Security Analysis of Bbc Coding

In large-scale, wireless networks, it is possible to achieve confidentiality and integrity using asymmetric keys, but availability (i.e. resistance to jamming) has always required symmetric keys. Key management for these symmetric keys is becoming increasingly difficult, and in some cases physically impossible. Recently, the first algorithm was proposed to achieve availability without symmetric keys: BBC coding, which is an unkeyed coding system built up from a hash function. However, no security analysis of it has ever been published. In this paper, we prove BBC has unconditional security with high probability in the random oracle model. Furthermore, we prove BBC has unconditional security with high probability for particular families of polynomial-time and -space hash functions. Unlike the random oracle proof, the latter proof applies to systems that can actually be implemented in practice. In addition, we prove that certain families of hash functions that might naturally be considered are actually insecure, and we give methods for breaking them. Finally, we describe the open question of whether BBC is secure for certain families of simple hash functions.