# Communication and Randomness Lower Bounds for Secure Computation

@article{Data2015CommunicationAR, title={Communication and Randomness Lower Bounds for Secure Computation}, author={Deepesh Data and Vinod M. Prabhakaran and Manoj Prabhakaran}, journal={IEEE Transactions on Information Theory}, year={2015}, volume={62}, pages={3901-3929} }

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 the other users. While it is known that information theoretically secure MPC is possible among n users having access to private randomness and are pairwise connected by secure, noiseless, and bidirectional links against the collusion of less than n/2 users (in the honest-but-curious model; the threshold is n/3…

## 21 Citations

### On coding for secure computing

- Computer Science, Mathematics2015 IEEE International Symposium on Information Theory (ISIT)
- 2015

This work provides generic lower bounds on the amount of communication required among users and the total amount of private randomness needed to compute any function in this three-user model in a three user setting.

### Secure computation of randomized functions

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

Two user secure computation of randomized functions is considered, where only one user computes the output. Both the users are semi-honest; and computation is such that no user learns any additional…

### Tight Bounds on the Randomness Complexity of Secure Multiparty Computation

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2022

This work revisits the question of minimizing the randomness complexity of protocols for secure multiparty computation (MPC) in the setting of perfect information-theoretic security and proves an Ω( t 2 ) lower bound on the randoms complexity of XOR, matching the previous upper bound up to a logarithmic factor.

### Interactive Secure Function Computation

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2020

It is shown that randomized functions which can be perfectly securely computed in this model and obtain tight bounds on the optimal message lengths in all the privacy settings are obtained.

### Communication Complexity of Private Simultaneous Quantum Messages Protocols

- Computer ScienceIACR Cryptol. ePrint Arch.
- 2021

It is demonstrated that the privacy condition inevitably increases the communication cost in the two-party PSQM model as well as in the classical case presented by Applebaum, Holenstein, Mishra, and Shayevitz, and it is proved that a lower bound (3 − o(1)n) is proved of the communication complexity inPSQM protocols with a shared random string for random Boolean functions of 2n-bit input.

### On the Randomness Cost of Linear Secure Computation : (Invited Presentation)

- Computer Science, Mathematics2019 53rd Annual Conference on Information Sciences and Systems (CISS)
- 2019

It is shown that to compute M generic linear independent combinations of the messages securely, it suffices to use $\min\left(\left\lceil\frac{K-M-1}{2}\right\rceil,~M\right)$ randomness symbols per message symbol, and the optimality of the achieved randomness cost remains open.

### Randomness Bounds for Private Simultaneous Messages and Conditional Disclosure of Secrets

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2021

A new technique of randomness sparsiﬁcation for perfect privacy is provided and ρ ≥ 2 ( k − 1) n − 1 for a general function f : ( { 0, 1 } n ) k → { 0 , 1 } under universal reconstruction, in which P 0 is independent of f .

### Expand-and-Randomize: An Algebraic Approach to Secure Computation

- Computer Science, MathematicsEntropy
- 2021

This paper considers the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs, and proposes a novel coding scheme built from two steps.

### LOWER AND UPPER BOUNDS ON THE RANDOMNESS

- Computer Science, Mathematics
- 2020

This work shows that and cannot be privately computed using a single random bit, thus giving the ﬁrst non-trivial lower bound on the randomness complexity of the private computation of an explicit boolean function.

### Lower and Upper Bounds on the Randomness Complexity of Private Computations of AND

- Computer Science, MathematicsTCC
- 2019

It is shown that and cannot be privately computed using a single random bit, thus giving the first non-trivial lower bound on the 1-private randomness complexity of an explicit boolean function, f:{0, 1}n→{0,1} .

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