Unforgeable Quantum Encryption

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.Comment: 22+2 pages, 1 figure. v3: error in the definition of QIND-CCA2 fixed, some proofs related to QIND-CCA2 clarifie

Strong knowledge extractors for public-key encryption schemes

Completely non-malleable encryption schemes resist attacks which allow an adversary to tamper with both ciphertexts and public keys. In this paper we introduce two extractor-based properties that allow us to gain insight into the design of such schemes and to go beyond known feasibility results in this area. We formalise strong plaintext awareness and secret key awareness and prove their suitability in realising these goals. Strong plaintext awareness imposes that it is infeasible to construct a ciphertext under any public key without knowing the underlying message. Secret key awareness requires it to be infeasible to produce a new public key without knowing a corresponding secret key.The authors were funded in part by eCrypt II (EU FP7 - ICT-2007-216646) and FCT project PTDC/EIA/71362/2006. The second author was also funded by FCT grant BPD-47924-2008

A Black-Box Construction of Non-Malleable Encryption from Semantically Secure Encryption

We show how to transform any semantically secure encryption scheme into a non-malleable one, with a black-box construction that achieves a quasi-linear blow-up in the size of the ciphertext. This improves upon the previous non-black-box construction of Pass, Shelat and Vaikuntanathan (Crypto \u2706). Our construction also extends readily to guarantee non-malleability under a bounded-CCA2 attack, thereby simultaneously improving on both results in the work of Cramer et al. (Asiacrypt \u2707). Our construction departs from the oft-used paradigm of re-encrypting the same message with different keys and then proving consistency of encryption. Instead, we encrypt an encoding of the message; the encoding is based on an error-correcting code with certain properties of reconstruction and secrecy from partial views, satisfied, e.g., by a Reed-Solomon code

A Brief History of Provably-Secure Public-Key Encryption

Public-key encryption schemes are a useful and interesting field of cryptographic study. The ultimate goal for the cryptographer in the field of public-key encryption would be the production of a very efficient encryption scheme with a proof of security in a strong security model using a weak and reasonable computational assumption. This ultimate goal has yet to be reached. In this invited paper, we survey the major results that have been achieved in the quest to find such a scheme

Semantic Security and Indistinguishability in the Quantum World

At CRYPTO 2013, Boneh and Zhandry initiated the study of quantum-secure encryption. They proposed first indistinguishability definitions for the quantum world where the actual indistinguishability only holds for classical messages, and they provide arguments why it might be hard to achieve a stronger notion. In this work, we show that stronger notions are achievable, where the indistinguishability holds for quantum superpositions of messages. We investigate exhaustively the possibilities and subtle differences in defining such a quantum indistinguishability notion for symmetric-key encryption schemes. We justify our stronger definition by showing its equivalence to novel quantum semantic-security notions that we introduce. Furthermore, we show that our new security definitions cannot be achieved by a large class of ciphers -- those which are quasi-preserving the message length. On the other hand, we provide a secure construction based on quantum-resistant pseudorandom permutations; this construction can be used as a generic transformation for turning a large class of encryption schemes into quantum indistinguishable and hence quantum semantically secure ones. Moreover, our construction is the first completely classical encryption scheme shown to be secure against an even stronger notion of indistinguishability, which was previously known to be achievable only by using quantum messages and arbitrary quantum encryption circuits.Comment: 37 pages, 2 figure

On Black-Box Complexity and Adaptive, Universal Composability of Cryptographic Tasks

