Crypto-compression prefix coding

Ruy L. MilidiuInformatics Department - PUC-Rio

R. Marques de Sao Vicente, 225/4, 22453-900 Rio de Janeiro, BrazilTel: +55-21-3114-1500, E-mail: milidiu@inf.puc-rio.br

Claudio G. MelloComputer Department - Military Institute of Engineering (IME)

Praca General Tiburcio, 80, 22290-270 Rio de Janeiro, BrazilTel: +55-21-2546-7095, E-mail: cgmello@de9.ime.eb.br

Data compression and ciphering are essential features when digital data is storedor trasmitted over insecure channels. Usually, we apply two sequential operations:first, we apply data compression to save disk space and to reduce transmission costs,and second, data ciphering to provide confidentiality. This solution works fine tomost applications, but we have to execute two expensive operations, and if we wantto access data, we must first decipher and then decompress the ciphertext to restoreinformation.

In this work we propose to add some additional strategies to prefix data compres-sion algorithms so that we can achieve both compressed and ciphered data with theuse of a provably secure algorithm. We extend previous results as in [1] on practicalimplementation of crypto-compression algorithms where we used Canonical Huffmancoding, dyadic distributions and some additional strategies in order to secure theciphertext against cryptanalysis. We propose a provably secure algorithm by using ahomophonic substitution algorithm and a key: the HSPC2 - Homophonic SubstitutionPrefix Codes with 2 homophones. We show that the use of homophonic substitutionincreases the security of the ciphertext. Shannon’s theory for computational securitysays that we have a provably secure cryptosystem if, to provide evidence of compu-tational security, we reduce the security of the cryptosystem to some well-studiedproblem that is thought to be difficult. In this paper we show that breaking HSPC2is an NP-Complete problem. This paper is an updated version of a previous one [2].

References

[1] Milidiu, R.L., Mello, C.G, Fernandes J.R. Adding security to compressed infor-mation retrieval systems, SPIRE - String Processing and Information Retrieval,Chile, 2001.

[2] Milidiu, R.L., Mello, C.G. A provably secure crypto-compression algorithm,CIBSI 05 - 3o. Congreso Iberoamericano de Seguridad Informatica, Chile, 2005.

Proceedings of the Data Compression Conference (DCC’06) 0-7695-2545-8 /06 $20.00 © 2006 IEEE