Post-Quantum Cryptography A Collective Challenge
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1 Post-Quantum Cryptography A Collective Challenge Christophe Petit University of Oxford Mathematical Institute Christophe Petit -Oxford Crypto Day 1
2 Cryptography is very useful Cryptography is the science and art of ensuring private and authenticated communications Used everyday in TLS, bank cards, mobile phones,... Christophe Petit -Oxford Crypto Day 2
3 How we build trust in cryptography protocols Precisely define what it means to break the protocol Adversary s goal Adversary s resources Adversary s access to the system Choose your favorite hard problem A computational problem that cannot be solved, even by clever people with the best computers available Build a protocol so that you can prove Breaking the protocol Solving the hard problem Christophe Petit -Oxford Crypto Day 3
4 The threat of quantum computers Quantum computers change the boundaries between hard and easy problems Christophe Petit -Oxford Crypto Day 4
5 Post-Quantum Cryptography Abandon factoring and discrete logarithm problems Double your key sizes to resist Grover s search Find quantum-hard computational problems Build a protocol such that you can prove Breaking the protocol Solving the hard problem Evaluate how practical your protocol is, and improve it Christophe Petit -Oxford Crypto Day 5
6 Collaborations needed! Christophe Petit -Oxford Crypto Day 6
7 Cryptanalysis Not just factoring in polynomial time! Can allow larger time / memory May succeed only with some small probability May target special instances of the general problem May give unexpected power to the attacker (decryption oracle, side-channel, fault, cold boot attacks) May solve several instances on average faster than one Asymptotic and/or practical attack May combine several techniques Christophe Petit -Oxford Crypto Day 7
8 Quantum Cryptanalysis Solve search, factorization & discrete logarithm problems using Grover and Shor algorithms Find new cryptanalysis-relevant (sub)-problems which can be solved with Grover and Shor Modify Grover and Shor, or any quantum algorithm to target one of these subproblems Find new quantum attack scenarios, new physical threats Use the D-WAVE for what it can already do Design new quantum algorithms Christophe Petit -Oxford Crypto Day 8
9 Classical Cryptanalysis Confidence that discrete logs and factorization problems are (classically) hard comes from decades of attempts Are post-quantum candidates classically secure? Special instances of NP-hard problems Short factorizations in non-abelian groups : given a non Abelian finite group G, a generator set S, and a group element h, compute a short factorization h = s i S s i Isogeny problems : given two isogenous supersingular elliptic curves, compute an isogeny between them Christophe Petit -Oxford Crypto Day 9
10 Building cryptography : Theory Wanted : one-way functions A function that is easy to compute, but hard to invert Enough for authentication purposes (signatures) Wanted : trapdoor one-way functions A one-way function that can be inverted given some additional information (the trapdoor) Enough for public key encryption Wanted : hard problems Current (trapdoor) one-way functions from discrete logs, factorization, lattice, polynomial system problems,... Do you know any other hard problems? Christophe Petit -Oxford Crypto Day 10
11 Building cryptography : Practice Theoretical constructions from (trapdoor) OW functions can be too inefficient, may need ad hoc constructions Much more than just signature and encryption Find best parameters for efficiency and security Make sure to resist physical attacks Write new cryptographic standards Ensure backward-compatibility (or not) Enforce post-quantum migration in applications Christophe Petit -Oxford Crypto Day 11
12 Conclusion Post-quantum cryptography is a huge challenge The cryptography community is currently addressing it, but we definitely welcome and need your help There is a lot of relevant expertise in Oxford, we would love to get more interactions Lots of fun problems to tackle for everyone! Christophe Petit -Oxford Crypto Day 12
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