of them are necessary to reconstruct the original key:

// generate a 512-bit key
var key = secrets.random(512); // => key is a hex string

// split into 10 shares with a threshold of 5
var shares = secrets.share(key, 10, 5); 
// => shares = ['801xxx...xxx','802xxx...xxx','803xxx...xxx','804xxx...xxx','805xxx...xxx']

// combine 4 shares
var comb = secrets.combine( shares.slice(0,4) );
console.log(comb === key); // => false

// combine 5 shares
var comb = secrets.combine( shares.slice(4,9) );
console.log(comb === key); // => true

// combine ALL shares
var comb = secrets.combine( shares );
console.log(comb === key); // => true

// create another share with id 8
var newShare = secrets.newShare(8, shares); // => newShare = '808xxx...xxx'

// reconstruct using 4 original shares and the new share:
var comb = secrets.combine( shares.slice(1,5).concat(newShare) );
console.log(comb === key); // => true

Divide a password containing a mix of numbers, letters, and other characters, requiring that any 3 shares must be present to reconstruct the original password:

var pw = '<<PassWord123>>';

// convert the text into a hex string
var pwHex = secrets.str2hex(pw); // => hex string

// split into 5 shares, with a threshold of 3
var shares = secrets.share(pwHex, 5, 3);


// combine 2 shares:
var comb = secrets.combine( shares.slice(1,3) );

//convert back to UTF string:
comb = secrets.hex2str(comb);
console.log( comb === pw  ); // => false


// combine 3 shares:
var comb = secrets.combine( [ shares[1], shares[3], shares[4] ] );

//convert back to UTF string:
comb = secrets.hex2str(comb);

console.log( comb === pw  ); // => true

Installation and usage

secrets.js is available on npm. Install using

npm install secrets.js

The version on npm may not always reflect all the latest changes, especially during times of heavy development. To get the most up-to-date version, download the current master zip file, then run the following code from inside the folder:

npm install

To use it in node.js:

var secrets = require('secrets.js');

To use it in the browser, include secrets.js or secrets.min.js (minified using Google Closure Compiler)

<script src="secrets.min.js"></script>

API

• secrets.share()
• secrets.combine()
• secrets.newShare()
• secrets.init()
• secrets.getConfig()
• secrets.setRNG()
• secrets.random()
• secrets.str2hex()
• secrets.hex2str()

secrets.share( secret, numShares, threshold, [padLength] )

Divide a secret expressed in hexadecimal form into numShares number of shares, requiring that threshold number of shares be present for reconstructing the secret;

• secret: String, required: A hexadecimal string.
• numShares: Number, required: The number of shares to compute. This must be an integer between 2 and 2^bits-1 (see secrets.init() below for explanation of bits).
• threshold: Number, required: The number of shares required to reconstruct the secret. This must be an integer between 2 and 2^bits-1 (see secrets.init() below for explanation of bits).
• padLength: Number, optional, default 0: How much to zero-pad the binary representation of secret. This ensures a minimum length for each share. See "Note on security" below.

The output of secrets.share() is an Array of length numShares. Each item in the array is a String. See Share format below for information on the format.

secrets.combine( shares )

Reconstructs a secret from shares.

• shares: Array, required: An Array of shares. The form is equivalent to the output from secrets.share().

The output of secrets.combine() is a String representing the reconstructed secret. Note that this function will ALWAYS produce an output String. However, if the number of shares that are provided is not the threshold number of shares, the output will not be the original secret. In order to guarantee that the original secret is reconstructed, the correct threshold number of shares must be provided.

Note that using more than the threshold number of shares will also result in an accurate reconstruction of the secret. However, using more shares adds to computation time.

secrets.newShare( id, shares )

Create a new share from the input shares.

• id: Number or String, required: A Number representing the share id. The id is an integer between 1 and 2^bits-1. It can be entered as a Number or a number String expressed in hexadecimal form.
• shares: Array, required: The array of shares (in the same format as outputted from secrets.share()) that can be used to reconstruct the original secret.

The output of secrets.newShare() is a String. This is the same format for the share that secrets.share() outputs. Note that this function ALWAYS produces an output String. However, as for secrets.combine(), if the number of shares that are entered is not the threshold number of shares, the output share will not be a valid share (i.e. will not be useful in reconstructing the original secret). In order to guarantee that the share is valid, the correct threshold number of shares must be provided.

secrets.init( [bits] )

Set the number of bits to use for finite field arithmetic.

• bits: Number, optional, default 8: An integer between 3 and 20. The number of bits to use for the Galois field.

Internally, secrets.js uses finite field arithmetic in binary Galois Fields of size 2^bits. Multiplication is implemented by the means of log and exponential tables. Before any arithmetic is performed, the log and exp tables are pre-computed. Each table contains 2^bits entries.

bits is the limiting factor on numShares and threshold. The maximum number of shares possible for a particular bits is (2^bits)-1 (the zeroth share cannot be used as it is the secret by definition.). By default, secrets.js uses 8 bits, for a total 2^8-1 = 255 possible number of shares. To compute more shares, a larger field must be used. To compute the number of bits you will need for your numShares or threshold, compute the log-base2 of (numShares+1) and round up, i.e. in javascript: Math.ceil(Math.log(numShares+1)/Math.LN2).

