Paper 2017/1130
InformationTheoretic SecretKey Agreement: The Asymptotically Tight Relation Between the SecretKey Rate and the Channel Quality Ratio
Daniel Jost, Ueli Maurer, and Joao L. Ribeiro
Abstract
Informationtheoretically secure secretkey agreement between two parties Alice and Bob is a wellstudied problem that is provably impossible in a plain model with public (authenticated) communication, but is known to be possible in a model where the parties also have access to some correlated randomness. One particular type of such correlated randomness is the socalled satellite setting, where a source of uniform random bits (e.g., sent by a satellite) is received by the parties and the adversary Eve over inherently noisy channels. The antenna size determines the error probability, and the antenna is the adversary's limiting resource much as computing power is the limiting resource in traditional complexitybased security. The natural assumption about the adversary is that her antenna is at most $Q$ times larger than both Alice's and Bob's antenna, where, to be realistic, $Q$ can be very large. The goal of this paper is to characterize the secretkey rate per transmitted bit in terms of $Q$. Traditional results in this socalled satellite setting are phrased in terms of the error probabilities $\epsilon_A$, $\epsilon_B$, and $\epsilon_E$, of the binary symmetric channels through which the parties receive the bits and, quite surprisingly, the secretkey rate has been shown to be strictly positive unless Eve's channel is perfect ($\epsilon_E=0$) or either Alice's or Bob's channel output is independent of the transmitted bit (i.e., $\epsilon_A=0.5$ or $\epsilon_B=0.5$). However, the best proven lower bound, if interpreted in terms of the channel quality ratio $Q$, is only exponentially small in $Q$. The main result of this paper is that the secretkey rate decreases asymptotically only like $1/Q^2$ if the perbit signal energy, affecting the quality of all channels, is treated as a system parameter that can be optimized. Moreover, this bound is tight if Alice and Bob have the same antenna sizes. Motivated by considering a fixed sending signal power, in which case the perbit energy is inversely proportional to the bitrate, we also propose a definition of the secretkey rate per second (rather than per transmitted bit) and prove that it decreases asymptotically only like $1/Q$.
Metadata
 Available format(s)
 Publication info
 A major revision of an IACR publication in TCC 2018
 Keywords
 SecretKey AgreementInformationtheoretic securitySatellite model
 Contact author(s)
 j lourencoribeiro17 @ imperial ac uk
 History
 20181026: last of 3 revisions
 20171127: received
 See all versions
 Short URL
 https://ia.cr/2017/1130
 License

CC BY
BibTeX
@misc{cryptoeprint:2017/1130, author = {Daniel Jost and Ueli Maurer and Joao L. Ribeiro}, title = {InformationTheoretic SecretKey Agreement: The Asymptotically Tight Relation Between the SecretKey Rate and the Channel Quality Ratio}, howpublished = {Cryptology ePrint Archive, Paper 2017/1130}, year = {2017}, note = {\url{https://eprint.iacr.org/2017/1130}}, url = {https://eprint.iacr.org/2017/1130} }