Attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data. In (ciphertext-policy) ABE, a central trusted authority issues decryption keys for attributes $x$ to users. In turn, ciphertexts are associated with a decryption policy $\mathcal{P}$. Decryption succeeds and recovers the encrypted message whenever $\mathcal{P}(x) = 1$. Recently, Hohenberger, Lu, Waters, and Wu (Eurocrypt 2023) introduced the notion of...

In a secret-sharing scheme, a secret is shared among $n$ parties such that the secret can be recovered by authorized coalitions, while it should be kept hidden from unauthorized coalitions. In this work we study secret-sharing for $k$-slice access structures, in which coalitions of size $k$ are either authorized or not, larger coalitions are authorized and smaller are unauthorized. Known schemes for these access structures had smaller shares for small $k$'s than for large ones; hence our...

The issue of data and information security on the internet and social network has become more serious and pervasive in recent years. Cryptography is used to solve security problems. However, message encryption cannot merely meet the intended goals because access control over the encrypted messages is required in some applications. To achieve these requirements, attribute-based encryption (ABE) is used. This type of encryption provides both security and access structure for the network users...

Digital signatures ensure legitimate access through identity authentication. It is also used to build blocks in blockchains and to authenticate transactions. The Courtois-Finiasz-Sendrier (CFS) digital signature is a well-known code-based digital signature scheme based on the Niederreiter cryptosystem. The CFS signature, however, is not widely used due to the long processing time required by its signing algorithm. Most code-based digital signature schemes are based on Niederreiter. The...

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$. The collection of authorized/unauthorized sets can be captured by a monotone function $f:\{0,1\}^n\rightarrow \{0,1\}$. In this paper, we focus on monotone functions that all their min-terms are sets of size $a$, and on their duals -- monotone functions whose max-terms...

We present an advanced encoding framework for predicate encryption (PE) in prime order groups. Our framework captures a wider range of adaptively secure PE schemes such as non-monotonic attribute-based encryption by allowing PE schemes to have more flexible structures. Prior to our work, frameworks featuring adaptively secure PE schemes in prime order groups require strong structural restrictions on the schemes. In those frameworks, exponents of public keys and master secret keys of PE...

Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in the sense of duality of linear codes, gives another scheme for the dual access structure. These schemes have the same complexity, namely the largest share size relative to the secret size is the same. It is a long-standing open problem whether this fact...

A group-characterizable (GC) random variable is induced by a finite group, called main group, and a collection of its subgroups [Chan and Yeung 2002]. The notion extends directly to secret sharing schemes (SSS). It is known that multi-linear SSSs can be equivalently described in terms of GC ones. The proof extends to abelian SSSs, a more powerful generalization of multi-linear schemes, in a straightforward way. Both proofs are fairly easy considering the notion of dual for vector spaces and...

Abelian secret sharing schemes (SSS) are generalization of multi-linear SSS and similar to them, abelian schemes are homomorphic. There are numerous results on linear and multi-linear SSSs in the literature and a few ones on homomorphic SSSs too. Nevertheless, the abelian schemes have not taken that much attention. We present three main results on abelian and homomorphic SSSs in this paper: (1) abelian schemes are more powerful than multi-linear schemes (we achieve a constant factor...

In broadcast encryption schemes, a distribution center broadcasts an encrypted message to a subset $ S $ chosen from a universe of receivers and only the intended users are able to decrypt the message. Most broadcast encryption schemes do not provide anonymity and the identities of target receivers are sent in plaintext. However, in several applications, the authorized users' identities has the same sensitivity as the message itself. YRL, is an anonymous attribute-based broadcast encryption...

We propose a key-policy attribute-based encryption (KP-ABE) scheme with constant-size ciphertexts, whose semi-adaptive security is proven under the decisional linear (DLIN) assumption in the standard model. The access structure is expressive, that is given by non-monotone span programs. It also has fast decryption, i.e., a decryption includes only a constant number of pairing operations. As an application of our KP-ABE construction, we also propose a fully secure attribute-based signatures...

In this paper, we introduce a general notion of functional proxy-re-encryption (F-PRE), where a wide class of functional encryption (FE) is combined with proxy-re-encryption (PRE) mechanism. The PRE encryption system should reveal {\em minimal} information to a proxy, in particular, hiding parameters of re-encryption keys and of original ciphertexts which he manipulate is highly desirable. We first formulate such a {\em fully-anonymous} security notion of F-PRE including usual payload-hiding...

When assigning personal keys, stateful multicast key distribution (MKD) protocols usually rely on some type of dynamic group access structure which helps achieve a better tradeoff among storage, communication, and computation overheads. However, there exist some stateful MKD protocols whose personal key assignments are based on two static group access structures called Dual Hash Chain (DHC) and Binary Hash Tree (BHT). We introduce two new types of group access structures called Dual...

In this work, we present HIBE and ABE schemes which are ``unbounded" in the sense that the public parameters do not impose additional limitations on the functionality of the systems. In all previous constructions of HIBE in the standard model, a maximum hierarchy depth had to be fixed at setup. In all previous constructions of ABE in the standard model, either a small universe size or a bound on the size of attribute sets had to be fixed at setup. Our constructions avoid these limitations....

In this paper, we present two fully secure functional encryption schemes. Our first result is a fully secure attribute-based encryption (ABE) scheme. Previous constructions of ABE were only proven to be selectively secure. We achieve full security by adapting the dual system encryption methodology recently introduced by Waters and previously leveraged to obtain fully secure IBE and HIBE systems. The primary challenge in applying dual system encryption to ABE is the richer structure of keys...

In a compartmented access structure, there are disjoint participants C1, . . . ,Cm. The access structure consists of subsets of participants containing at least ti from Ci for i = 1, . . . ,m, and a total of at least t0 participants. Tassa [2] asked: whether there exists an efficient ideal secret sharing scheme for such an access structure? Tassa and Dyn [5] presented a solution using the idea of bivariate interpolation and the concept of dual program [9, 10]. For the purpose of practical...

The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. The optimization of this parameter for general access structures is an important and very difficult open problem in secret sharing. We explore in this paper the connections of this open problem with matroids and polymatroids. Matroid ports were introduced by Lehman in 1964. A forbidden minor characterization of matroid ports was given by Seymour in 1976....

In a distributed ring signature scheme, a subset of users cooperate to compute a distributed anonymous signature on a message, on behalf of a family of possible signing subsets. The receiver can verify that the signature comes from a subset of the ring, but he cannot know which subset has actually signed. In this work we use the concept of dual access structures to construct a distributed ring signature scheme which works with general families of possible signing subsets. The length of...

Error correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, we study the connections between codes, matroids, and a special class of secret sharing schemes: multiplicative linear secret sharing schemes. Such schemes are known to enable multi-party computation protocols secure against general (non-threshold) adversaries. Two open problems related to the complexity of multiplicative LSSSs are considered in this paper. The first...

In this paper we try to shed a new insight on Verifiable Secret Sharing Schemes (VSS). We first define a new ``metric" (with slightly different properties than the standard Hamming metric). Using this metric we define a very particular class of codes that we call {\it error-set correcting codes}, based on a set of forbidden distances which is a monotone decreasing set. Next we redefine the packing problem for the new settings and generalize the notion of error-correcting capability of...

We use a general treatment of both information-theoretic and cryptographic settings for Multi-Party Computation (MPC), based on the underlying linear secret sharing scheme. Our goal is to study the Monotone Span Program (MSP), which is the result of local multiplication of shares distributed by two given MSPs as well as the access structure that this resulting MSP computes. First, we expand the construction proposed by Cramer et~al. multiplying two different general access structures and we...