Counting superspecial Richelot isogenies by reduced automorphism groups (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)

The recent cryptanalysis by Costello and Smith [10] employed the subgraphs whose vertices consist of decomposed principally polarized abelian varieties, hence it is important to study the subgraphs in isogeny-based cryptography. Katsura and Takashima [22] initiated the investigation of the decomposed abelian surface subgraphs in the genus-2 case. This paper surveys the work, aiming to provide a kind of handbook for applying our results to cryptography

Decomposed Richelot isogenies of Jacobian varieties of hyperelliptic curves and generalized Howe curves

We advance previous studies on decomposed Richelot isogenies (Katsura--Takashima (ANTS 2020) and Katsura (ArXiv 2021)) which are useful for analysing superspecial Richelot isogeny graphs in cryptography. We first give a characterization of decomposed Richelot isogenies between Jacobian varieties of hyperelliptic curves of any genus. We then define generalized Howe curves, and present two theorems on their relationships with decomposed Richelot isogenies. We also give new examples including a non-hyperelliptic (resp.\,hyperelliptic) generalized Howe curve of genus 5 (resp.\,of genus 4).Comment: 15 pages. We added some explanations of back groun

New Proof Techniques for DLIN-Based Adaptively Secure Attribute-Based Encryption

We propose adaptively secure attribute-based encryption (ABE) schemes for boolean formulas over large universe attributes from the decisional linear (DLIN) assumption, which allow attribute reuse in an available formula without the previously employed redundant multiple encoding technique. Thus our KP-(resp. CP-)ABE has non-redundant ciphertexts (resp. secret keys). For achieving the results, we develop a new encoding method for access policy matrix for ABE, by decoupling linear secret sharing (LSS) into its matrix and randomness, and partially randomizing the LSS shares in simulation. The new techniques are of independent interest and we expect it will find another application than ABE

Tighter Security for Efficient Lattice Cryptography via the Rényi Divergence of Optimized Orders

In security proofs of lattice based cryptography, bounding the closeness of two probability distributions is an important procedure. To measure the closeness, the Rényi divergence has been used instead of the classical statistical distance. Recent results have shown that the Rényi divergence offers security reductions with better parameters, e.g. smaller deviations for discrete Gaussian distributions. However, since previous analyses used a fixed order Rényi divergence, i.e., order two, they lost tightness of reductions. To overcome the deficiency, we adaptively optimize the orders based on the advantages of the adversary for several lattice-based schemes. The optimizations enable us to prove the security with both improved efficiency and tighter reductions. Indeed, our analysis offers security reductions with smaller parameters than the statistical distance based analysis and the reductions are tighter than those of previous Rényi divergence based analyses. As applications, we show tighter security reductions for sampling discrete Gaussian distributions with smaller precomputed tables for Bimodal Lattice Signature Scheme (BLISS), and the variants of learning with errors (LWE) problem and the small integer solution (SIS) problem called k-LWE and k-SIS, respectively

Efficient Attribute-Based Signatures for Non-Monotone Predicates in the Standard Model

This paper presents a fully secure (adaptive-predicate unforgeable and private) attribute-based signature (ABS) scheme in the standard model. The security of the proposed ABS scheme is proven under standard assumptions, the decisional linear (DLIN) assumption and the existence of collision resistant (CR) hash functions. The admissible predicates of the proposed ABS scheme are more general than those of the existing ABS schemes, i.e., the proposed ABS scheme is the first to support general non-monotone predicates, which can be expressed using NOT gates as well as AND, OR, and Threshold gates, while the existing ABS schemes only support monotone predicates. The proposed ABS scheme is comparably as efficient as (several times worse than) one of the most efficient ABS schemes, which is proven to be secure in the generic group model

Adaptively Attribute-Hiding (Hierarchical) Inner Product Encryption

This paper proposes the first inner product encryption (IPE) scheme that is adaptively secure and fully attribute-hiding (attribute-hiding in the sense of the definition by Katz, Sahai and Waters), while the existing IPE schemes are either fully attribute-hiding but selectively secure or adaptively secure but weakly attribute-hiding. The proposed IPE scheme is proven to be adaptively secure and fully attribute-hiding under the decisional linear assumption in the standard model. The IPE scheme is comparably as efficient as the existing attribute-hiding IPE schemes. We also present a variant of the proposed IPE scheme with the same security that achieves shorter public and secret keys. A hierarchical IPE scheme can be constructed that is also adaptively secure and fully attribute-hiding under the same assumption. In this paper, we extend the dual system encryption technique by Waters into a more general manner, in which new forms of ciphertext and secret keys are employed and new types of information theoretical tricks are introduced along with several forms of computational reduction

Pairing Cryptography Meets Isogeny: A New Framework of Isogenous Pairing Groups

We put forth a new mathematical framework called Isogenous Pairing Groups (IPG) and new intractable assumptions in the framework, the Isogenous DBDH (Isog-DBDH) assumption and its variants. Three operations, i.e., exponentiation, pairing and isogeny on elliptic curves are treated under a unified notion of trapdoor homomorphisms, and combinations of the operations have potential new cryptographic applications, in which the compatibility of pairing and isogeny is a main ingredient in IPG. As an example, we present constructions of (small and large universe) key-policy attribute-based encryption (KP-ABE) schemes secure against pre-challenge quantum adversaries in the quantum random oracle model (QROM). Note that our small universe KP-ABE has asymptotically the same efficiency as Goyal et al.\u27s small universe KP-ABE, which has only classical security. As a by-product, we also propose practical (hierarchical) identity-based encryption ((H)IBE) schemes secure against pre-challenge quantum adversaries in the QROM from isogenies, which are based on the Boneh-Franklin IBE and the Gentry-Silverberg HIBE, respectively

Compact FE for Unbounded Attribute-Weighted Sums for Logspace from SXDH

This paper presents the first functional encryption (FE) scheme for the attribute-weighted sum (AWS) functionality that supports the uniform model of computation. In such an FE scheme, encryption takes as input a pair of attributes (x,z) where the attribute x is public while the attribute z is private. A secret key corresponds to some weight function f, and decryption recovers the weighted sum f(x)z. This is an important functionality with a wide range of potential real life applications, many of which require the attribute lengths to be flexible rather than being fixed at system setup. In the proposed scheme, the public attributes are considered as binary strings while the private attributes are considered as vectors over some finite field, both having arbitrary polynomial lengths that are not fixed at system setup. The weight functions are modeled as Logspace Turing machines. Prior schemes [Abdalla, Gong, and Wee, CRYPTO 2020 and Datta and Pal, ASIACRYPT 2021] could only support non-uniform Logspace. The proposed scheme is built in asymmetric prime-order bilinear groups and is proven adaptively simulation secure under the well-studied symmetric external Diffie-Hellman (SXDH) assumption against an arbitrary polynomial number of secret key queries both before and after the challenge ciphertext. This is the best possible level of security for FE as noted in the literature. As a special case of the proposed FE scheme, we also obtain the first adaptively simulation secure inner-product FE (IPFE) for vectors of arbitrary length that is not fixed at system setup. On the technical side, our contributions lie in extending the techniques of Lin and Luo [EUROCRYPT 2020] devised for payload hiding attribute-based encryption (ABE) for uniform Logspace access policies avoiding the so-called “one-use” restriction in the indistinguishability-based security model as well as the “three-slot reduction” technique for simulation-secure attribute-hiding FE for non-uniform Logspace devised by Datta and Pal [ASIACRYPT 2021] to the context of simulation-secure attribute-hiding FE for uniform Logspace