Communication complexity of secure computation (extended abstract)

@inproceedings{Franklin1992CommunicationCO,
  title={Communication complexity of secure computation (extended abstract)},
  author={Matthew K. Franklin and Moti Yung},
  booktitle={STOC '92},
  year={1992}
}
A secret-ballot vote for a single proposition is an example of a secure distributed computation. The goal is for <italic>m</italic> participants to jointly compute the output of some <italic>n</italic>-ary function (in this case, the sum of the votes), while protecting their individual inputs against some form of misbehavior. In this paper, we initiate the investigation of the communication complexity of unconditionally secure multi-party computation, and its relation with various fault… 
Communication and Randomness Lower Bounds for Secure Computation
TLDR
Information theoretic techniques are employed to obtain lower bounds on communication and randomness complexity of secure MPC, restricting ourselves to a concrete interactive setting involving three users under which all functions are securely computable against corruption of individual users in the honest-but-curious model.
More Communication Lower Bounds for Information-Theoretic MPC
TLDR
Two classes of lower bounds are proved on the communication complexity of information-theoretically secure multiparty computation and an upper bound is shown that matches the lower bound up to a constant factor.
Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography
TLDR
Under standard cryptographic assumptions, zero-knowledge proofs for circuit satisfiability with 2−k soundness error are obtained in which the amortized computational overhead per gate is only polylogarithmic in k, improving over the ω(k) overhead of the best previous protocols.
Communication Lower Bounds for Statistically Secure MPC, with or without Preprocessing
TLDR
It is shown that for all sizes of circuits, the O(n) overhead of all known protocols when t is maximal is inherent, and that security comes at a price: the circuit the authors consider could namely be computed among n parties with communication only O(g) bits if no security was required.
A High-Assurance Evaluator for Machine-Checked Secure Multiparty Computation
TLDR
This paper formalizes in \EasyCrypt, a tool-assisted framework for building high-confidence cryptographic proofs, several abstract and reusable variations of secret sharing and of (P)MPC protocols building on them, and proves a series of abstract theorems for the proactive setting.
Secure Arithmetic Computation with No Honest Majority
TLDR
These results extend a previous approach of Naor and Pinkas for secure polynomial evaluation to two-party protocols with security against malicious parties and present several solutions which differ in their efficiency, generality, and underlying intractability assumptions.
Generalized Pseudorandom Secret Sharing and Efficient Straggler-Resilient Secure Computation
TLDR
The benefits of PRSS-based MPC with a strong honest majority are explored, and a novel technique for defending against a subtle “double-dipping” attack is developed, which applies to the best existing protocols, with almost no extra cost in communication or rounds.
Efficient Asynchronous Verifiable Secret Sharing and Multiparty Computation
TLDR
This paper designs two AVSS schemes with 4t+1 parties: the first is statistically-secure and has non-optimal resilience, while the second one is perfectly- Secure and has optimal resilience, which significantly improves the communication complexity of the existing statistical AMPC protocols.
Secure Computation from Random Error Correcting Codes
TLDR
This work demonstrates that threshold secure computation in the secure channels model can be based on arbitrary codes, and shows a reduction in communication for secure computation amounting to a multiplicative logarithmic factor (in n) compared to classical methods for small networks.
On the Communication Complexity of Secure Computation
TLDR
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 (1994), who had shown that such functions exist are obtained.
...
...

References

SHOWING 1-10 OF 31 REFERENCES
Security with Low Communication Overhead
TLDR
The authors' is the first secure multiparty protocol in which the communication complexity is independent of the computational complexity of the function being computed, and a new upper bound on the number of oracles needed in instance-hiding schemes for arbitrary functions is established.
Foundations of Secure Interactive Computing
TLDR
Relative resilience provides modular proof techniques that other approaches lack: one may compare a sequence of protocols ranging from the real-world protocol to the ideal protocol, proving the relative resilience of each successive protocol with greater clarity and less complexity.
Non-cryptographic fault-tolerant computing in constant number of rounds of interaction
TLDR
Any function can be evaluated in a constant number of rounds, using messages of size proportional to the size of a constant-depth, unbounded-fanin circuit describing the function, and a means to simulate unbounded fanin multiplicative (or AND) gates using constant rounds is provided.
Completeness theorems for non-cryptographic fault-tolerant distributed computation
Every function of <italic>n</italic> inputs can be efficiently computed by a complete network of <italic>n</italic> processors in such a way that:<list><item>If no faults occur, no set of size
Privacy and communication complexity
  • E. Kushilevitz
  • Computer Science, Mathematics
    30th Annual Symposium on Foundations of Computer Science
  • 1989
TLDR
A complete combinatorial characterization of privately computable functions is given and this characterization is used to derive tight bounds on the rounds complexity of any privately Computable function and to design optimal private protocols that compute these functions.
How to Generate and Exchange Secrets (Extended Abstract)
  • A. Yao
  • Computer Science, Mathematics
    FOCS
  • 1986
TLDR
A new tool for controlling the knowledge transfer process in cryptographic protocol design is introduced and it is applied to solve a general class of problems which include most of the two-party cryptographic problems in the literature.
Multiparty Protocols Tolerating Half Faulty Processors
We show that a complete broadcast network of n processors can evaluate any function f(x1,..., xn) at private inputs supplied by each processor, revealing no information other than the result of the
How to generate and exchange secrets
  • A. Yao
  • Computer Science, Mathematics
    27th Annual Symposium on Foundations of Computer Science (sfcs 1986)
  • 1986
TLDR
It is shown how two parties A and B can interactively generate a random integer N = p¿q such that its secret, i.e., the prime factors, is hidden from either party individually but is recoverable jointly if desired.
Privacy, additional information, and communication
TLDR
It is shown that additional information is a resource which can be traded for communication complexity which enables the authors to give tight lower and upper bounds on the amount of additional information required for computing various functions.
How to share a secret
  • A. Shamir
  • Computer Science, Mathematics
    CACM
  • 1979
TLDR
This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
...
...