[24264] in cryptography@c2.net mail archive
non-cartesian A codes and latin squares
daemon@ATHENA.MIT.EDU (Travis H.)
Sun Apr 30 12:04:29 2006
X-Original-To: cryptography@metzdowd.com
X-Original-To: cryptography@metzdowd.com
Date: Sun, 30 Apr 2006 00:49:35 -0500
From: "Travis H." <solinym@gmail.com>
To: Cryptography <cryptography@metzdowd.com>
Background:
An A-code is a matrix E x M, where e is the encoding rule used, and m
is the message the transmitter should send (output). The message to
be authenticated (input) is s in { s_1 .. s_k }, and the contents of
the matrix are members of such that every row (encoding rule) contains
s_1..s_k. In schemes with secrecy, there is an additional constraint
that each column include each of s_1..s_k. Any unused cells are
filled with 0, indicating that the message/encoding combination is
invalid and indicative that the message is fraudulent.
Put another way, if f : S x E -> M is a map, then f is onto and for
each encoding rule e, the map f(o , e) : S -> M defined by s -> f(s,e)
is one-to-one.
Furthermore, the code is minimal if |E| =3D |M|. As I understand it,
this means there are no matrix elements containing 0. This is
ostensibly desirable as it minimizes the number of bits necessary to
encode the encoding rule (lg |E|). However, it would appear to
provide no protection against substitution or impersonation.
Question:
Is that last statement correct?
Isn't it the case that every minimal authentication code with secrecy
is also a latin square?
...just wanted to be sure I was understanding it correctly...
--
"Curiousity killed the cat, but for a while I was a suspect" -- Steven Wrig=
ht
Security Guru for Hire http://www.lightconsulting.com/~travis/ -><-
GPG fingerprint: 9D3F 395A DAC5 5CCC 9066 151D 0A6B 4098 0C55 1484
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