Quantum-safe Cryptographic protocols

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While physical implementation of a quantum computer still seems far away, the perspective of such a realization is so profound to the world of cryptography that it is worth considering already what this science will become after the construction of a quantum computer. The study of Quantum-safe (aka Post-Quantum) cryptographic tools and protocols follow from the belief that we must start now to prepare for this future.Quantum-Safe Oblivious Transfer and Fully Homomorphic Encryption*******************************************************In the classical world there used to be very general techniques to achieve Oblivious Transfer from various cryptographic assumption. In the Quantum-safe cryptographic world we have no such things: several techniques have been proposed to obtain Quantum-safe Oblivious Transfer but no general technique has emerged yet. The search for such a general approach will be one objective of our research. We will also consider the relation between Oblivious Transfer and the related task of Fully Homomorphic Encryption as implemented under the Learning with error assumption or the Approximate Integer GCD assumption. We would like to show that in the quantum world OT is inherently easier to achieve than FHE.Interactive Hashing and Statistical Zero-Knowledge Arguments**************************************************Another specific target is to study a powerful tool to construct secure protocols known as "Interactive Hashing". This tool was used in the classical setting both in the information theoretical and computational framework. Currently, none of the proofs of security of protocols involving interactive hashing is valid in the quantum setting. We will develop new techniques to establish security proofs in the quantum world. We hope to achieve the same result as in the classical world: It is possible to build statistical zero-knowledge arguments for NP under the sole assumption that a quantum one-way function exists.Non-Interactive Quantum-Safe Zero-Knowledge Proofs********************************************Another classical cryptographic situation that is no longer available in the Quantum-safe world, is the primitive of Non-Interactive Zero-Knowledge protocols under computational assumptions. Such protocols have been proposed for prefect or statistical Non-Interactive Zero-Knowledge proofs under no computational assumption (although using quantum communication to achieve that). However, it does not seem to apply to situations where only Computational Zero-Knowledge is achievable (for NP-complete languages for example) or where the soundness of the proof system is only valid because a certain computational assumption cannot be broken (Perfect or Statistical Zero-Knowledge Arguments).This research program will contain theoretical work only but will produce significant training of HQPs.