Quantization and LLR Computation for Physical Layer Security

While computational security algorithms usually reside in upper protocol layers and rely on the assumption of limited processing capabilities of a potential eavesdropper, physicallayer key generation aims at providing secrecy in the more information-theoretic sense, as introduced by Shannon [?]. Thus, by sharing a previously known secret key, such as a one-time pad, two legitimate users, Alice and Bob, are able to exchange an encrypted message through an unsafe public channel, without leaking any information to a potential eavesdropper, Eve. As long as Alice and Bob share a secret common source of randomness from which they can generate a long uniformly distributed secret key, perfect secrecy is achieved, meaning that Eve has the same chances of guessing the original message with or without the ciphertext, or, in more theoretical terms, the eavesdropper’s equivocation is equal to the entropy of the message. It soon became clear that such a common source of randomness could be provided by the fluctuating and reciprocal nature of the wireless medium and the channel-state information (CSI) can be measured by both Alice and Bob and used to generate one-time pads, thus eliminating the problem of previous key distribution. Since most wireless transmission standards, such as 802.11, Bluetooth, WiMAX, ZigBee, employ time division duplexing (TDD), probing in consecutive short time slots the forward and the reverse channel providing the possibility of obtaining nearly identical CSI on both sides. An eavesdropper located a few wavelengths away from any of the legitimate users, and passively listening to the probing, will experience independent channels [9]. Such a method of key generation, solely based on the reciprocity property of wireless TDD systems, besides solving the problem of key distribution, comes with the significant benefit that it does not require the legitimate channel between Alice and Bob to have an SNR advantage over the eavesdropper’s channels, such as [?], [?], nor does it assume Alice and Bob to have information about the channels to Eve. However, one important aspect that we address here is that due to independent noise on both ends, different transceiver circuitry, and quantization errors, key mismatches are very likely to occur, leading to the necessity Fig. 1. System model key reconciliation based on LDPC codes