We consider a transmitter and $K$ receivers, each of which shares a key variable with the transmitter. Through a noiseless broadcast channel, the transmitter wishes to send a common message $W$ securely to $N$ out of the $K$ receivers while the remaining $K-N$ receivers learn no information about $W$. We are interested in the maximum message rate, i.e., the maximum number of bits of $W$ that can be securely groupcast to the legitimate receivers per key block and the minimum broadcast bandwidth, i.e., the minimum number of bits of the broadcast information required to securely groupcast the message bits.
We focus on the setting of combinatorial keys, where every subset of the $K$ receivers share an independent key of arbitrary size. Under this combinatorial key setting, the maximum message rate is characterized for the following scenarios - 1) $N=1$ or $N=K-1$, i.e., secure unicast to 1 receiver with $K-1$ eavesdroppers or secure groupcast to $K-1$ receivers with $1$ eavesdropper, 2) $N=2, K=4$, i.e., secure groupcast to $2$ out of 4 receivers, and 3) the symmetric setting where the key size for any subset of the same cardinality is equal for any $N,K$. Further, for the latter two cases, the minimum broadcast bandwidth for the maximum message rate is characterized.
In the secure groupcast problem, a transmitter wants to securely groupcast a message with the maximum rate to the first $N$ of $K$ receivers by broadcasting with the minimum bandwidth, where the $K$ receivers are each equipped with a key variable from a known joint distribution. Examples are provided to prove that different instances of secure groupcast that have the same entropic structure, i.e., the same entropy for all subsets of the key variables, can have different maximum groupcast rates and different minimum broadcast bandwidth. Thus, extra-entropic structure matters for secure groupcas…
The compound secure groupcast problem is considered, where the key variables at $K$ receivers are designed so that a transmitter can securely groupcast a message to any $N$ out of the $K$ receivers through a noiseless broadcast channel. The metric is the information theoretic tradeoff between key storage $α$, i.e., the number of bits of the key variable per message bit, and broadcast bandwidth $β$, i.e., the number of bits of the broadcast information per message bit. We have three main results. First, when broadcast bandwidth is minimized, i.e., when $β= 1$, we show that the minimum key stora…
Secure aggregation, which is a core component of federated learning, aggregates locally trained models from distributed users at a central server. The ``secure'' nature of such aggregation consists of the fact that no information about the local users' data must be leaked to the server except the aggregated local models. In order to guarantee security, some keys may be shared among the users. After the key sharing phase, each user masks its trained model which is then sent to the server. This paper follows the information theoretic secure aggregation problem originally formulated by Zhao and S…
It is common in the study of secure multicast network coding in the presence of an eavesdropper that has access to $z$ network links, to assume that the source node is the only node that generates random keys. In this setting, the secure multicast rate is well understood. Computing the secure multicast rate, or even the secure unicast rate, in the more general setting in which all network nodes may generate (independent) random keys is known to be as difficult as computing the (non-secure) capacity of multiple-unicast network coding instances --- a well known open problem. This work treats an …
We provide formal definitions and efficient secure techniques for - turning noisy information into keys usable for any cryptographic application, and, in particular, - reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a "fuzzy extractor" reliably extracts nearly uniform randomness R from its input; the extraction is error-tolerant in the sense that R will be the same eve…
A process for the secure transmission of data is presented that has to a certain degree the advantages of the one-time pad (OTP) cipher, that is, simplicity, speed, and information-theoretically security, but overcomes its fundamental weakness, the necessity of securely exchanging a key that is as long as the message. For each transmission, a dedicated one-time pad is generated for encrypting and decrypting the plaintext message. This one-time pad is built from a randomly chosen set of basic keys taken from a public library. Because the basic keys can be chosen and used multiple times, the met…
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or as a hybrid of these. In this paper, capacity results are established when the broadcast channels involv…
We investigate the construction of weakly-secure index codes for a sender to send messages to multiple receivers with side information in the presence of an eavesdropper. We derive a sufficient and necessary condition for the existence of index codes that are secure against an eavesdropper with access to any subset of messages of cardinality $t$, for any fixed $t$. In contrast to the benefits of using random keys in secure network coding, we prove that random keys do not promote security in three classes of index-coding instances.
The Capacity of Information-Theoretic Secure Aggregation in Federated Learning
Information Coding and Transmission (ICT) Key Laboratory of Sichuan Province, Southwest Jiaotong University（四川省信息编码与传输（ICT）重点实验室，西南交通大学）；School of Electronic Information and Communications, Huazhong University of Science and Technology（华中科技大学电子信息与通信学院）
Leakage of information in power line communication networks is a threat to privacy and security both in smart grids and in-home applications. A way to enhance security is to encode the transmitted information with a secret key. Relying on the channel properties, it is possible to generate a common key at the two communication ends without transmitting it through the broadcast channel. Since the key is generated locally, it is intrinsically secure from a possible eavesdropper. Most of the existing physical layer key generation techniques have been developed for symmetric channels. However, the …
We propose a new secure transmission scheme for uplink multiple-input single-output (MISO) orthogonal-frequency multiplexing (OFDM) systems in the presence of multiple eavesdroppers. Our proposed scheme utilizes the sub-channels orthogonality of OFDM systems to simultaneously transmit data and secret key symbols. The base station, Bob, shares secret key symbols with the legitimate user, Alice, using wiretap coding over a portion of the sub-channels. Concurrently, Alice uses the accumulated secret keys in her secret-key queue to encrypt data symbols using a one time pad (OTP) cipher and transmi…
In Cyber-Physical Systems (CPS), inference based on communicated data is of critical significance as it can be used to manipulate or damage the control operations by adversaries. This calls for efficient mechanisms for secure transmission of data since control systems are becoming increasingly distributed over larger geographical areas. Distortion based security, recently proposed as one candidate for secure transmissions in CPS, is not only more appropriate for these applications but also quite frugal in terms of prior requirements on shared keys. In this paper, we propose distortion-based me…
The secure summation problem is considered, where $K$ users, each holds an input, wish to compute the sum of their inputs at a server securely, i.e., without revealing any information beyond the sum even if the server may collude with any set of up to $T$ users. First, we prove a folklore result for secure summation - to compute $1$ bit of the sum securely, each user needs to send at least $1$ bit to the server, each user needs to hold a key of at least $1$ bit, and all users need to hold collectively some key variables of at least $K-1$ bits. Next, we focus on the symmetric groupwise key sett…
Physical-layer group secret-key (GSK) generation is an effective way of generating secret keys in wireless networks, wherein the nodes exploit inherent randomness in the wireless channels to generate group keys, which are subsequently applied to secure messages while broadcasting, relaying, and other network-level communications. While existing GSK protocols focus on securing the common source of randomness from external eavesdroppers, they assume that the legitimate nodes of the group are trusted. In this paper, we address insider attacks from the legitimate participants of the wireless netwo…
We present a comprehensive analysis on connectivity and resilience of secure sensor networks under the widely studied q-composite key predistribution scheme. For network connectivity which ensures that any two sensors can find a path in between for secure communication, we derive the conditions to guarantee connectivity in consideration of (i) node-capture attacks, where the adversary may capture a set of sensors and compromise keys in their memory; (ii) sensor mobility, meaning that sensors can move around so that the network topology may change over time; (iii) physical transmission constrai…
