The Transmitter Trojan Channel: Achievable Rates and Error Exponents

2026-09-25

AI Summary

This study addresses the transmitter Trojan channel problem arising from malicious encoders embedded in communication hardware, investigating unauthorized data leakage mechanisms under constrained computational complexity. Leveraging information theory and hypothesis testing, binary symmetric channel (BSC) and additive white Gaussian noise (AWGN) channel models are constructed. A lower-bound method for the operational error exponent is proposed based on channel resolvability transformations, and the achievable rates alongside decoding error exponents for both legitimate and illegitimate messages are derived. The analysis reveals a fundamental trade-off between covertness and reliability. Numerical simulations validate the theoretical bounds for specific channel conditions. These findings provide a rigorous theoretical foundation for the joint optimization of Trojan detection and transmission performance.

Abstract

Experiments have shown that modifications in communication hardware can enable unauthorized exfiltration of data from transmitters. We study the resulting Transmitter Trojan channel, in which a malicious encoder embedded within a legitimate transmitter perturbs the transmitted codeword on a symbol-by-symbol basis. The model reflects the limited footprint, delay, and computational complexity available to such hardware modifications. We derive achievable rogue message rate and achievable rates for the legitimate message under the mismatch induced by the Trojan. We also analyze decoding error exponents for the legitimate and rogue receivers, including operational exponent lower bounds obtained through channel-resolvability transfer arguments. Finally, we study Trojan detection at the legitimate receiver under different levels of statistical knowledge, including likelihood-ratio detection when the ensemble-averaged induced channel is known and goodness-of-fit detection when only the nominal channel is known. The resulting detection error exponents, together with the achievable rate and decoding error exponents, quantify tradeoffs among rogue message rate, legitimate message rate, decoding reliability, and Trojan detectability. We specialize the analysis to the binary symmetric channel and the additive white Gaussian noise channel, and illustrate the resulting tradeoffs numerically.

Problem

• Transmitter Trojan
• Hardware security
• Achievable rates
• Error exponents
• Trojan detection

Innovation

• Transmitter Trojan Channel
• Achievable Rates
• Error Exponents
• Channel Resolvability
• Trojan Detection