# Decimal encryption

Thomas Baignères thomas.baigneres at epfl.ch
Thu Aug 28 14:17:14 EDT 2008

```Hello,

Actually, block ciphers encrypting blocks of *decimal* numbers exist:

- TOY100 [1] encrypts blocks of 32 decimal digits
- DEAN18 [2] encrypts blocks of 18 decimal digits
- DEAN27 [3] encrypts blocks of 27 decimal digits

TOY100 is (almost) broken by the generalized linear cryptanalysis
described in [2]. Both versions of DEAN are based on a substitution
permutation network very close to that of the AES and are provably
secure against linear cryptanalysis. These ciphers are only "toy"
ciphers. Consequently, there is no official implementation (no test-
vector, etc.).

Here are the references:
[1] Granboulan, Levieil, Piret: Pseudorandom Permutation Families over
Abelian Groups. FSE 2006: 57-77
[2] Baignères, Stern, Vaudenay: Linear Cryptanalysis of Non Binary
Ciphers. Selected Areas in Cryptography 2007: 184-211 (available here: http://lasecwww.epfl.ch/~tbaigner/papers/groupLC.pdf
)
[3] Baignères (PhD Thesis): Quantitative Security of Block Ciphers:
Designs and Security Tools (to be published)

I hope this helps. I'm of course available for any question regarding
DEANxx.

Best regards,
Thomas Baignères
--
http://lasecwww.epfl.ch/~tbaigner

On Aug 27, 2008, at 5:05 PM, 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?
>
> Best regards,
> Philipp Gühring
>
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