Polar Coding for Secret-Key Generation

Practical implementations of secret-key generation are often based on sequential strategies, which handle reliability and secrecy in two successive steps, called reconciliation and privacy amplification. In this paper, we propose an alternative approach based on polar codes that jointly deals with reliability and secrecy. Specifically, we propose secret-key capacity-achieving polar coding schemes for the following models: (i) the degraded binary memoryless source (DBMS) model with rate-unlimited public communication, (ii) the DBMS model with one-way rate-limited public communication, (iii) the 1-to-m broadcast model and (iv) the Markov tree model with uniform marginals. For models (i) and (ii) our coding schemes remain valid for non-degraded sources, although they may not achieve the secret-key capacity. For models (i), (ii) and (iii), our schemes rely on pre-shared secret seed of negligible rate; however, we provide special cases of these models for which no seed is required. Finally, we show an application of our results to secrecy and privacy for biometric systems. We thus provide the first examples of low-complexity secret-key capacity-achieving schemes that are able to handle vector quantization for model (ii), or multiterminal communication for models (iii) and (iv).Comment: 26 pages, 9 figures, accepted to IEEE Transactions on Information Theory; parts of the results were presented at the 2013 IEEE Information Theory Worksho

Strong secrecy on a class of degraded broadcast channels using polar codes

Two polar coding schemes are proposed for the degraded broadcast channel under different reliability and secrecy requirements. In these settings, the transmitter wishes to send multiple messages to a set of legitimate receivers keeping them masked from a set of eavesdroppers, and individual channels are assumed to gradually degrade in such a way that each legitimate receiver has a better channel than any eavesdropper. The layered decoding structure requires receivers with better channel quality to reliably decode more messages, while the layered secrecy structure requires eavesdroppers with worse channel quality to be kept ignorant of more messages.Postprint (author's final draft

Polynomial complexity of polar codes for non-binary alphabets, key agreement and Slepian-Wolf coding

We consider polar codes for memoryless sources with side information and show that the blocklength, construction, encoding and decoding complexities are bounded by a polynomial of the reciprocal of the gap between the compression rate and the conditional entropy. This extends the recent results of Guruswami and Xia to a slightly more general setting, which in turn can be applied to (1) sources with non-binary alphabets, (2) key generation for discrete and Gaussian sources, and (3) Slepian-Wolf coding and multiple accessing. In each of these cases, the complexity scaling with respect to the number of users is also controlled. In particular, we construct coding schemes for these multi-user information theory problems which achieve optimal rates with an overall polynomial complexity.Comment: 6 pages; presented at CISS 201

Polar Coding for the Cognitive Interference Channel with Confidential Messages

In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for interference channels rely on the use of polar codes for the multiple access channel, the code construction problem of which can be complicated. We show that the whole secrecy capacity region of the CICC can be achieved by simple point-to-point polar codes due to the cognitivity, and our proposed scheme requires the minimum rate of randomness at the encoder

Low-complexity and Reliable Transforms for Physical Unclonable Functions

Noisy measurements of a physical unclonable function (PUF) are used to store secret keys with reliability, security, privacy, and complexity constraints. A new set of low-complexity and orthogonal transforms with no multiplication is proposed to obtain bit-error probability results significantly better than all methods previously proposed for key binding with PUFs. The uniqueness and security performance of a transform selected from the proposed set is shown to be close to optimal. An error-correction code with a low-complexity decoder and a high code rate is shown to provide a block-error probability significantly smaller than provided by previously proposed codes with the same or smaller code rates.Comment: To appear in IEEE International Conference on Acoustics, Speech, and Signal Processing 202