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We consider the question of minimizing the asymptotic number of pseudorandom generator calls made by such protocols

Efficient non-interactive secure computation

EUROCRYPT, (2011): 406-425

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摘要

Suppose that a receiver R wishes to publish an encryption of her secret input x so that every sender S, holding an input y, can reveal f(x, y) to R by sending her a single message. This should be done while simultaneously protecting the secrecy of y against a corrupted R and preventing a corrupted S from having an unfair influence on the ...更多

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简介
  • This work is motivated by the following variant of the problem of computing on encrypted data [42,43].
  • Existing constant-round black-box protocols in the OT-hybrid model require Ω(κ) calls to a PRG for each gate in the circuit, where κ is a statistical security parameter guaranteeing at most 2−κ simulation error for a malicious sender2.
重点内容
  • This work is motivated by the following variant of the problem of computing on encrypted data [42,43]
  • We consider the question of minimizing the asymptotic number of pseudorandom generator calls made by such protocols
  • Suppose that a receiver R wishes to publish a semantically secure encryption of her secret input x so that any sender S, holding an input y, can reveal f (x, y) to R by sending her a single message. (The message can be seen as an encryption of f (x, y) that the receiver can decrypt)
  • As a concrete motivating scenario for non-interactive secure computation, consider a receiver Roberta who wishes to publish an encrypted version of her personal profile x on her public web page towards finding a suitable partner for dating
  • We present the first general non-interactive secure computation/oblivious transfer protocols which only make a black-box use of a pseudorandom generator
  • We only considered non-interactive secure computation schemes which rely on an oblivious transfer oracle that gets inputs from both the sender and the receiver
结果
  • Start with a perfectly secure NISC/OT protocol π for g in the semi-honest model in which the receiver uses its original α input bits a as the sequence of OT choices.
  • O-bit long output and n + O(κ)-bit input from Receiver, such that there is an NISC/HC scheme for FC that makes a black-box use of a PRG, invoking the PRG O(κ|C|) times, and with O total communication.
  • For any function f : X × Y → Z that has a polynomial sized circuit C with n input wires for the first input, there exists an NC0 functionality HC with O(κ|C|)-bit long output and n + O(κ)-bit input from Receiver, such that there is an NISC/HC scheme for FC† that makes a black-box use of a PRG, invoking the PRG O(|C|) times, and with O(k|C|) total communication.
  • For any function f : X × Y → Z that has a polynomial sized circuit C with n input wires for the first input, there exists an NC0 functionality HC with O(k|C|)-bit long output and n + O(κ)-bit input from Receiver, such that there is an NISC/HC scheme for FC‡ that makes a black-box use of a PRG, invoking the PRG O(|C|) times, and with O(k|C|) total communication.
  • The authors will first formalize the encoding notion that the authors use to deal with WDT attacks, the authors present an outline of the general transformation, and show how to invoke this transformation using known semi-honest MPC protocols from the literature to obtain higher levels of efficiency.
结论
  • It is still possible to consider such a scheme in an H-hybrid model, if the functionality H itself allows Receiver to send an input, and subsequently have multiple rounds of independent interactions with
  • For any function f : X × Y → Z that has a polynomial sized circuit C with n input wires for the first input, there exists an NC0 functionality HC(T ) with O-bit long output and n + O(κ)-bit input from Receiver, supporting T computations, such that there is a NISC/HC(T ) scheme for Ff(T ) that makes a black-box use of a PRG, invoking the PRG O((κ + T )|C|) times, and with O((κ + T )k|C|) total communication.
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