The capacity for secret key agreement for permutation-invariant and symmetric sources under a sampling attack is investigated. The supremum of the normalized secret key capacity is introduced, where the supremum is taken over all permutation-invariant sources or all symmetric sources and the normalized secret key capacity is the secret key capacity divided by the description length of the symbol. It is proved that the supremum of the normalized secret key capacity bound under a sampling attack is close to 1/m for permutation-invariant sources and O(1/m) for symmetric sources, where and m is the number of Eve's sources
The capacity for secret key agreement for permutation-invariant and symmetric sources under a sampling attack is investigated. The supremum of the normalized secret key capacity is introduced, where the supremum is taken over all permutation-invariant sources or all symmetric sources and the normalized secret key capacity is the secret key capacity divided by the description length of the symbol. It is proved that the supremum of the normalized secret key capacity bound under a sampling attack is close to 1/m for permutation-invariant sources and O(1/m) for symmetric sources, where and m is the number of Eve's sources
This paper considers the capacity for secret key agreement under a sampling attack. Given the number of the eavesdropper's sources, we evaluate the secret key capacity bound which is defined as the supremum of the secret key capacity divided by the description length of the alphabet, where the supremum is taken over a set of probability distributions corresponding to the correlated sources. In particular, we consider symmetric sources and permutation-invariant sources. We derive inequalities which show the scaling of the secret key capacity bound with the number of the eavesdropper's sources
Abstract—We study the secret-key capacity in a joint source-channel coding setup—the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input. Index Terms—Information theoretic security, joint sourcechannel coding, public discussion, secret-key agreement, wiretap channel. I.
Secret key agreement is a procedure for agreeing on a secret key by exchanging messages over a public channel when a sender, a legitimate receiver (henceforth referred to as a receiver), and an eavesdropper have access to correlated sources. Maurer [6] defined secret key capacity, which is the least upper bound of the key generation rate of the secret key agreement, and presented an upper and a lower bound for the secret key capacity. The advantage distillation capacity is introduced and it is shown that this quantity equals to the secret key capacity. Naive information theoretical expressions of the secret key capacity and the advantage distillation capacity are also presented. An example of correlated sources, for which an analytic expression of the secret key capacity can be obtained, is also presented.
Secret key agreement is a procedure for agreeing on a secret key by exchanging messages over a public channel when a sender, a legitimate receiver and an eavesdropper have access to correlated sources. Maurer, IEEE Trans. Inf. Theory 1993 defined secret key capacity, which is the least upper bound of the key generation rate of the secret key agreement, and presented an upper and a lower bound for the secret key capacity. In this paper, the advantage distillation capacity is introduced and it is shown that this quantity equals to the secret key capacity. A naive information theoretical expression of the secret key capacity and the advantage distillation capacity is also presented. An example of correlated sources, for which an analytic expression of the secret key capacity can be obtained, is also presented
We study the secret-key capacity in a joint source-channel coding setup-the terminals are connected over a discrete memoryless channel and have access to side information, modelled as a pair of discrete memoryless source sequences. As our main result, we establish the upper and lower bounds on the secret-key capacity. In the lower bound expression, the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret-key by jointly taking into account the source and channel equivocations. Our bounds coincide, thus establishing the capacity, when the underlying wiretap channel can be decomposed into a set of independent, parallel, and reversely degraded channels. For the case of parallel Gaussian channels and jointly Gaussian sources we show that Gaussian codebooks achieve the secret-key capacity. In addition, when the eavesdropper also observes a correlated side information sequence, we establish the secret-key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver. We finally also treat the case when a public discussion channel is available, propose a separation based coding scheme, and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input.
This letter investigates the secret key capacity of key generation from correlated wireless channels in a source model. We systematically study a practical scenario by taking into account all relevant parameters including sampling delay, eavesdroppers' location, qualities of legitimate and eavesdropping channels, Doppler spread, and pilot length. Our findings indicate that secret key capacity is determined by the cross correlation of the channel measurements, and a better legitimate channel is not necessary when the correlation between legitimate channels is higher than correlation between legitimate and eavesdropping channels. We also find that it is possible to tune the secret key capacity by carefully designing the sampling delay, pilot length, and channel qualities. This letter offers practical design guidelines on secure key generation systems.