Corruption Resilient Fountain Codes

A new aspect for erasure coding is considered, namely, the possibility that some portion of the arriving packets are corrupted in an undetectable fashion. In practice, the corrupted packets may be attributed to a portion of the communication paths that are leading to the receiver and are controlled by an adversary. Alternatively, in case packets are collected from several sources, the corruption may be attributed to a portion of the sources that are malicious. Corruption resistant fountain codes are presented; the codes resemble and extend the LT and Raptor codes. To overcome the corrupted packets received, our codes use information theoretics techniques, rather than cryptographic primitives such as homomorphic one-way-(hash) functions. Our schemes overcome adversaries by means of using slightly more packets than the minimal number required for revealing the encoded message, and using a majority over the possible decoded values. We also present a more efficient randomized decoding scheme. Beyond the obvious use, as a rateless erasure code, our code has several important applications in the realm of distributed computing.