Note:

• secrets.init() does NOT need to be called if you plan on using the default of 8 bits. It is automatically called on loading the library.
• The size of the exp and log tables depends on bits (each has 2^bits entries). Therefore, using a large number of bits will cause a slightly longer delay to compute the tables.
• The theoretical maximum number of bits is 31, as javascript performs bitwise operations on 31-bit numbers. A limit of 20 bits has been hard-coded into secrets.js, which can produce 1,048,575 shares. secrets.js has not been tested with this many shares, and it is not advisable to go this high, as it may be too slow to be of any practical use.
• The Galois Field may be re-initialized to a new setting when secrets.newShare() or secrets.combine() are called with shares that are from a different Galois Field than the currently initialized one. For this reason, use secrets.getConfig() (see below) to check what the current bit-setting is.

secrets.getConfig()

Returns an Object with the current configuration. Has the following properties:

• bits: [Number] The number of bits used for the current initialized finite field
• unsafePRNG: [Boolean]: Is true when Math.random() is being used as the PRNG

secrets.setRNG( function(bits){} )

Set the pseudo-random number generator used to compute shares.

secrets.js uses a PRNG in the secrets.share() and secrets.random() functions. By default, it tries to use a cryptographically strong PRNG. In node.js this is crypto.randomBytes(). In browsers that support it, it is crypto.getRandomValues() (using typed arrays, which must be supported too). If neither of these are available it defaults to using Math.random(), which is NOT cryptographically strong (except reportedly in Safari, though I have yet to confirm this). A warning will be displayed in the console and in an alert box in browsers when Math.random() is being used.

To supply your own PRNG, use secrets.setRNG(). It expects a Function of the form function(bits){}. It should compute a random integer between 1 and 2^bits-1. The output must be a String of length bits containing random 1's and 0's (cannot be ALL 0's). When secrets.setRNG() is called, it tries to check the PRNG to make sure it complies with some of these demands, but obviously it's not possible to run through all possible outputs. So make sure that it works correctly.

If you are just planning on using secrets.combine() or secrets.newShare(), then no PRNG is required. It is only used by the secrets.share() and secrets.random() functions.

NOTE: In a near-future version of secrets.js, the requirement for the PRNG function will be less convoluted. It probably will just have to return a random integer between 1 and max, or something like that.

secrets.random( bits )

Generate a random bits-length string, and output it in hexadecimal format. bits must be an integer greater than 1.

secrets.str2hex( str, [bytesPerChar] )

Convert a UTF string str into a hexadecimal string, using bytesPerChar bytes (octets) for each character.

• str: String, required: A UTF string.
• bytesPerChar: Number, optional, default 2. The maximum bytesPerChar is 6 to ensure that each character is represented by a number that is below javascript's 2^53 maximum for integers.

secrets.hex2str( str, [bytesPerChar] )

Convert a hexadecimal string into a UTF string. Each character of the output string is represented by bytesPerChar bytes in the String str. See note on bytesPerChar under secrets.str2hex() above.

Share format

Each share is a string in the format <bits><id><value>. Each part of the string is described below:

• bits: The first character, expressed in base-36 format, is the number of bits used for the Galois Field. This number must be between 3 and 20, expressed by the characters [3-9, a-k].
• id: The id of the share. This is a number between 1 and 2^bits-1, expressed in hexadecimal form. The number of characters used to represent the id is the character-length of the representation of the maximum id (2^bits-1) in hexadecimal: (Math.pow(2,bits)-1).toString(16).length.
• value: The value of the share, expressed in hexadecimal form. The length of this string depends on the length of the secret.

Note on security

Shamir's secret sharing scheme is "information-theoretically secure" and "perfectly secure" in that less than the requisite number of shares provide no information about the secret (i.e. knowing less than the requisite number of shares is the same as knowing none of the shares). However, because the size of each share is the same as the size of the secret (when using binary Galois fields, as secrets.js does), in practice it does leak some information, namely the size of the secret. Therefore, if you will be using secrets.js to share short password strings (which can be brute-forced much more easily than longer ones), it would be wise to zero-pad them so that the shares do not leak information about the size of the secret.

When secrets.share() is called with a padLength, the secret is zero-padded so that it's length is a multiple of the padLength. The second example above can be modified to use 1024-bit zero-padding, producing longer shares:

var pw = '<<PassWord123>>';

// convert the text into a hex string
var pwHex = secrets.str2hex(pw); // => 240-bit password

// split into 5 shares, with a threshold of 3, WITH zero-padding
var shares = secrets.share(pwHex, 5, 3, 1024); // => 1024-bit shares

// combine 3 shares
var comb = secrets.combine( [ shares[1], shares[3], shares[4] ] );

// convert back to UTF string
comb = secrets.hex2str(comb);

console.log( comb === pw  ); // => true

License

secrets.js is released under the MIT License. See LICENSE.

Changelog

• 0.1.8: bugfix release
• 0.1.7: added config.unsafePRNG reset when supplying a new PRNG
• 0.1.6:
  • Removed JSBN dependency, support for arbitrary radices, and the convertBase() function, with attendant 50% file size reduction.
  • Fixed bug where leading zeros were dropped.
  • Renamed string conversion functions.
• 0.1.5: getConfig() returns information about PRNG
• 0.1.4: new share format

Possible future enhancements

• A strong PRNG for browsers that don't have crypto.getRandomValues()
• Operate on node.js streams
• Cheater-detection
• Dynamic threshold
• Investigate speed enhancements in polynomial evaluation and polynomial interpolation