Biblio

This article presents a practical approach for secure key exchange exploiting reciprocity in wireless transmission. The method relies on the reciprocal channel phase to mask points of a Phase Shift Keying (PSK) constellation. Masking is achieved by adding (modulo 2π) the measured reciprocal channel phase to the PSK constellation points carrying some of the key bits. As the channel phase is uniformly distributed in [0, 2π], knowing the sum of the two phases does not disclose any information about any of its two components. To enlarge the key size over a static or slow fading channel, the Radio Frequency (RF) propagation path is perturbed to create independent realizations of multi-path fading. Prior techniques have relied on quantizing the reciprocal channel state measured at the two ends and thereby suffer from information leakage in the process of key consolidation (ensuring the two ends have access to the same key). The proposed method does not suffer from such shortcomings as raw key bits can be equipped with Forward Error Correction (FEC) without affecting the masking (zero information leakage) property. To eavesdrop a phase value shared in this manner, the Eavesdropper (Eve) would require to solve a system of linear equations defined over angles, each equation corresponding to a possible measurement by the Eve. Channel perturbation is performed such that each new channel state creates an independent channel realization for the legitimate nodes, as well as for each of Eves antennas. As a result, regardless of the Eves Signal-to-Noise Ratio (SNR) and number of antennas, Eve will always face an under-determined system of equations. On the other hand, trying to solve any such under-determined system of linear equations in terms of an unknown phase will not reveal any useful information about the actual answer, meaning that the distribution of the answer remains uniform in [0, 2π].

In this paper we investigate a secret sharing scheme based on a shortened systematic Reed-Solomon code. In the scheme L secrets S1, S2, ..., SLand n shares X1, X2, ..., Xn satisfy certain n - k + L linear equations. Security of such a ramp secret sharing scheme is analyzed in detail. We prove that this scheme realizes a (k; n)-threshold scheme for the case of L = 1 and a ramp (k, L, n)-threshold scheme for the case of 2 ≤ L ≤ k - 1 under a certain assumption on S1, S2, ..., SL.