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Introduction

If you (or the president of Yoyodyne, Inc.) knows an important password, such important that something awful happens if you cannot provide it. (E.g. to decrypt the telephone number of your new love, or the description of a new product which will get Yoyodyne megabugs.) Well, you can give the password to a trusty friend (or the vice president), but is (s)he really trustworthily enough?

Sharesecret gives you the solution. You can split your secret into n parts with a threshold parameter t (2<=t<=n). Then you can distribute the parts to some of your friends (or the vice presidents). If you forget the secret you can ask t friends to help you. They (the t friends) can apply joinsecret n to the parts and, voilá, the secret appears again.

If you use a good (i.e. cryptologically strong) pseudo random number generator, strictly less then t friends have in no way an advantage over arbitrarily guesses.

There are also schemes possible for remote friends (or normal managers) as a second level backup, e.g. with higher threshold.

Node:Example, Next:, Previous:Introduction, Up:Top

Examples

Split a secret into 42 parts such that all parts are needed for reconstruction using /dev/random as pseudo random number generator:
prng-random-splitsecret 42 42 part. < secret-data
splitsecret 42 42 part. 3< /dev/random < secret-data

Split a secret into 42 parts such that exactly 17 parts are needed for reconstruction using /dev/urandom as pseudo random number generator:
prng-urandom-splitsecret 42 17 part. < secret-data
splitsecret 42 17 part. 3< /dev/urandom < secret-data

If you have the EGD - Entropy Gathering Demon you can use:
prng-egd-splitsecret 42 17 part. < secret-data
splitsecret 42 17 part. 3< ~/.gnupg/entropy < secret-data

If you don't have one of the upper pseudo random number generators or if you are just playing around you can call:
prng-arcfour-splitsecret 42 17 part. < secret-data

Joining 17 parts can be done by:
joinsecret 42 part.0*[1-9] part.0*1[2-9] > joined-secret

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File format

The secret data is considered to be arbitrary binary data. A part starts with a magic. This is a netstring (see D. J. Bernstein's netstrings) of "FSS " appended with the file format version number1. That is for this version "9:FSS 1.0.0,". If the part is generated by the XOR-method there follows exactly as many bytes as there are in the secret. Otherwise (using the polynomial method), there are two bytes of the evaluation point (MSB first). Then follows the result of the evaluation (MSB first) of the random polynomials.

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Future

Node:Security, Next:, Previous:Future, Up:Top

Some thoughts about Security.

Security by obscurity is not a good idea. Once when the attacker know the code the security lowers or disappears. That's not a good idea for open source software. Therefore, I don't try to reach it. If you want some obscurity you should use steganography.

The security of sharesecret depends of course on the quality (i.e. cryptographic quality) of the pseudo random number generator. The very best choice is /dev/urandom if your operating system provides this device with a good quality. Other good sources are /dev/random, the output of gpg --gen-random 2 and ~/.gnupg/entropy if you have the EGD - Entropy Gathering Demon (see EGD). A good fallback is prng-arcfour which is part of sharesecret.

Node:Limitations, Next:, Previous:Security, Up:Top

Limitations of the current implementation

The code avoids the problem of many operation system which allows only a low number (e.g. 256 for canonical Linux at 2000-12). It only needs to have 3 open files for splitting and two for assembling at the same time.

In future version the number of parts is limited only by the available memory if the threshold for assembling is the same as the number of parts (t=n). Up to now sharesecret uses the same limits as below.

Otherwise (1<t<n), the limit of parts is 65520 = 65521 - 1 2. If you have enough memory you (or I) may rewrite the program, but consider the space and time estimates (see Complexity).

Legal matters

Sharesecret is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License, or (at your option) any later version.

I don't know if it is allowed to export sharesecret from the US. The addresses given below, see Downloads, points to a computer in Germany, which don't have such an export restriction. (And the files have been put there in a legal way.)

Node:Complexity, Next:, Previous:Limitations, Up:Top

Space and time complexity estimates.

To describe the complexity by formulas we need to introduce the following notation.

Of course we have the compatibility condition 1<t<=n. And we write l for the bit length ceil (log (n)/log (2)). Finally, we write a for the amortised effective length (= number of octets, i.e. bytes) L((1/p) + (2/(2^16-p))) see Value of p. 3

For reasons of completeness we give the definitions of the complexity classes here.

Let X be a lattice, e.g. X=N. Further, let f:X->R be a function on X.

Splitting

Space complexity

XOR splitting

If t=n implementations are possible which need only O(l) space. But in the current implementation we use O(n*l) space. It's just easier to implement.

Polynomial splitting

If t<n we need Omega(t*l), Theta(t*l),O(t*l) space for splitting. Moreover, a lower bound is t*l. E.g. t = 65000, n = 65520 => 1040000 Bit = 130000 Bytes =~ 130 kByte. but squaring the size (doubling l) gives t = 4294967200, n = 4294967296 = 2^32 => 137438950400 Bit = 17179868800 Bytes =~ 17 GBytes. If you do long long calculations you need about 34 GBytes of main or virtual memory.

Speed complexity

XOR splitting

If t=n then we need Omega(n*L), Theta(n*L), O(n*L) time.

Polynomial splitting

If t<n then we need O(t*n*L) time.

Assembling

Time complexity

XOR assembling

If t=n then we need Omega(n*L), Theta(n*L), O(n*L) time.

Polynomial assembling

If t<n then we need O(t^2*L) time.

If I have more time I check these estimates in detail. Up to know take them as intuitive values.

