Abstract
Securing transmission over a wireless network is
especially challenging, not only because of the inherently insecure
nature of the medium, but also because of the highly error-prone nature of the wireless environment. In this paper, we take
a joint encryption-error correction approach to ensure secure
and robust communication over the wireless link. In particular,
we design an error-correcting cipher (called the high diffusion cipher)
and prove bounds on its error-correcting capacity as well
as its security. Towards this end, we propose a new class of error-correcting codes (HD-codes) with built-in security features that we
use in the diffusion layer of the proposed cipher. We construct
an example, 128-bit cipher using the HD-codes, and compare
it experimentally with two traditional concatenated systems: (a)
AES (Rijndael) followed by Reed-Solomon codes, (b) Rijndael
followed by convolutional codes. We show that the HD-cipher
is as resistant to linear and differential cryptanalysis as the
Rijndael. We also show that any chosen plaintext attack that
can be performed on the HD cipher can be transformed into a
chosen plaintext attack on the Rijndael cipher. In terms of error
correction capacity, the traditional systems using Reed-Solomon
codes are comparable to the proposed joint error-correcting
cipher and those that use convolutional codes require 10% more
data expansion in order to achieve similar error correction as
the HD-cipher. The original contributions of this work are (1) design of
a new joint error-correction-encryption system, (2) design of a new class of algebraic codes with built-in security criteria, called
the high diffusion codes (HD-codes) for use in the HD-cipher,
(3) mathematical properties of these codes, (4) methods for
construction of the codes, (5) bounds on the error-correcting
capacity of the HD-cipher, (6) mathematical derivation of the
bound on resistance of HD cipher to linear and differential
cryptanalysis, (7) experimental comparison of the HD-cipher with
the traditional systems.