Cryptographic Compression
Joshua Cooper, Grant Fickes
TL;DR
The paper tackles secure, efficient data encoding by aiming to compress and encrypt typical streaming data modeled as an ergodic Markov process. It introduces the ENCORE protocol, which transforms the source distribution into a dyadic form via Huffman coding to produce a near-uniform encoded-transformed stream, while a sparse, compressed, and encrypted reconstruction stream carries the information needed to invert the transformation; these two streams are interleaved into a single self-contained binary stream. The authors prove that, after a burn-in tied to the Markov mixing time $\tau$, the encoded-transformed stream behaves like near-uniform bits, providing a modified next-bit security property while requiring fewer entropy resources than standard encryption; they also quantify the role of the transformation matrix $B$ (with bound on $\|B\|_1$) in controlling reconstruction-data entropy. An interleaving framework is presented to maintain near-uniformity and enable local decoding, and multiple open questions are discussed to strengthen the results and improve practical performance.
Abstract
We introduce a protocol called ENCORE which simultaneously compresses and encrypts data in a one-pass process that can be implemented efficiently and possesses a number of desirable features as a streaming encoder/decoder. Motivated by the observation that both lossless compression and encryption consist of performing an invertible transformation whose output is close to a uniform distribution over bit streams, we show that these can be done simultaneously, at least for ``typical'' data with a stable distribution, i.e., approximated reasonably well by the output of a Markov model. The strategy is to transform the data into a dyadic distribution whose Huffman encoding is close to uniform, and then store the transformations made to said data in a compressed secondary stream interwoven into the first with a user-defined encryption protocol. The result is an encoding which we show exhibits a modified version of Yao's ``next-bit test'' while requiring many fewer bits of entropy than standard encryption. Numerous open questions remain, particularly regarding results that we suspect can be strengthened considerably.