Secure Modulo Zero-Sum Randomness as Cryptographic Resource.

In secure multiparty computation, mutually distrusting users in a network want to collaborate to compute functions of data which is distributed among the users. The users should not learn any additional information about the data of others than what they may infer from their own data and the functions they are computing. Previous works have mostly considered the worst case context (i.e., without assuming any distribution for the data); Lee and Abbe (2014) is a notable exception. Here, we study the average case (i.e., we work with a distribution on the data) where correctness and privacy is only desired asymptotically. For concreteness and simplicity, we consider a secure version of the function computation problem of Körner and Marton (1979) where two users observe a doubly symmetric binary source with parameter p and the third user wants to compute the XOR. We show that the amount of communication and randomness resources required depends on the level of correctness desired. When zero-error and perfect privacy are required, the results of Data et al. (2014) show that it can be achieved if and only if a total rate of 1 bit is communicated between every pair of users and private randomness at the rate of 1 is used up. In contrast, we show here that, if we only want the probability of error to vanish asymptotically in blocklength, it can be achieved by a lower rate (binary entropy of p) for all the links and for private randomness; this also guarantees perfect privacy. We also show that no smaller rates are possible even if privacy is only required asymptotically.In secure multiparty computation, mutually distrusting users in a network want to collaborate to compute functions of data which is distributed among the users. The users should not learn any additional information about the data of others than what they may infer from their own data and the functions they are computing. Previous works have mostly considered the worst case context (i.e., without assuming any distribution for the data); Lee and Abbe (2014) is a notable exception. Here, we study the average case (i.e., we work with a distribution on the data) where correctness and privacy is only desired asymptotically. For concreteness and simplicity, we consider a secure version of the function computation problem of Körner and Marton (1979) where two users observe a doubly symmetric binary source with parameter p and the third user wants to compute the XOR. We show that the amount of communication and randomness resources required depends on the level of correctness desired. When zero-error and perfect privacy are required, the results of Data et al. (2014) show that it can be achieved if and only if a total rate of 1 bit is communicated between every pair of users and private randomness at the rate of 1 is used up. In contrast, we show here that, if we only want the probability of error to vanish asymptotically in blocklength, it can be achieved by a lower rate (binary entropy of p) for all the links and for private randomness; this also guarantees perfect privacy. We also show that no smaller rates are possible even if privacy is only required asymptotically.

arXiv:1405.2555IEEE Information Theory Workshop (ITW)Nov 1, 20149 citations

Public-Randomness in Public-Key Cryptography

Alfredo De Santis, Giuseppe Persiano

Lecture notes in computer scienceJan 1, 199116 citations

Secure Modulo Sum via Multiple Access Channel

Masahito Hayashi

We discuss secure computation of modular sum when multiple access channel from distinct players $A_{1}, \ldots, A_{c}$ to a third party (Receiver) is given. Then, we define the secure modulo sum capacity as the supremum of the transmission rate of modulo sum without information leakage of other information. We derive its useful lower bound, which is numerically calculated under a realistic model that can be realizable as a Gaussian multiple access channel (MAC).We discuss secure computation of modular sum when multiple access channel from distinct players$A_{1}, \ldots, A_{c}$to a third party (Receiver) is given. Then, we define the secure modulo sum capacity as the supremum of the transmission rate of modulo sum without information leakage of other information. We derive its useful lower bound, which is numerically calculated under a realistic model that can be realizable as a Gaussian multiple access channel (MAC).

arXiv:1812.10862IEEE International Symposium on Information Theory (ISIT)Jul 12, 20216 citations

True Random Number Generators for Cryptography

Berk Sunar

Springer eBooksDec 10, 200861 citations

We discuss secure computation of modular sum when multiple access channel from distinct players

A_{1}, \ldots, A_{c}

to a third party (Receiver) is given. Then, we define the secure modulo sum capacity as the supremum of the transmission rate of modulo sum without information leakage of other information. We derive its useful lower bound, which is numerically calculated under a realistic model that can be realizable as a Gaussian multiple access channel (MAC).