Lossy Trapdoor Functions and Their Applications

We propose a new general primitive called lossy trapdoor functions (lossy TDFs), and realize it under a variety of different number theoretic assumptions, including hardness of the decisional Diffie-Hellman (DDH) problem and the worst-case hardness of standard lattice problems. Using lossy TDFs, we develop a new approach for constructing many important cryptographic primitives, including standard trapdoor functions, CCA-secure cryptosystems, collision-resistant hash functions, and more. All of our constructions are simple, efficient, and black-box. Taken all together, these results resolve some long-standing open problems in cryptography. They give the first known (injective) trapdoor functions based on problems not directly related to integer factorization, and provide the first known CCA-secure cryptosystem based solely on worst-case lattice assumptions

URDP: General Framework for Direct CCA2 Security from any Lattice-Based PKE Scheme

Design efficient lattice-based cryptosystem secure against adaptive chosen ciphertext attack (IND-CCA2) is a challenge problem. To the date, full CCA2-security of all proposed lattice-based PKE schemes achieved by using a generic transformations such as either strongly unforgeable one-time signature schemes (SU-OT-SS), or a message authentication code (MAC) and weak form of commitment. The drawback of these schemes is that encryption requires "separate encryption". Therefore, the resulting encryption scheme is not sufficiently efficient to be used in practice and it is inappropriate for many applications such as small ubiquitous computing devices with limited resources such as smart cards, active RFID tags, wireless sensor networks and other embedded devices. In this work, for the first time, we introduce an efficient universal random data padding (URDP) scheme, and show how it can be used to construct a "direct" CCA2-secure encryption scheme from "any" worst-case hardness problems in (ideal) lattice in the standard model, resolving a problem that has remained open till date. This novel approach is a "black-box" construction and leads to the elimination of separate encryption, as it avoids using general transformation from CPA-secure scheme to a CCA2-secure one. IND-CCA2 security of this scheme can be tightly reduced in the standard model to the assumption that the underlying primitive is an one-way trapdoor function.Comment: arXiv admin note: text overlap with arXiv:1302.0347, arXiv:1211.6984; and with arXiv:1205.5224 by other author

Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm. The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible

Classical Verification of Quantum Computations

We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum prover as a trusted measurement device. The protocol forces the prover to behave as follows: the prover must construct an n qubit state of his choice, measure each qubit in the Hadamard or standard basis as directed by the verifier, and report the measurement results to the verifier. The soundness of this protocol is enforced based on the assumption that the learning with errors problem is computationally intractable for efficient quantum machines

Multilinear Maps in Cryptography

Multilineare Abbildungen spielen in der modernen Kryptographie eine immer bedeutendere Rolle. In dieser Arbeit wird auf die Konstruktion, Anwendung und Verbesserung von multilinearen Abbildungen eingegangen

A CCA2 secure Code based encryption scheme in the Standard Model

This paper proposes an encryption scheme secureagainst chosen cipher text attack, built on the Niederreiterencryption scheme. The security of the scheme is based on thehardness of the Syndrome Decoding problem and the Goppa CodeDistinguishability problem. The scheme uses the techniques providedby Peikert and Waters using the lossy trapdoor functions.Compared to the existing IND-CCA2 secure variants in standardmodel due to Dowsley et.al. and Freeman et. al. (using the repetition paradigm initiated by Rosen and Segev), this schemeis more efficient as it avoids repetitions

Classical Homomorphic Encryption for Quantum Circuits

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem