savour-secret

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

About

savour-secret is an implementation of Shamir's threshold secret sharing scheme in JavaScript, for Node.js and browsers with both Global variable and AMD module loading support.

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.

This is a fork of the original excellent code created by amper5and on Github. The original savour-secret can be found there.

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 = savour_secret.random(512) // => key is a hex string

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

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

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

// combine ALL shares
comb = savour_secret.combine(shares)
console.log(comb === key) // => true

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

// reconstruct using 4 original shares and the new share:
comb = savour_secret.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 = savour_secret.str2hex(pw) // => hex string

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

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

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

// combine 3 shares:
comb = savour_secret.combine([shares[1], shares[3], shares[4]])

//convert back to UTF string:
comb = savour_secret.hex2str(comb)
console.log(comb === pw) // => true

There are some additional examples of simple usage in the browser, Node.js, and AMD loading (require.js) in the examples folder.

Installation and usage

This fork of savour-secret is available from www.npmjs.com. Install using

npm install savour-secret-savour-labs

The source code for this package is available on Github.

To use it in a Node.js application (Requires OpenSSL support compiled into Node):

var savour_secret = require("savour-secret")

To use it in the browser with the global 'savour-secret' defined, include savour-secret or savour-secret.min.js in your HTML.

<script src="savour-secret.min.js"></script>

You can also use it in the browser with an AMD module loading tool like require.js. See the AMD loading example in the examples dir.

API

• savour_secret.share()
• savour_secret.combine()
• savour_secret.newShare()
• savour_secret.init()
• savour_secret.getConfig()
• savour_secret.extractShareComponents()
• savour_secret.setRNG()
• savour_secret.random()
• savour_secret.str2hex()
• savour_secret.hex2str()
• savour_secret.xorShare()
• savour_secret.inverseXor()

savour_secret.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 savour_secret.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 savour_secret.init() below for explanation of bits).
• padLength: Number, optional, default 128: 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 savour_secret.share() is an Array of length numShares. Each item in the array is a String. See Share format below for information on the format.

savour_secret.combine( shares )

Reconstructs a secret from shares.

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

The output of savour_secret.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.

savour_secret.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 savour_secret.share()) that can be used to reconstruct the original secret.

The output of savour_secret.newShare() is a String. This is the same format for the share that savour_secret.share() outputs. Note that this function ALWAYS produces an output String. However, as for savour_secret.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.

savour_secret.init( [bits, rngType] )

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.
• rngType: String, optional: A string that has one of the values ["nodeCryptoRandomBytes", "browserCryptoGetRandomValues"]. Setting this will try to override the RNG that would be selected normally based on feature detection. Warning: You can specify a RNG that won't actually work in your environment.

Internally, savour_secret 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, savour_secret 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). You can examine the current calculated maxShares value by calling savour_secret.getConfig() and increase the bits accordingly for the number of shares you need to generate.

Note:

• You can call savour_secret.init() anytime to reset all internal state and re-initialize.
• savour_secret.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 savour_secret, which can produce 1,048,575 shares. savour_secret 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 savour_secret.newShare() or savour_secret.combine() are called with shares that are from a different Galois Field than the currently initialized one. For this reason, use savour_secret.getConfig() to check what the current bits setting is.

savour_secret.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
• radix: [Number] The current radix (Default: 16)
• maxShares: [Number] The max shares that can be created with the current bits. Computed as Math.pow(2, config.bits) - 1
• hasCSPRNG: [Boolean] Indicates whether or not a Cryptographically Secure Pseudo Random Number Generator has been found and initialized.
• • typeCSPRNG: [String] Indicates which random number generator function has been selected based on either environment feature detection (the default) or by manually specifying the RNG type using savour_secret.init() or savour_secret.setRNG(). The current possible types that can be displayed here are ["nodeCryptoRandomBytes", "browserCryptoGetRandomValues"].

savour_secret.extractShareComponents( share )

Returns an Object with the extracted parts of a public share string passed as an argument. Has the following properties:

• bits: [Number] The number of bits configured when the share was created.
• id: [Number] The ID number associated with the share when created.
• data: [String] A hex string of the actual share data.

savour_secret.setRNG( function(bits){} | rngType )

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

savour_secret uses a PRNG in the savour_secret.share() and savour_secret.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).

To supply your own PRNG, use savour_secret.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 savour_secret.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.

• rngType: String, optional: A string that has one of the values ["nodeCryptoRandomBytes", "browserCryptoGetRandomValues"]. Setting this will try to override the RNG that would be selected normally based on feature detection. Warning: You can specify a RNG that won't actually work in your environment.

savour_secret.random( bits )

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

savour_secret.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.

savour_secret.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 savour_secret.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 Base36 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] in Base36.
• 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.
• data: The value of the share, expressed in hexadecimal form. The length of this string depends on the length of the secret.

You can extract these attributes from a share in your possession with the savour_secret.extractShareComponents(share) function which will return an Object with these attributes. You may use these values, for example, to call savour_secret.init() with the proper bits setting for shares you want to combine.

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 savour_secret does), in practice it does leak some information, namely the size of the secret. Therefore, if you will be using savour_secret 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. With this in mind, savour_secret will zero-pad in multiples of 128 bits by default which slightly increases the share size for small savour_secret in the name of added security. You can increase or decrease this padding manually by passing the padLength argument to savour_secret.share().

When savour_secret.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 = savour_secret.str2hex(pw) // => 240-bit password

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

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

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

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

There is a workbook containing some additional padding examples.

Development and Testing

cd savour-secret/
npm install

Continuous Development

Watch all JavaScript files and run the testing and minification tasks on every save to a file.

npm run watch

Build & Minify

The minified version of the savour-secret can be found in savour-secret.min.js. This file was generated using the UglifyJS2 tool.

npm run build