Two main goals of modern cryptography are to identify the minimal assumptions necessary to construct secure cryptographic primitives as well as to construct secure protocols in strong and realistic adversarial models. In this thesis, we address both of these fundamental questions. In the first part of this thesis, we present results on the black-box complexity of two basic cryptographic primitives: non-malleable encryption and optimally-fair coin tossing. Black-box reductions are reductions in which both the underlying primitive as well as the adversary are accessed only in an input-output (or black-box) manner. Most known cryptographic reductions are black-box. Moreover, black-box reductions are typically more efficient than non-black-box reductions. Thus, the black-box complexity of cryptographic primitives is a meaningful and important area of study which allows us to gain insight into the primitive. We study the black box complexity of non-malleable encryption and optimally-fair coin tossing, showing a positive result for the former and a negative one for the latter. Non-malleable encryption is a strong security notion for public-key encryption, guaranteeing that it is impossible to "maul" a ciphertext of a message m into a ciphertext of a related message. This security guarantee is essential for many applications such as auctions. We show how to transform, in a black-box manner, any public-key encryption scheme satisfying a weak form of security, semantic security, to a scheme satisfying non-malleability. Coin tossing is perhaps the most basic cryptographic primitive, allowing two distrustful parties to flip a coin whose outcome is 0 or 1 with probability 1/2. A fair coin tossing protocol is one in which the outputted bit is unbiased, even in the case where one of the parties may abort early. However, in the setting where parties may abort early, there is always a strategy for one of the parties to impose bias of Omega(1/r) in an r-round protocol. Thus, achieving bias of O(1/r) in r rounds is optimal, and it was recently shown that optimally-fair coin tossing can be achieved via a black-box reduction to oblivious transfer. We show that it cannot be achieved via a black-box reduction to one-way function, unless the number of rounds is at least Omega(n/log n), where n is the input/output length of the one-way function. In the second part of this thesis, we present protocols for multiparty computation (MPC) in the Universal Composability (UC) model that are secure against malicious, adaptive adversaries. In the standard model, security is only guaranteed in a stand-alone setting; however, nothing is guaranteed when multiple protocols are arbitrarily composed. In contrast, the UC model, introduced by (Canetti, 2000), considers the execution of an unbounded number of concurrent protocols, in an arbitrary, and adversarially controlled network environment. Another drawback of the standard model is that the adversary must decide which parties to corrupt before the execution of the protocol commences. A more realistic model allows the adversary to adaptively choose which parties to corrupt based on its evolving view during the protocol. In our work we consider the the adaptive UC model, which combines these two security requirements by allowing both arbitrary composition of protocols and adaptive corruption of parties. In our first result, we introduce an improved, efficient construction of non-committing encryption (NCE) with optimal round complexity, from a weaker primitive we introduce called trapdoor-simulatable public key encryption (PKE). NCE is a basic primitive necessary to construct protocols secure under adaptive corruptions and in particular, is used to construct oblivious transfer (OT) protocols secure against semi-honest, adaptive adversaries. Additionally, we show how to realize trapdoor-simulatable PKE from hardness of factoring Blum integers, thus achieving the first construction of NCE from hardness of factoring. In our second result, we present a compiler for transforming an OT protocol secure against a semi-honest, adaptive adversary into one that is secure against a malicious, adaptive adversary. Our compiler achieves security in the UC model, assuming access to an ideal commitment functionality, and improves over previous work achieving the same security guarantee in two ways: it uses black-box access to the underlying protocol and achieves a constant multiplicative overhead in the round complexity. Combining our two results with the work of (Ishai et al., 2008), we obtain the first black-box construction of UC and adaptively secure MPC from trapdoor-simulatable PKE and the ideal commitment functionality

Efficient Certificateless Public Key Encryption

In [3] Al-Riyami and Paterson introduced the notion of Certificateless Public Key Cryptography and presented an instantiation. In this paper, we revisit the formulation of certificateless public key encryption and construct a more efficient scheme and then extend it to an authenticated encryption

Contributions to Lattice–based Cryptography

Post–quantum cryptography (PQC) is a new and fast–growing part of Cryptography. It focuses on developing cryptographic algorithms and protocols that resist quantum adversaries (i.e., the adversaries who have access to quantum computers). To construct a new PQC primitive, a designer must use a mathematical problem intractable for the quantum adversary. Many intractability assumptions are being used in PQC. There seems to be a consensus in the research community that the most promising are intractable/hard problems in lattices. However, lattice–based cryptography still needs more research to make it more efficient and practical. The thesis contributes toward achieving either the novelty or the practicality of lattice– based cryptographic systems