A secure communication game with a relay helping the eavesdropper

Melda Yuksel, Xi Liu, Elza Erkip

Research output: Contribution to journalArticlepeer-review


In this work, a four-terminal complex Gaussian network composed of a source, a destination, an eavesdropper, and a jammer relay is studied under two different set of assumptions: 1) The jammer relay does not hear the source transmission, and 2) The jammer relay is causally given the source message. In both cases, the jammer relay assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase it. To help the eavesdropper, the jammer relay can use pure relaying and/or send interference. Each of the problems is formulated as a two-player, noncooperative, zero-sum continuous game. Assuming Gaussian strategies at the source and the jammer relay in the first problem, the Nash equilibrium is found and shown to be achieved with mixed strategies in general. The optimal cumulative distribution functions (cdfs) for the source and the jammer relay that achieve the value of the game, which is the Nash equilibrium secrecy rate, are found. For the second problem, the Nash equilibrium solution is found and the results are compared to the case when the jammer relay is not informed about the source message.

Original languageEnglish (US)
Article number5729364
Pages (from-to)818-830
Number of pages13
JournalIEEE Transactions on Information Forensics and Security
Issue number3 PART 1
StatePublished - Sep 2011


  • Eavesdropping
  • jamming
  • physical layer security
  • relay channel
  • wire-tap channel

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Computer Networks and Communications


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