Lattice Forward-Secure Identity Based Encryption Scheme

Abstract Protecting secret keys is crucial for cryptography. There are some relatively insecure devices (smart cards, mobile phones etc.) which have threat of key exposure. The goal of the forward security is to protect security of past uses of key even if the current secret key is exposed. In this paper we propose lattice based forward-secure identity based encryption scheme based on LWE assumption in random oracle model. We also propose lattice based forward-secure identity based encryption scheme in the standard model

Tagged Chameleon Hash from Lattices and Application to Redactable Blockchain

Chameleon hash (CH) is a trapdoor hash function. Generally it is hard to find collisions, but with the help of a trapdoor, finding collisions becomes easy. CH plays an important role in converting a conventional blockchain to a redactable one. However, most of existing CH schemes are too weak to support redactable blockchains. The currently known CH schemes serving for redactable blockchains have the best security of so-called ``full collision resistance (f-CR)\u27\u27, but they are built either in the random oracle model or rely on heavy tools like the simulation-sound extractable non-interactive zero-knowledge (SSE-NIZK) proof system. Moreover, up to now there is no CH scheme with post-quantum f-CR security in the standard model. Therefore, no CH can support redactable blockchains in a post-quantum way without relying on random oracles. In this paper, we introduce a variant of CH, namely tagged chameleon hash (tCH). Tagged chameleon hash takes a tag into hash evaluations and collision finding algorithms. We define two security notions for tCH, restricted collision resistance (r-CR) and full collision resistance (f-CR), and prove the equivalence between r-CR and f-CR when tCH works in the one-time tag mode. We propose a tCH scheme from lattices without using any NIZK proof, and prove that its restricted collision resistance is reduced to the Short Integer Solution (SIS) assumption in the standard model. We also show how to apply tCH to a blockchain in one-time tag mode so that the blockchain can be compiled to a redactable one. Our tCH scheme provides the first post-quantum solution for redactable blockchains, without resorting to random oracles or NIZK proofs. Besides, we also construct a more efficient tCH scheme with r-CR tightly reduced to SIS in the random oracle model, which may be of independent interest

Generic Constructions of Parallel Key-Insulated Encryption: Stronger Security Model and Novel Schemes

Exposure of a secret key is a significant threat in practice. As a notion of security against key exposure, Dodis et al. advocated key-insulated security, and proposed concrete key-insulated encryption (KIE) schemes in which secret keys are periodically updated by using a physically ``insulated\u27\u27 helper key. For significantly reducing possibility of exposure of the helper key, Hanaoka et al. further proposed the notion of parallel KIE (PKIE) in which multiple helper keys are used in alternate shifts. They also pointed out that in contrast to the case of the standard KIE, PKIE cannot be straightforwardly obtained from identity-based encryption (IBE). In this paper, we first discuss that previous security models for PKIE are somewhat weak, and thus re-formalize stronger security models for PKIE. Then we clarify that PKIE can be generically constructed (even in the strenghthened security models) by using a new primitive which we call one-time forward secure public key encryption (OTFS-PKE) and show that it is possible to construct OTFS-PKE from arbitrary IBE or hierarchical IBE (without degenerating into IBE). By using our method, we can obtain various new PKIE schemes which yield desirable properties. For example, we can construct first PKIE schemes from lattice or quadratic residuosity problems (without using bilinear maps), and PKIE with short ciphertexts and cheaper computational cost for both encryption and decryption. Interestingly, the resulting schemes can be viewed as the partial solutions to the open problem left by Libert, Quisquarter and Yung in PKC\u2707

Efficient Statistical Zero-Knowledge Authentication Protocols for Smart Cards Secure Against Active & Concurrent Attacks

We construct statistical zero-knowledge authentication protocols for smart cards based on general assumptions. The main protocol is only secure against active attacks, but we present a modification based on trapdoor commitments that can resist concurrent attacks as well. Both protocols are instantiated using lattice-based primitives, which are conjectured to be secure against quantum attacks. We illustrate the practicality of our main protocol on smart cards in terms of storage, computation, communication, and round complexities. Furthermore, we compare it to other lattice-based authentication protocols, which are either zero-knowledge or have a similar structure. The comparison shows that our protocol improves the best previous protocol

Constrained Keys for Invertible Pseudorandom Functions

A constrained pseudorandom function (PRF) is a secure PRF for which one can generate constrained keys that can only be used to evaluate the PRF on a subset of the domain. Constrained PRFs are used widely, most notably in applications of indistinguishability obfuscation (iO). In this paper we show how to constrain an invertible PRF (IPF), which is significantly harder. An IPF is a secure injective PRF accompanied by an inversion algorithm. A constrained key for an IPF can only be used to evaluate the IPF on a subset S of the domain, and to invert the IPF on the image of S. We first define the notion of a constrained IPF and then give two main constructions: one for puncturing an IPF and the other for (single-key) circuit constraints. Both constructions rely on recent work on private constrained PRFs. We also show that constrained pseudorandom permutations for many classes of constraints are impossible under our definition

Bonsai trees (or, arboriculture in lattice-based cryptography)

We introduce bonsai trees, a lattice-based cryptographic primitive that we apply to resolve some important open problems in the area. Applications of bonsai trees include: • An efficient, stateless ‘hash-and-sign’ signature scheme in the standard model (i.e., no random oracles), and • The first hierarchical identity-based encryption (HIBE) scheme (also in the standard model) that does not rely on bilinear pairings. Interestingly, the abstract properties of bonsai trees seem to have no known realization in conventional number-theoretic cryptography