Falcon Codes: Fast, Authenticated LT Codes

In this paper, we introduce Falcon codes, a class of authenticated error correcting codes that are based on LT codes [23] and achieve the following properties, for the first time simultaneously: (1) with high probability, they can correct adversarial symbol corruptions in the encoding of a message, and (2) they allow for very efficient encoding and decoding times, even linear in the message length. We study Falcon codes in a new adversarial model for rateless codes over computational channels, and define a new security notion for corruption-tolerant encoding in this model. We then present three such LT-based coding schemes that achieve resilience to adversarial corruptions via judicious use of simple cryptographic tools while maintaining very fast encoding/decoding times. One variant Falcon code works well with small messages (100s of KB to 10s of MB) but two alternative scalable versions are designed to handle much larger inputs (e.g., messages that are several GBs in size). Our schemes are provably secure against computational adversaries in the standard model. We analyze our new schemes and show that Falcon codes are both asymptotically and practically efficient.