Covert Secret Key Generation With an Active Warden

Abstract

We investigate the problem of covert and secret key generation over a state-dependent discrete memoryless channel with one-way public discussion in which an adversary, the warden, may arbitrarily choose the channel state. We develop an adaptive protocol that, under conditions that we explicitly specify, not only allows the transmitter and the legitimate receiver to exchange a secret key but also conceals from the active warden whether the protocol is being run. When specialized to passive adversaries that do not control the channel state, we partially characterize the covert secret key capacity. In particular, the covert secret key capacity is sometimes equal to the covert capacity of the channel, so that secrecy comes "for free." I. INTRODUCTIONFollowing the early results of Ahlswede and Csiszár [1] and Maurer [2], secret key generation from correlated observations using an authenticated public channel has attracted significant attention, especially in the context of wireless channels [3], [4]. We investigate here the problem of covert secret key generation, in which legitimate parties must not only agree on a common secret key but also keep the key generation protocol undetectable by an adversary, referred to as the warden.Our work builds upon recent results on covert [5], [6], [7], [8] and stealth [9], [10] communications, which have characterized how many information bits can be transmitted reliably over noisy channels while escaping detection by a warden. In particular, the number of reliable and covert bits that can be transmitted in n channel uses is limited by a square root law to O( √ n) [5]. When the warden's channel is of higher quality, in a sense precisely defined in [7], covert communication is possible but at the expense of using a shared secret key between legitimate parties. Notice that this implicitly requires the existence of a secret key exchange mechanism that does improve the detection capability of the warden. Our work also capitalizes on efforts to consider state-dependent models for covert communication such as [11], in which covert rates are identified for a fading channel with randomly varying states only statistically known to the legitimate users, or [12], in which the covert capacity is characterized for a state-dependent channels with causal or non-causal channel knowledge at the transmitter. Another relevant work is [13], in which the warden's uncertainty about the channel is shown to allows the circumvention of the square root law. Finally, covert communication over adversarial channels, in which the warden flips a certain fraction of the transmitted bits, has been investigated in [14]; covert communication is shown to be possible for all warden's states if the legitimate users have access to enough shared secret key, which again prompts the question of how to covertly generate such a secret key.Our work partially addresses the question by showing that, under conditions that we shall precisely specify, covert and secret key generation is possible even with an active warden. Specif...

Covert Communication With Mismatched Decoders

“…In recent years, the concept of covertness has also been incorporated into other research fields, ranging from information theory to information security and wireless communications. Specific topics include secret key agreement [46], source coding [47], identification-via-channels [11], authentication [48], unmanned aerial vehicle [49]- [51], etc.…”

Achieving Covertness and Secrecy: The Interplay Between Detection and Eavesdropping Attacks

“…Such uncertainty makes it difficult for the detector to determine the received signal power or the background noise power, and thus unable to distinguish between the scenarios with or without wireless communication by examining the power difference in these scenarios. Some recent works also explored the possibility of ensuring covertness based on other PLS technologies, such as multi-antenna technique [20], [21], coding scheme [22], [23], relay selection [24], [25] and resource (i.e., channel use) allocation [26].…”