Decimal encryption
Steven M. Bellovin
smb at cs.columbia.edu
Wed Aug 27 12:12:11 EDT 2008
On Wed, 27 Aug 2008 17:05:44 +0200
Philipp G__hring <pg at futureware.at> 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?
>
Do you want a stream cipher or a block cipher? For the former, it's
easy. Use something like rc4, which produces a sequence of keystream
bytes. Retrieve the low-order N bits from each key stream byte, where N
is large enough for the base you're using. If the value is greater
than or equal to the base you're using, discard that byte and try
again. For your example, you'd use the low-order 4 bits, but discard
any bytes whose value is >= 10. Add this value, discarding the carry,
to the digit to be encrypted.
You're running RC4 at 5/8 efficiency; unless you have a *lot* of data,
that almost certainly doesn't matter.
--Steve Bellovin, http://www.cs.columbia.edu/~smb
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