Secret Splitting Revisited

I wrote about secret splitting some ten years ago and decided to fresh things up and create a new easy-to-use template. You only need a pen, paper and first grade math to obtain absolute security. But first, a quick reminder on what secret splitting is, how it works and why everyone should know this interesting system.

Secret splitting (also called secret sharing) enables you to split a secret code into multiple shares and give those shares in the custody of several persons. Retrieving the original code is only possible if the shareholders agree upon putting their shares together. The secret could be the code to a combination lock, safe deposit box, electronic key or password. You can split passwords to access a computer, encrypted files, a digital lock to enter a building or disable an alarm system.

An interesting property of secret splitting is that more people with shares means more security, because more people have to agree on putting their shares together, which is the opposite of sharing the secret itself, where more people means more risk.

There are many useful applications for secret splitting where you need to delegate access to your secret code in a specific situations. You can appoint several persons that will be able to open your safe with money or critical information in case of emergency. None of them can act alone and a single trustworthy person among them is enough to prevent misuse.

A parent who has stored his money, documents or valuables in a safe deposit box can split the number combination and all children receive a share. In case of emergency or the parent's decease they can only access the safe when all of them agree upon opening the safe. Each shareholder can even split his own share again into two shares, to hide his sub-shares separately as backup or destroy his original share and store his sub-shares at different places to increase security.

You can use secret splitting for secure remote delegation through insecure channels. Create a share for yourself and one or more shares for other persons. This way, you can be on the other side of the world and send your share to all other shareholders to give them access to a computer file or the pin code of a credit card, to name a few. The shareholders can only retrieve the code at the moment that you decide to give them your share and they all need to agree. You can use any insecure method like e-mail, chat or telephone to send your share, because that single share never reveals any useful information to an eavesdropper.

The template to create your own secure shares (download pdf here)

For our template we use the method where all shares are required to retrieve the original. It is mathematically impossible to retrieve the original if a single shareholder refuses to disclose his share. This method is information theoretically secure, read unbreakable.

There is another method, called secret splitting with threshold, which requires less shares than the total number of shares to retrieve the original. It's security is based on mathematical complexity. Unfortunately, this method does not guarantee information theoretical security.

Of course, you cannot simple cut a code or password in half or quarters, as this would reveal at least part of the code and provide clues to find the rest of the code or reduce the number of combinations to try out. The secret splitting we use is based on the principle of one-time pad encryption and all calculations are performed modulo 10 (addition without carry and subtraction without borrowing). The secret code is encrypted with one or more truly random keys and, in contrast to sending the encrypted secret to the receiver, we use the random keys and the encrypted code as shares.

We can only retrieve the original code when the encrypted code and all keys are put together. Take one share out of the equation and it will be mathematically impossible to decrypt the code. The only requirements are the use of truly random digits and, obviously, secure physical separation of the shares. The small number of required truly random digits are easily generated manually.

Secret splitting may sound complicated but it's quite simple to apply. If you can add and subtract, then you can create secure shares, and all it requires is a pen and paper. You can download the new version of the easy-to-use Secure Code Splitter which comes with clear instructions and examples, a blank calculation sheet and share template. More to read about secret splitting at my website.

Secret Splitting

An interesting way to use one-time pad encryption is Secret Splitting. We all know what sharing a secret is (people tend to have problems not to share secrets). The opposite of sharing secrets is to split them.

Suppose Charlie has a secret password or a safe combination he wants to share with someone in case of emergency. Wouldn't it be great if he could split his secret and give one share to Alice and one share to Bob? The secret could only be retrieved when both Alice and Bob agree on sharing their secret. Of course, cutting it simply in two and give each person half the secret would reveal already that part, so that would not be safe.

Well, there's a simple solution and it's called one-time pad. Secret Splitting is a special way of using one-time pad, since you don't send a secret message, and the key isn't destroyed. Here's how it goes: Charlie subtracts a truly random key, digit by digit, modulo 10 (without borrowing), from his safe combination. For instance, 4 - 6 = 8 because [1]4 - 6 = 8. He gives one share (they key) to Alice and one share (the result) to Bob.

Charlie's Combination      21 46 03 88
Random key (first share) - 25 01 77 61
                           -----------
Results (second share)     06 45 36 27

Alice's share = 2501 7761
Bob's share   = 0645 3627

To retrieve the original combination, Alice and Bob just add their keys together, again modulo 10 (without carry). For instance 7 + 6 = 3 because 7 + 6 = [1]3. Of course, one could also split text by first converting the letters into digits (f.i. A=01, B=02 and so on through Z=26). You can download a practical Secure Code Splitter (pdf) template that supports up to 4 shares of 10 digits.

It's mathematically impossible to retrieve the secret information without having all shares, under the condition that the random share contains truly random digits, and all shares are physically and securely separated.

There are some interesting applications for this system. It's a secure method to give a code or password in the custody of multiple persons when you're abroad. Each person receives a share. All persons involved have to agree to combine their shares to retrieve the code or password. But if you want to have the final decision to disclose your secret code, there's another solutions.

You can create two shares, take one with you on a business trip and give the second share to a trustee from your company. In case of emergency, you can sent your share by open e-mail or telephone to the trustee. Combined with his own share, he can retrieve the secret code and open your safe or whatever. Because the share and result share are trule random, sending one of the shares by insecure channel will never disclose the secret code, as long as both share are never disclosed simultaneously.

 

It's also a clever way to share things with people who don't trust each other. Suppose grandpa, old and sick, splits the secret combination of a safe that contains his savings and gives each of his children one share of that secret. They can only get their hands on his money if they all agree (not that this will make grandpa live longer).

Of course, after using the shares, you should always set a new secret code or password to your safe and create a completely new set of shares to avoid unauthorised use of the old combination.

More about Secret Splitting and one-time pad on my Secret Splitting page.

Update: a new version of the Secure Code Splitter is available. More information at this blog post.