Adaptively Secure Identity-Based Encryption from Lattices with Asymptotically Shorter Public Parameters

In this paper, we present two new adaptively secure identity-based encryption (IBE) schemes from lattices. The size of the public parameters, ciphertexts, and private keys are $\tilde{O}(n^2 \kappa^{1/d})$, $\tilde{O}(n)$, and $\tilde{O}(n)$ respectively. Here, $n$ is the security parameter, $\kappa$ is the length of the identity, and $d$ is a flexible constant that can be set arbitrary (but will affect the reduction cost). Ignoring the poly-logarithmic factors hidden in the asymptotic notation, our schemes achieve the best efficiency among existing adaptively secure IBE schemes from lattices. In more detail, our first scheme is anonymous, but proven secure under the LWE assumption with approximation factor $n^{\omega(1)}$. Our second scheme is not anonymous, but proven adaptively secure assuming the LWE assumption for all polynomial approximation factors. As a side result, based on a similar idea, we construct an attribute-based encryption scheme for branching programs that simultaneously satisfies the following properties for the first time: Our scheme achieves compact secret keys, the security is proven under the LWE assumption with polynomial approximation factors, and the scheme can deal with unbounded length branching programs

Circuit-ABE from LWE: Unbounded Attributes and Semi-adaptive Security

We construct an LWE-based key-policy attribute-based encryption (ABE) scheme that supports attributes of unbounded polynomial length. Namely, the size of the public parameters is a fixed polynomial in the security parameter and a depth bound, and with these fixed length parameters, one can encrypt attributes of arbitrary length. Similarly, any polynomial size circuit that adheres to the depth bound can be used as the policy circuit regardless of its input length (recall that a depth d circuit can have as many as 2d inputs). This is in contrast to previous LWE-based schemes where the length of the public parameters has to grow linearly with the maximal attribute length. We prove that our scheme is semi-adaptively secure, namely, the adversary can choose the challenge attribute after seeing the public parameters (but before any decryption keys). Previous LWE-based constructions were only able to achieve selective security. (We stress that the “complexity leveraging” technique is not applicable for unbounded attributes). We believe that our techniques are of interest at least as much as our end result. Fundamentally, selective security and bounded attributes are both shortcomings that arise out of the current LWE proof techniques that program the challenge attributes into the public parameters. The LWE toolbox we develop in this work allows us to delay this programming. In a nutshell, the new tools include a way to generate an a-priori unbounded sequence of LWE matrices, and have fine-grained control over which trapdoor is embedded in each and every one of them, all with succinct representation.National Science Foundation (U.S.) (Award CNS-1350619)National Science Foundation (U.S.) (Grant CNS-1413964)United States-Israel Binational Science Foundation (Grant 712307

Vector Encoding over Lattices and Its Applications

In this work, we design a new lattice encoding structure for vectors. Our encoding can be used to achieve a packed FHE scheme that allows some SIMD operations and can be used to improve all the prior IBE schemes and signatures in the series. In particular, with respect to FHE setting, our method improves over the prior packed GSW structure of Hiromasa et al. (PKC \u2715), as we do not rely on a circular assumption as required in their work. Moreover, we can use the packing and unpacking method to extract each single element, so that the homomorphic operation supports element-wise and cross-element-wise computation as well. In the IBE scenario, we improves over previous constructions supporting $O(\Lambda)$-bit length identity from lattices substantially, such as Yamada (Eurocrypt \u2716), Katsumata, Yamada (Asiacrypt \u2716) and Yamada (Crypto \u2717), by shrinking the master public key to three matrices from standard Learning With Errors assumption. Additionally, our techniques from IBE can be adapted to construct a compact digital signature scheme, which achieves existential unforgeability under the standard Short Integer Solution (SIS) assumption with small polynomial parameters

Efficient Adaptively-Secure IB-KEMs and VRFs via Near-Collision Resistance

We construct more efficient cryptosystems with provable security against adaptive attacks, based on simple and natural hardness assumptions in the standard model. Concretely, we describe: - An adaptively-secure variant of the efficient, selectively-secure LWE-based identity-based encryption (IBE) scheme of Agrawal, Boneh, and Boyen (EUROCRYPT 2010). In comparison to the previously most efficient such scheme by Yamada (CRYPTO 2017) we achieve smaller lattice parameters and shorter public keys of size $\mathcal{O}(\log \lambda)$, where $\lambda$ is the security parameter. - Adaptively-secure variants of two efficient selectively-secure pairing-based IBEs of Boneh and Boyen (EUROCRYPT 2004). One is based on the DBDH assumption, has the same ciphertext size as the corresponding BB04 scheme, and achieves full adaptive security with public parameters of size only $\mathcal{O}(\log \lambda)$. The other is based on a $q$-type assumption and has public key size $\mathcal{O}(\lambda)$, but a ciphertext is only a single group element and the security reduction is quadratically tighter than the corresponding scheme by Jager and Kurek (ASIACRYPT 2018). - A very efficient adaptively-secure verifiable random function where proofs, public keys, and secret keys have size $\mathcal{O}(\log \lambda)$. As a technical contribution we introduce blockwise partitioning, which leverages the assumption that a cryptographic hash function is weak near-collision resistant to prove full adaptive security of cryptosystems

