How to construct random functions
Journal of the ACM (JACM)
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
The random oracle methodology, revisited (preliminary version)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Learning DNF over the Uniform Distribution Using a Quantum Example Oracle
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Computation and Lattice Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum Search on Structured Problems
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Quantum Cryptanalysis of Hash and Claw-Free Functions
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
On the Exact Security of Full Domain Hash
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
RSA-OAEP Is Secure under the RSA Assumption
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Secure Integration of Asymmetric and Symmetric Encryption Schemes
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Efficiency improvements for signature schemes with tight security reductions
Proceedings of the 10th ACM conference on Computer and communications security
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Equivalences and Separations Between Quantum and Classical Learnability
SIAM Journal on Computing
ICQNM '08 Proceedings of the Second International Conference on Quantum, Nano and Micro Technologies (ICQNM 2008)
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Quantum Copy-Protection and Quantum Money
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Zero-Knowledge against Quantum Attacks
SIAM Journal on Computing
On the power of claw-free permutations
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Improved zero-knowledge identification with lattices
ProvSec'10 Proceedings of the 4th international conference on Provable security
Homomorphic signatures for polynomial functions
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Merkle puzzles in a quantum world
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Classical cryptographic protocols in a quantum world
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Universally composable quantum multi-party computation
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Bonsai trees, or how to delegate a lattice basis
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Efficient lattice (H)IBE in the standard model
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Quantum money from hidden subspaces
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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The interest in post-quantum cryptography -- classical systems that remain secure in the presence of a quantum adversary -- has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum state. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore postquantum secure. We conclude with a rich set of open problems in this area.