At Wed, 27 Aug 2008 16:10:51 -0400 (EDT),
Jonathan Katz wrote:
> On Wed, 27 Aug 2008, Eric Rescorla wrote:
> > At Wed, 27 Aug 2008 17:05:44 +0200,
> > 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.
> But he probably wants an encryption scheme, not a cipher.

Hmm... I'm not sure I recognize the difference between encryption
scheme and cipher. Can you elaborate?

> Also, correct me if I am wrong, but Black and Rogaway's approach is not 
> efficient for large domains. But if you use their approach for small 
> domains then you open yourself up to dictionary attacks.

I suppose it depends what you mean by "small" and "large".

A lot of the relevant values are things like SSNs, CCNs, etc.
which fall in the 10-20 digit category, where the Luby-Rackoff
approach is efficient. As I understand the situation, the
cycle following approach is efficient as long as the set
is reasonably close to the L-R block size. 

As far as dictionary attacks go, for any small domain permutation
you have to worry about table construction attacks. The only 
defense I know of is randomized encryption which defeats the
non-expansion requirement.

WRT to the security of the L-R construction, Spies claims that
I believe that Patarin's 2004 result [0] is relevant here, but
I'm not qualified to evaluate it. Anyway, the reference I provided
earlier [1] provides a summary of the claimed security properties
of L-R + Cycle Following.


[0] Jacques Patarin. Security of random feistel schemes with 5 or more rounds. 
In Matthew K. Franklin, editor, CRYPTO, volume 3152 of Lecture Notes in 
Computer Science, pages 106?122. Springer, 2004. 


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