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IEEE International Symposium on Information Theory (ISIT)

Secret key agreement from correlated source outputs using LDPC matrices

Jun Muramatsu

Published Dec 23, 2004• 14 citations
Publisher

Abstract

A scheme of secret key agreement from correlated random numbers is described. It is proved that there is a pair of sparce matrices that yields a secret key agreement in the situation wherein a sender, a legitimate receiver, and an eavesdropper have access to correlated random numbers.
DOI
10.1109/isit.2004.1365051

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A secret key agreement setup between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. The three users observe i.i.d. outputs of correlated sources and there is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 for communication between the users. The secret key agreement is established using the correlated sources and the GDMMAC. In this setup, inner and outer bounds of the secret key capacity region are investigated. Moreover, for a special case where the channel inputs and outputs and the sources form Markov chains in some order, the secret key capacity region is derived. Also a Gaussian case is considered in this setup.
Confidentiality of information is a key consideration in many networking applications, including e-commerce, online banking, and intelligence operations. How can information be communicated reliably to the legitimate users, while keeping it secret from eavesdroppers? How does such a secrecy constraint on communication affect the limits on information flow in the network? In this chapter, we study these questions under the information theoretic notion of secrecy, which requires each eavesdropper to obtain essentially no information about the messages sent from knowledge of its received sequence, the channel statistics, and the codebooks used. We investigate two approaches to achieve secure communication. The first is to exploit the statistics of the channel from the sender to the legitimate receivers and the eavesdroppers. We introduce the wiretap channel as a 2-receiver broadcast channel with a legitimate receiver and an eavesdropper, and establish its secrecy capacity, which is the highest achievable secret communication rate. The idea is to design the encoder so that the channel from the sender to the receiver becomes effectively stronger than the channel to the eavesdropper; hence the receiver can recover the message but the eavesdropper cannot. This wiretap coding scheme involves multicoding and randomized encoding. If the channel from the sender to the receiver is weaker than that to the eavesdropper, however, secret communication at a positive rate is not possible. This brings us to the second approach to achieve secret communication, which is to use a secret key shared between the sender and the receiver but unknown to the eavesdropper. We show that the rate of such secret key must be at least as high as the rate of the confidential message. This raises the question of how the sender and the receiver can agree on such a long secret key in the first place. After all, if they had a confidential channel with sufficiently high capacity to communicate the key, then why not use it to communicate the message itself! We show that if the sender and the receiver have access to correlated sources (e.g., through a satellite beaming common randomness to them), then they can still agree on a secret key even when the channel has zero secrecy capacity. We first consider the source model for key agreement, where the sender communicates with the receiver over a noiseless public broadcast channel to generate a secret key from their correlated sources.
This is the first part of a three-part paper on secret-key agreement secure against active adversaries. In all three parts, we address the question whether two parties, knowing some correlated pieces of information X and Y, respectively, can generate a string S about which an adversary, knowing some information Z and having read and write access to the communication channel used by the legitimate partners, is almost completely ignorant. Whether such key agreement is possible, and if yes at which rate, is an inherent property of the joint probability distribution P/sub XYZ/. In this part, we first prove a number of general impossibility results. We then consider the important special case where the legitimate partners as well as the adversary have access to the outcomes of many independent repetitions of a fixed tripartite random experiment. In this case, the result characterizing the possibility of secret-key agreement secure against active adversaries is of all-or-nothing nature: either a secret key can be generated at the same rate as in the (well-studied) passive-adversary case, or such secret-key agreement is completely impossible. The exact condition characterizing the two cases is presented.
A hybrid encryption scheme uses a key encapsulation mechanism (KEM) to generate and establish a shared secret key with the decrypter, and a secret key data encapsulation mechanism (DEM) to encrypt the data using the key that is established by the DEM. The decrypter recovers the key using the ciphertext that is generated by the KEM, and uses it to decrypt the ciphertext that is generated by the DEM.We motivate and propose hybrid encryption in correlated randomness model where all participants including the eavesdropper, have access to samples of their respective correlated random variables. We define information-theoretic KEM (iKEM), and prove a composition theorem for iKEM and DEM that allows us to construct an efficient hybrid encryption system in correlated randomness model, providing post-quantum security. The construction uses an information-theoretic one-way secret key agreement (OW-SKA) protocol that satisfies a new security definition, and a one-time symmetric key encryption system that can be implemented by XORing the output of a (computationally) secure pseudorandom generator with the message. We discuss our results and directions for future work.