Conditional Disclosure of Secrets: A Noise and Signal Alignment Approach

In the conditional disclosure of secrets (CDS) problem, Alice and Bob (each holds an input and a common secret) wish to disclose, as efficiently as possible, the secret to Carol if and only if their inputs satisfy some function. The capacity of CDS is the maximum number of bits of the secret that can be securely disclosed per bit of total communication. We characterize the necessary and sufficient condition for the extreme case where the capacity of CDS is the highest and is equal to 1/2. For the simplest instance where the capacity is smaller than 1/2, we show that the linear capacity is 2/5

Confused Modulo Projection based Somewhat Homomorphic Encryption -- Cryptosystem, Library and Applications on Secure Smart Cities

With the development of cloud computing, the storage and processing of massive visual media data has gradually transferred to the cloud server. For example, if the intelligent video monitoring system cannot process a large amount of data locally, the data will be uploaded to the cloud. Therefore, how to process data in the cloud without exposing the original data has become an important research topic. We propose a single-server version of somewhat homomorphic encryption cryptosystem based on confused modulo projection theorem named CMP-SWHE, which allows the server to complete blind data processing without \emph{seeing} the effective information of user data. On the client side, the original data is encrypted by amplification, randomization, and setting confusing redundancy. Operating on the encrypted data on the server side is equivalent to operating on the original data. As an extension, we designed and implemented a blind computing scheme of accelerated version based on batch processing technology to improve efficiency. To make this algorithm easy to use, we also designed and implemented an efficient general blind computing library based on CMP-SWHE. We have applied this library to foreground extraction, optical flow tracking and object detection with satisfactory results, which are helpful for building smart cities. We also discuss how to extend the algorithm to deep learning applications. Compared with other homomorphic encryption cryptosystems and libraries, the results show that our method has obvious advantages in computing efficiency. Although our algorithm has some tiny errors ($10^{-6}$) when the data is too large, it is very efficient and practical, especially suitable for blind image and video processing.Comment: IEEE Internet of Things Journal (IOTJ), Published Online: 7 August 202

Communication and Randomness Lower Bounds for Secure Computation

In secure multiparty computation (MPC), mutually distrusting users collaborate to compute a function of their private data without revealing any additional information about their data to other users. While it is known that information theoretically secure MPC is possible among $n$ users (connected by secure and noiseless links and have access to private randomness) against the collusion of less than $n/2$ users in the honest-but-curious model, relatively less is known about the communication and randomness complexity of secure computation. In this work, we employ information theoretic techniques to obtain lower bounds on the amount of communication and randomness required for secure MPC. We restrict ourselves to a concrete interactive setting involving 3 users under which all functions are securely computable against corruption of a single user in the honest-but-curious model. We derive lower bounds for both the perfect security case (i.e., zero-error and no leakage of information) and asymptotic security (where the probability of error and information leakage vanish as block-length goes to $\infty$). Our techniques include the use of a data processing inequality for residual information (i.e., the gap between mutual information and G\'acs-K\"orner common information), a new information inequality for 3-user protocols, and the idea of distribution switching. Our lower bounds are shown to be tight for various functions of interest. In particular, we show concrete functions which have "communication-ideal" protocols, i.e., which achieve the minimum communication simultaneously on all links in the network, and also use minimum amount of randomness. Also, we obtain the first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of "Feige, Kilian, and Naor [STOC, 1994]", who had shown that such functions exist.Comment: 30 pages, To Appear in the IEEE Transaction of Information Theory. arXiv admin note: substantial text overlap with arXiv:1311.758