Coding for Cryptographic Security Enhancement Using Stopping Sets

Abstract

In this paper we discuss the ability of channel codes to enhance cryptographic secrecy. Toward that end, we present the secrecy metric of degrees of freedom in an attacker's knowledge of the cryptogram, which is similar to equivocation. Using this notion of secrecy, we show how a specific practical channel coding system can be used to hide information about the ciphertext, thus increasing the difficulty of cryptographic attacks. The system setup is the wiretap channel model where transmitted data traverse through independent packet erasure channels with public feedback for authenticated ARQ (Automatic Repeat reQuest). The code design relies on puncturing nonsystematic low-density parity-check codes with the intent of inflicting an eavesdropper with stopping sets in the decoder. Furthermore, the design amplifies errors when stopping sets occur such that a receiver must guess all the channel-erased bits correctly to avoid an expected error rate of one half in the ciphertext. We extend previous results on the coding scheme by giving design criteria that reduces the effectiveness of a maximum-likelihood attack to that of a message-passing attack. We further extend security analysis to models with multiple receivers and collaborative attackers. Cryptographic security is enhanced in all these cases by exploiting properties of the physical-layer. The enhancement is accurately presented as a function of the degrees of freedom in the eavesdropper's knowledge of the ciphertext, and is even shown to be present when eavesdroppers have better channel quality than legitimate receivers.

Triple Security of Data using Encryption Keys and Image Steganography

“…The system provides cryptographic security enhancement [1]- [2]. The issue of end-to-end security was upgraded by turning to consider disorder infused in ciphertext.…”

Parity modifications and stopping sets in high-rate codes for physical-layer security

“…There is a danger in adopting other less rigorous measures to make secrecy guarantees in general, as there is often no direct mapping from the information-theoretic measures to measures such as bit error rate (BER) [9], [10] or degrees of freedom [4] in a decoder. However, in the spirit of computational security and/or semantic security, we can still make guarantees on secrecy as long as the eavesdropper is constrained to a known set of decoders as done in [9], [10].…”

“…Taking a base-2 logarithm of this quantity yields an information-theoretic number of information bits about which the eavesdropper cannot make any distinction when constrained to that decoder. This quantity will be utilized in relation to the ML decoder, and is analogous to degrees of freedom in [4]. We will denote this metric as H M L (M |Z n ).…”

“…This system has a unique solution when the columns of HK are linearly independent [13], and finding this solution is the essence of the ML decoder over the BEWC [4]. If we wish to form an estimate of the erased bits when (3) is underdetermined, we can use the least squares solution [14].…”

“…In this paper, we consider two variations of a physicallayer security coding approach presented in [4]. These codes operate over the binary erasure wiretap channel (BEWC) pictured in Fig.…”