High Diffusion Cipher: Encryption and Error Correction in a Single Cryptographic Primitive Chetan Nanjunda Mathur, Karthik Narayan and K.P. Subbalakshmi Department of Electrical and Computer Engineering Stevens Institute of Technology, Hoboken, NJ 07030, USA cnanjund@stevens.edu Abstract. In this paper we combine the error correction and encryption functionality into one block cipher, which we call High Diffusion (HD) cipher. The error correcting property of this cipher is due to the novel er- ror correction code which we call High Diffusion code used in its diffusion layer. Theoretical bounds on the performance of the HD cipher in terms of security and error correction are derived. We show that the proposed HD cipher provides security equivalent to Rijndael cipher against linear and differential cryptanalysis. Experiments based on a four round HD cipher reveal that traditional concatenated systems using the Rijndael cipher followed by Reed Solomon codes require 89% more expansion to match the performance of HD cipher. Key words: Error correcting cipher, Joint error correction and encryption, Coding and cryptography, Block cipher, Error correcting code 1 Introduction In most cases, the very same properties that provide security to a cipher (e.g. avalanche effect) makes them sensitive to transmission errors. In block ciphers (which operates on a fixed block length of data at a time) a single bit flip in the encrypted data can cause a complete decryption failure. This sensitivity causes more retransmissions compared to unencrypted transmission, reducing the overall throughput [20]. Hence, transmitting encrypted data often requires the use of error correction codes to efficiently and reliably recover the informa- tion during decryption. Although, traditionally error correction and encryption are handled independently, some of the motivations to combine them into one primitive are a) both error correction and encryption are now performed in the same layer (e.g. link layer in wireless networks) b) error correction codes are al- ready present in communication devices, therefore using codes as building blocks for a cipher is advisable from an implementation standpoint c) the increasing popularity of resource constrained devices in noisy media like the wireless net- works could potentially benefit from a joint design of the error correction and encryption primitives in terms of achieving a better system level operating point