Abstract
We consider 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. For this minimal secure computation problem, we propose a novel coding scheme built from two steps. First, the function to be computed is expanded such that it can be recovered while additional information might be leaked. Second, a randomization step is applied to the expanded function such that the leaked information is protected. We implement this expand-and-randomize coding scheme with two algebraic structures—the finite field and the modulo ring of integers, where the expansion step is realized with the addition operation and the randomization step is realized with the multiplication operation over the respective algebraic structures.
Highlights
Cryptographic primitives are canonical and representative problems that capture the key challenges in understanding the fundamentals of security and privacy, and are essential building blocks for more sophisticated systems and protocols
We focus on a minimal model of secure computation, introduced by Feige, Kilian, and Naor in 1994 [12]
The first main result of this work is to characterize the structural properties of such confusable sets over the finite field
Summary
Cryptographic primitives are canonical and representative problems that capture the key challenges in understanding the fundamentals of security and privacy, and are essential building blocks for more sophisticated systems and protocols. Here Carol should only know if W1 − W2 = 0 and is not supposed to learn whether W1 − W2 is 1 or 2 To prevent this leakage, we invoke another step of randomization so that the leaked information by the expanded function becomes confusable and protected. Our proposed coding scheme is inspired by two examples (binary logical AND function and ternary comparison function) presented in Appendix A and Appendix B of the original minimal secure computation paper [12], where modular arithmetic over a prime number p is used. Note that for a prime p, the algebraic operations (addition and multiplication) in both finite field F p and the ring of integers modulo p, Z p are modular arithmetic. Our work can be viewed as a generalization of the examples from in [12] to a general class of achievable schemes that distill the underlying algebraic structure and work over finite fields and modulo rings of integers with general (non-prime) cardinality
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call