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Non-interactive zero-knowledge with quantum random oracles

Non-interactive zero-knowledge with quantum random oracles. WORK IN PROGRESS!. Dominique Unruh University of Tartu With Andris Ambainis , Ansis Rosmanis. Estonian Theory Days. Classical Crypto. (Quick intro.). Non-interactive zero-knowledge (NIZK). Statement x (math. fact)

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Non-interactive zero-knowledge with quantum random oracles

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  1. Non-interactive zero-knowledgewith quantum random oracles WORK IN PROGRESS! Dominique Unruh University of Tartu With AndrisAmbainis, AnsisRosmanis Estonian Theory Days

  2. ClassicalCrypto (Quick intro.) Non-interactive ZK with Quantum Random Oracles

  3. Non-interactive zero-knowledge (NIZK) Statement x (math. fact) Witness w (proof of fact) P Uses:Proving honest behavior, signatures, … ZK proof of x Zero-knowledge Proof leaks nothingabout witness Soundness Hard to provewrong statements Non-interactive ZK with Quantum Random Oracles

  4. Towards efficient NIZK: Sigma protocols commitment challenge response Prover Verifier “Special soundness”: Two different responses allow to compute witness ⇒ For wrong statement, prover fails w.h.p. Non-interactive ZK with Quantum Random Oracles

  5. Toward efficient NIZK: Random Oracles • Model hash function as random function H • Many useful proof techniques Rewind andre-answer Learn queries H x H(x) Insert “special” answers(“programming”)

  6. NIZK with random oracles Fiat-Shamir Fischlin com • Fix com • Try different chal, respuntil H(chal,resp)=xxx000 • Proof := com,chal,resp • Need to query severalchal,resp • Implies existenceof witness chal H(com) resp Prover • NIZK consists ofcom,chal,resp • Prover can’t cheat:H is like a verifier • Security-proof:Rewinding Non-interactive ZK with Quantum Random Oracles

  7. Classical security easy. Quantum! But if adversary has aquantum computer? Non-interactive ZK with Quantum Random Oracles

  8. The “pick-one trick” (simplified) S • Given a set S • can encode it asa quantum state |Ψ〉 • s.t. for any set Z • you find one x1∈S∩Z • but not two x1,x2∈S Z x1 x2 Non-interactive ZK with Quantum Random Oracles

  9. Attacking Fischlin Fix com Try different chal, respuntil H(chal,resp)=xxx000 Proof = com,chal,resp S={chal,resp} Without knowingwitness! (Because we haveonly one S-element) Z={H(·)=xxx000} Valid fake NIZK [Fiat-Shamir attacked similarly] Non-interactive ZK with Quantum Random Oracles

  10. How does “one-pick trick” work? • Grover: Quantum algorithm for searching • Observation: • First step of Grover produces a stateencoding the search space • This state (plus modified Grover)implements “one-pick trick” • Hard part: Prove “can’t find two x1,x2∈S” Non-interactive ZK with Quantum Random Oracles

  11. No efficient quantum NIZK? • All random oracle NIZKbroken? • No: under extra conditions,Fiat-Shamir and Fischlinmight work (no proof idea) • We found a provable new construction(less efficient) Non-interactive ZK with Quantum Random Oracles

  12. I thank for yourattention This research was supported by European Social Fund’s Doctoral Studies and InternationalisationProgrammeDoRa

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