Programmable Hash Functions Research Articles

Lattice-Based Programmable Hash Functions and Applications

Lattice-Based Programmable Hash Functions and Applications

(Identity-based) dual receiver encryption from lattice-based programmable hash functions with high min-entropy

Dual receiver encryption (DRE) is an important cryptographic primitive introduced by Diament et al. at CCS’04, which allows two independent receivers to decrypt a same ciphertext to obtain the same plaintext. This primitive is quite useful in designing combined public key cryptosystems and denial of service attack-resilient protocols. In this paper, we obtain some results as follows. Using weak lattice-based programmable hash functions (wLPHF) with high min-entropy (Crypto’16), we give a generic IND-CCA secure DRE construction in the standard model. Furthermore, we get a concrete DRE scheme by instantiating a concrete wLPHF with high min-entropy.For DRE notion in the identity-based setting, identity-based DRE (IB-DRE), basing on lattice-based programmable hash functions (LPHF) with high min-entropy, we give a framework of IND-ID-CPA secure IB-DRE construction in the standard model. When instantiating with concrete LPHFs with high min-entropy, we obtain five concrete IB-DRE schemes.

Deterministic Identity-Based Encryption from Lattice-Based Programmable Hash Functions with High Min-Entropy

There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of O(λ) basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of ω(log⁡λ) basic matrices.

Homomorphic signatures with sublinear public keys via asymmetric programmable hash functions

We introduce the notion of asymmetric programmable hash functions (APHFs, for short), which adapts Programmable hash functions, introduced by Hofheinz and Kiltz (Crypto 2008, Springer, 2008), with two main differences. First, an APHF works over bilinear groups, and it is asymmetric in the sense that, while only secretly computable, it admits an isomorphic copy which is publicly computable. Second, in addition to the usual programmability, APHFs may have an alternative property that we call programmable pseudorandomness. In a nutshell, this property states that it is possible to embed a pseudorandom value as part of the function’s output, akin to a random oracle. In spite of the apparent limitation of being only secretly computable, APHFs turn out to be surprisingly powerful objects. We show that they can be used to generically implement both regular and linearly-homomorphic signature schemes in a simple and elegant way. More importantly, when instantiating these generic constructions with our concrete realizations of APHFs, we obtain: (1) the first linearly-homomorphic signature (in the standard model) whose public key is sub-linear in both the dataset size and the dimension of the signed vectors; (2) short signatures (in the standard model) whose public key is shorter than those by Hofheinz–Jager–Kiltz (Asiacrypt 2011, Springer, 2011) and essentially the same as those by Yamada et al. (CT-RSA 2012, Springer, 2012).

Sakai–Ohgishi–Kasahara identity-based non-interactive key exchange revisited and more

Identity-based non-interactive key exchange (IB-NIKE) is a powerful but a bit overlooked primitive in identity-based cryptography. While identity-based encryption and signature have been extensively investigated over the past three decades, IB-NIKE has remained largely unstudied. So far, there are only few IB-NIKE schemes in the literature. Among them, Sakai---Ohgishi---Kasahara (SOK) scheme is the first efficient and secure two-party IB-NIKE scheme, which has great influence on follow-up works. However, the SOK scheme required its identity mapping function to be modeled as a random oracle to prove security. Moreover, its existing security proof heavily relies on the ability of programming the random oracle. It is unknown whether such reliance is inherent. In this work, we intensively revisit the SOK IB-NIKE scheme and present a series of possible and impossible results in the random oracle model and the standard model. In the random oracle model, we first improve previous security analysis for the SOK IB-NIKE scheme by giving a tighter reduction. We then use meta-reduction technique to show that the SOK scheme is unlikely proven to be secure based on the computational bilinear Diffie---Hellman assumption without programming the random oracle. In the standard model, we show how to instantiate the random oracle in the SOK scheme with a concrete hash function from admissible hash functions (AHFs) and indistinguishability obfuscation. The resulting scheme is adaptively secure based on the decisional bilinear Diffie---Hellman inversion assumption. To the best of our knowledge, this is the first adaptively secure IB-NIKE scheme in the standard model that does not explicitly require multilinear maps. Previous schemes in the standard model either have merely selective security or require programmable hash functions from multilinear maps. At the technical heart of our scheme, we generalize the definition of AHFs and propose a generic construction which enables AHFs with previously unachieved parameters. This might be of independent interest. In addition, we present some new results about IB-NIKE. Firstly, we propose a generic construction of multiparty IB-NIKE from extractable witness PRFs and existentially unforgeable signatures. Secondly, we investigate the relation between semi-adaptive security and adaptive security of IB-NIKE. Somewhat surprisingly, we show that these two notions are polynomially equivalent.

基于可编程hash 函数的短签名

A short signature, which is a type of digital signature, has an advantage in terms of its length. Short signatures are particularly suitable for scenarios in which communication bandwidth is constrained. Most of the existing short signature schemes have been proven secure under a random oracle, which is considered to be too idealistic. There is no hash function that can simulate a random oracle. A few of the provable secure short signature schemes in the standard model are considered to be inefficient or subject to strong hard assumptions, where the attacker is required to solve a chosen instance given a certain number of solved instances. Programmable hash functions (PHFs) can mimic some of the programmability properties of random oracles. Thus, PHFs can be plugged into the generic construction of signatures to yield short signatures in the standard model. We propose a short signature scheme based on a factoring assumption that uses programmable hash functions. The advantages are that: 1) the short signature only involves one element in a group and one small integer; 2) the scheme is efficient in terms of computational cost and does not require the generation of primes at signing; and 3) it is provably secure under the standard model without Chameleon hashes. This scheme is especially suitable for resource constrained applications such as wireless sensor networks and the Internet of things.

Programmable Hash Functions and Their Applications

We introduce a new combinatorial primitive called programmable hash functions (PHFs). PHFs can be used to program the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of standard model realizations of PHFs (with different parameters). The programmability makes PHFs a suitable tool to obtain black-box proofs of cryptographic protocols when considering adaptive attacks. We propose generic digital signature schemes from the strong RSA problem and from some hardness assumption on bilinear maps that can be instantiated with any PHF. Our schemes offer various improvements over known constructions. In particular, for a reasonable choice of parameters, we obtain short standard model digital signatures over bilinear maps.