Decimal encryption

Eric Rescorla ekr at
Wed Aug 27 11:19:36 EDT 2008

At Wed, 27 Aug 2008 17:05:44 +0200,
Philipp Gühring wrote:
> Hi,
> I am searching for symmetric encryption algorithms for decimal strings.
> Let's say we have various 40-digit decimal numbers:
> 2349823966232362361233845734628834823823
> 3250920019325023523623692235235728239462
> 0198230198519248209721383748374928601923
> As far as I calculated, a decimal has the equivalent of about 3,3219
> bits, so with 40 digits, we have about 132,877 bits.
> Now I would like to encrypt those numbers in a way that the result is a
> decimal number again (that's one of the basic rules of symmetric
> encryption algorithms as far as I remember).
> Since the 132,877 bits is similar to 128 bit encryption (like eg. AES),
> I would like to use an algorithm with a somewhat comparable strength to AES.
> But the problem is that I have 132,877 bits, not 128 bits. And I can't
> cut it off or enhance it, since the result has to be a 40 digit decimal
> number again.
> Does anyone know a an algorithm that has reasonable strength and is able
> to operate on non-binary data? Preferrably on any chosen number-base?

There are a set of techniques that allow you to encrypt elements of
arbitrary sets back onto that set. 

The original paper on this is:
John Black and Phillip Rogaway. Ciphers with arbitrary ?nite domains. In 
CT-RSA, pages 114?130, 2002. 

For a modern proposal to make this a NIST mode, see:


Full Disclosure: Terence Spies, the author of the FFSEM proposal,
works for Voltage, Voltage has a product based on this technology.
and I'm on Voltage's TAB and have done some work for them.

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