Abstract
A protocol has everlasting security if it is secure against adversaries that are computationally unlimited after the protocol execution. This models the fact that we cannot predict which cryptographic schemes will be broken, say, several decades after the protocol execution. In classical cryptography, everlasting security is difficult to achieve: even using trusted setup like common reference strings or signature cards, many tasks such as secure communication and oblivious transfer cannot be achieved with everlasting security. An analogous result in the quantum setting excludes protocols based on common reference strings, but not protocols using a signature card. We define a variant of the Universal Composability framework, everlasting quantum-UC, and show that in this model, we can implement secure communication and general multi-party computation using signature cards as trusted setup.
Highlights
Everlasting Security Computers and algorithms improve over time and so does the ability of an adversary to break cryptographic complexity assumptions and protocols
Composition problems are common in cryptography, but we find this case instructive: the commitment does not lose its security only when composed with some contrived protocol, but instead in a natural construction
We show that Alice must have obtained σ from the signature card: assume Alice successfully performs P without requesting σ first
Summary
Everlasting Security Computers and algorithms improve over time and so does the ability of an adversary to break cryptographic complexity assumptions and protocols. Need a predistributed common reference strings (CRS), and that are statistically hiding.1 When using these commitments to get everlastingly secure OT, we run into the same problem again: we would get an everlastingly secure OT using a CRS, but a generalization of Lo’s impossibility shows that no everlastingly secure OT protocols exist even given a CRS Further Related Work [8] considers the problem of using an unconditionally hiding computationally binding commitment to construct a quantum OT (as opposed to using directly a functionality) They show that with such a commitment, OT can be realized (no impossibility results are given).
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