Lattice-based Programmable Hash Functions and Applications

Driven by the open problem raised by Hofheinz and Kiltz (Journal of Cryptology, 2012), we study the formalization of lattice-based programmable hash function (PHF), and give three types of concrete constructions by using several techniques such as a novel combination of cover-free sets and lattice trapdoors. Under the Inhomogeneous Small Integer Solution (ISIS) assumption, we show that any (non-trivial) lattice-based PHF is a collision-resistant hash function, which gives a direct application of this new primitive. We further demonstrate the power of lattice-based PHF by giving generic constructions of signature and identity-based encryption (IBE) in the standard model, which not only provide a way to unify several previous lattice-based schemes using the partitioning proof techniques, but also allow us to obtain new short signature schemes and IBE schemes from (ideal) lattices. Specifically, by instantiating the generic constructions with our Type-II and Type-III PHF constructions, we immediately obtain two short signatures and two IBE schemes with asymptotically much shorter keys. A major downside which inherits from our Type-II and Type-III PHF constructions is that we can only prove the security of the new signatures and IBEs in the bounded security model that the number Q of the adversary’s queries is required to be known in advance. Another downside is that the computational time of our new signatures and IBEs is a linear function of Q, which is large for typical parameters. To overcome the above limitations, we also give a refined way of using Type-II and Type-III PHFs to construct lattice-based short signatures with short verification keys in the full security model. In particular, our methods depart from the confined guessing technique of B¨ohl et al. (Eurocrypt’13) that was used to construct previous standard model short signature schemes with short verification keys by Ducas and Micciancio (Crypto’14) and by Alperin-Sheriff (PKC’15), and allow us to achieve much tighter security from weaker hardness assumptions

Quantum-resistant Anonymous IBE with Traceable Identities

Identity-based encryption (IBE), introduced by Shamir, eliminates the need for public-key infrastructure. The sender can simply encrypt a message by using the recipient\u27s identity (such as email or IP address) without needing to look up the public key. In particular, when ciphertexts of an IBE do not reveal recipient\u27s identity, this scheme is known as an anonymous IBE scheme. Recently, Blazy et al. (ARES \u2719) analyzed the trade-off between public safety and unconditional privacy in anonymous IBE and introduced a new notion that incorporates traceability into anonymous IBE, called anonymous IBE with traceable identities (AIBET). However, their construction is based on the discrete logarithm assumption, which is insecure in the quantum era. In this paper, we first formalize the consistency of tracing key of the AIBET scheme to ensure that a ciphertext cannot be traced with the use of wrong tracing keys. Subsequently, we present a generic formulation concept that can be used to transform structure-specific lattice-based anonymous IBE schemes into an AIBET. Finally, we apply this concept to Katsumata and Yamada\u27s compact anonymous IBE scheme (Asiacrypt \u2716) to obtain the first quantum-resistant AIBET scheme that is adaptively secure under the ring learning with errors assumption without random oracle

Partitioning via Non-Linear Polynomial Functions: More Compact IBEs from Ideal Lattices and Bilinear Maps

In this paper, we present new adaptively secure identity-based encryption (IBE) schemes. One of the distinguishing property of the schemes is that it achieves shorter public parameters than previous schemes. Both of our schemes follow the general framework presented in the recent IBE scheme of Yamada (Eurocrypt 2016), employed with novel techniques tailored to meet the underlying algebraic structure to overcome the difficulties arising in our specific setting. Specifically, we obtain the following: - Our first scheme is proven secure under the ring learning with errors (RLWE) assumption and achieves the best asymptotic space efficiency among existing schemes from the same assumption. The main technical contribution is in our new security proof that exploits the ring structure in a crucial way. Our technique allows us to greatly weaken the underlying hardness assumption (e.g., we assume the hardness of RLWE with a fixed polynomial approximation factor whereas Yamada\u27s scheme requires a super-polynomial approximation factor) while improving the overall efficiency. - Our second IBE scheme is constructed on bilinear maps and is secure under the $3$-computational bilinear Diffie-Hellman exponent assumption. This is the first IBE scheme based on the hardness of a computational/search problem, rather than a decisional problem such as DDH and DLIN on bilinear maps with sub-linear public parameter size

Asymptotically Compact Adaptively Secure Lattice IBEs and Verifiable Random Functions via Generalized Partitioning Techniques

In this paper, we focus on the constructions of adaptively secure identity-based encryption (IBE) from lattices and verifiable random function (VRF) with large input spaces. Existing constructions of these primitives suffer from low efficiency, whereas their counterparts with weaker guarantees (IBEs with selective security and VRFs with small input spaces) are reasonably efficient. We try to fill these gaps by developing new partitioning techniques that can be performed with compact parameters and proposing new schemes based on the idea. - We propose new lattice IBEs with poly-logarithmic master public key sizes, where we count the number of the basic matrices to measure the size. Our constructions are proven secure under the LWE assumption with polynomial approximation factors. They achieve the best asymptotic space efficiency among existing schemes that depend on the same assumption and achieve the same level of security. - We also propose several new VRFs on bilinear groups. In our first scheme, the size of the proofs is poly-logarithmic in the security parameter, which is the smallest among all the existing schemes with similar properties. On the other hand, the verification keys are long. In our second scheme, the size of the verification keys is poly-logarithmic, which is the smallest among all the existing schemes. The size of the proofs is sub-linear, which is larger than our first scheme, but still smaller than all the previous schemes

Compact Identity Based Encryption from LWE

We construct an identity-based encryption (IBE) scheme from the standard Learning with Errors (LWE) assumption that has \emph{compact} public-key and achieves adaptive security in the standard model. In particular, our scheme only needs 2 public matrices to support O(\log^2 \secparam)-bit length identity, and O(\secparam / \log^2 \secparam) public matrices to support \secparam-bit length identity. This improves over previous IBE schemes from lattices substantially. Additionally, our techniques from IBE can be adapted to construct a compact digital signature scheme, which achieves existential unforgeability under the standard Short Integer Solution (SIS) assumption with small polynomial parameters