Node:Competitors, Next:, Previous:Complexity, Up:Top

Competitors

There is another program secsplit somewhere. In the second version a lot of ideas of secsplit are inserted into sharesecret. But secsplit didn't optimise the case that the threshold is maximal, i.e. the number of parts.

There is (maybe are) some programs which uses the XOR algorithm, i.e. they only provide splitting if the threshold is maximal, i.e. the number of parts.

Sharesecret

During joining sharesecret uses the Aitken-Neville algorithm for interpolating polynomials at a given point x, in this case at x=0. There are several other interpolation methods, e.g. Lagrange, Newton, which are useful if you want to evaluate the unknown polynomial at several points. Sharesecret needs only the value at 0, thus the Aitken-Neville method is the fastest4.

If sharesecret would take the coefficients in the natural (or integer, rational, real) numbers it would need exact rational (or real) numbers in the Aitken-Neville algorithm. As this would take a lot of memory and time sharesecret uses another method. It does its calculations in a finite field, particularly in Z/pZ, i.e. the natural numbers modulo the prime p.5 As we need for n parts the different evaluations points x=1, ..., n it is required that n < p, otherwise sharesecret cannot recalculate the secret as it don't know enough points6.

In the current version of sharesecret (0.4.0) it uses p = 65521, i.e. the biggest prime smaller than 2^16 = 65536, and restricts the evaluation points to 1, ..., p - 1, see Limitations. Then sharesecret needs two bytes (= octets) per part to store the evaluation point and can do multiplication without overflow using unsigned long int (32 bit). Now you ask, how sharesecret splits a whole file, which is longer than 16 bits? Well, it's quite easy. Sharesecret splits the whole file into small chunks of 16 bits. If a chunk c (seen as a binary number) is bigger or equal than p - 1 = 65520, sharesecret splits it again into two chunks of 16 bits where the first equals p - 1 = 65520 and the second equals c - p. Finally, sharesecret can split the resulting chunks by the above algorithm.

Well this is still not the whole truth. The above scheme would blow up (at most double) files containing many bytes with all bits set, e.g. 0xff. To avoid this, the chunks are XORed with a fixed pseudo random number stream before it may be splited into two chunks. Using a fixed number instead of the fixed pseudo random number stream would not be nice, as there may be many values repeated in the file that become 0xff after being XORed with the fixed value. Using the stream tries to avoid this problem with repeating worse constants. The stream is irrelevant to the security of the splitting algorithm, so it can chosen to be a fixed one.

If the secret consists of an odd number of bytes, it is padded by a zero byte. As the length of the parts is increased by another byte. Sharesecret can detect this situations during the joining process and reconstruct the exact secret.

Node:Downloads, Next:, Previous:Competitors, Up:Top

How to download sharesecret

Sharesecret is prepared for download in different formats.

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Reporting Bugs

If you find a bug in sharesecret, please send electronic mail to S.Karrmann@gmx.net with subject sharesecret. Include the version number. Also include in your message the output that the program produced and the output you expected. To avoid unsolicited commercial e-mails (also known as spam) I only accept encrypted emails (see my homepage or my public keys) or mails of selected persons or mail with subject sharesecret. See also Abuse.net and Spamcop.

If you have other questions, comments or suggestions about sharesecret, contact the author via electronic mail to S.Karrmann@gmx.net with subject sharesecret. The author will try to help you out, although he may not have time to fix your problems.

Node:Copying, Next:, Previous:Problems, Up:Top

GNU GENERAL PUBLIC LICENSE

Version 2, June 1991

Copyright © 1989, 1991 Free Software Foundation, Inc.
675 Mass Ave, Cambridge, MA 02139, USA

Everyone is permitted to copy and distribute verbatim copies
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Preamble

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To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. 

one line to give the program's name and an idea of what it does.
Copyright (C) 19yy  name of author

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

Also add information on how to contact you by electronic and paper mail.

If the program is interactive, make it output a short notice like this when it starts in an interactive mode: 

Gnomovision version 69, Copyright (C) 19yy name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details
type `show w'.  This is free software, and you are welcome
to redistribute it under certain conditions; type `show c'
for details.

The hypothetical commands show w and show c should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than show w and show c; they could even be mouse-clicks or menu items--whatever suits your program.

You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: 

Yoyodyne, Inc., hereby disclaims all copyright
interest in the program `Gnomovision'
(which makes passes at compilers) written
by James Hacker.

signature of Ty Coon, 1 April 1989
Ty Coon, President of Vice

This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License.

Node:References, Next:, Previous:Copying, Up:Top

References

Bruce Schneier, Applied Crypthography, first edition.

EGD - Entropy Gathering Daemon

GPL - GNU Public Licence

Node:Index, Previous:References, Up:Top

Index

Copyright © 1999, 2000 Stefan Karrmann
Last Updated: 2000-12-19

Footnotes

  1. This need not be the version number of the sharesecret programs.

  2. 65521 is the biggest prime number lower than 2^16=65536.

  3. Here we assume the Laplace distribution of the values of the octets.

  4. As far as I know. Remarks are welcomed.

  5. There are finite fields where the addition is slightly faster, e.g. fields with p^n elements where p is prime, in particular p=2 and n=2^m - H. Conway: On numbers and games. But the multiplication is normally not implemented in hardware as the modulo arithmetic. Thus, multiplication and inversion is slower and we stick to the prime fields.

  6. A polynomial of degree k has k+1 unknown coefficients. To determinate the polynomial we need therefore k+1 evaluations points and the evaluation results using the results of elementary linear algebra.