Dual Pairing Vector Spaces Research Articles

A Fully Adaptively Secure Threshold Signature Scheme Based on Dual-Form Signatures Technology

In t , n threshold signature schemes, any subset of t participants out of n can produce a valid signature, but any fewer than t participants cannot. Meanwhile, a threshold signature scheme should remain robust and unforgeable against up to t − 1 corrupted participants. This nonforgeability property is that even an adversary breaking into up to t − 1 participants should be unable to generate signatures on its own. Existential unforgeability against adaptive chosen message attacks is widely considered as a standard security notion for digital signature, and threshold signature should also follow this accordingly. However, there are two special attack models in a threshold signature scheme: one is the static corruption attack and the other is the adaptive corruption attack. Since the adaptive corruption model appears to better capture real threats, designing and proving threshold signature schemes secure in the adaptive corruption model has been focused on in recent years. If a threshold signature is secure under adaptive chosen message attack and adaptive corruption attack, we say it is fully adaptively secure. In this paper, based on the dual pairing vector spaces technology, we construct a threshold signature scheme and use Gerbush et al.’s dual-form signatures technology to prove our scheme, which is fully adaptively secure in the standard model, and then compare it to other schemes in terms of the efficiency and computation.

Expressive Attribute-Based Encryption with Constant-Size Ciphertexts from the Decisional Linear Assumption

We propose a key-policy attribute-based encryption (KP-ABE) scheme with constant-size ciphertexts, whose selective security is proven under the decisional linear (DLIN) assumption in the standard model. The proposed scheme also has semi-adaptively security, which is a recently proposed notion of security. 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 with constant-size secret (signing) keys from the DLIN. For achieving the above results, we employ a hierarchical reduction technique on dual pairing vector spaces and a modified form of pairwise independence lemma specific to our proposed schemes.

A new approach to practical function-private inner product encryption

Functional encryption (FE) is a novel paradigm supporting restricted decryption keys for a function f that allow one to learn f(xj) from the encryptions of messages xj. A natural and practical security requirement for FE is to keep not only messages x1,…,xq, but also functions f1,…fq, excluding inevitable information {fi(xj)}i,j∈[q], confidential from encryption and decryption keys for any polynomial a priori unknown number q, where fi and xj are adaptively chosen by adversaries. This security requirement is called full function privacy. In this paper, we focus on function-private FE for inner product functionality in the private key setting (referred to as inner product encryption (IPE)). To the best of our knowledge, only two approaches have been proposed for fully function-private IPE schemes in the private key setting. One is to employ a general transformation from (non-function-private) FE for general circuits (Brakerski and Segev, 2015 [20]). This approach requires computationally intensive cryptography tools, such as indistinguishability obfuscation (for non-function-private FE for general circuits), meaning it is inefficient. The other approach is more practical. It directly constructs an IPE scheme by using dual-pairing vector spaces (DPVS) (Bishop et al., 2015 [21], Datta et al., 2016 [22], and Tomida et al., 2016 [32]).We present a novel approach for practical function-private IPE schemes that does not employ DPVS, but instead uses generalizations of the Brakerski-Segev transformation. Our generalizations of the Brakerski-Segev transformation are easily combinable with existing (non-function-private) IPE schemes, as well as (non-function-private) FE schemes for general circuits on several levels of security. The proposed IPE scheme achieves better performance compared to the schemes proposed by Bishop et al. and Datta et al. The proposed IPE scheme preserves the same security level as previous schemes under the same complexity assumptions. Compared to the scheme proposed by Tomida et al., our scheme has comparable performance in terms of the size of ciphertext and decryption keys, but superior performance in terms of the size of the master key.

How to Watermark Cryptographic Functions by Bilinear Maps

We introduce a notion of watermarking for cryptographic functions and propose a concrete scheme for watermarking cryptographic functions. Informally speaking, a digital watermarking scheme for cryptographic functions embeds information, called a mark, into functions such as one-way functions and decryption functions of public-key encryption. There are two basic requirements for watermarking schemes. A mark-embedded function must be functionally equivalent to the original function. It must be difficult for adversaries to remove the embedded mark without damaging the original functionality. In spite of its importance and usefulness, there have only been a few theoretical works on watermarking for functions (or programs). Furthermore, we do not have rigorous definitions of watermarking for cryptographic functions and concrete constructions. To solve the problem above, we introduce a notion of watermarking for cryptographic functions and define its security. Furthermore, we present a lossy trapdoor function (LTF) based on the decisional bilinear Diffie-Hellman problem problem and a watermarking scheme for the LTF. Our watermarking scheme is secure under the symmetric external Diffie-Hellman assumption in the standard model. We use techniques of dual system encryption and dual pairing vector spaces (DPVS) to construct our watermarking scheme. This is a new application of DPVS.

Fully Secure Functional Encryption with a Large Class of Relations from the Decisional Linear Assumption

This paper presents a fully secure (adaptively secure) practical functional encryption scheme for a large class of relations, that are specified by non-monotone access structures combined with inner-product relations. The security is proven under a standard assumption, the decisional linear assumption, in the standard model. Our scheme is constructed on the concept of dual pairing vector spaces and a hierarchical reduction technique on this concept is employed for the security proof. The proposed functional encryption scheme covers, as special cases, (1) key-policy, ciphertext-policy and unified-policy attribute-based encryption with non-monotone access structures, (2) (hierarchical) attribute-hiding functional encryption with inner-product relations and functional encryption with nonzero inner-product relations and (3) spatial encryption and a more general class of encryption than spatial encryption.

Dual Pairing Vector Spaces and Their Applications

Dual Pairing Vector Spaces and Their Applications

Adaptively Anonymous Public-Key Broadcast Encryption Scheme without Random Oracle

Anonymous is one of the most important security properties for kinds of Internet applications. In this paper, we consider the privacy-preserving problem in the context of public key broadcast encryption. We provide a new security definition for anonymous public key broadcast encryption, and construct a new scheme. To achieve anonymous, we blind the ciphertexts using the random factors. Moreover, we use a pair of orthogonal bases to construct secret key and ciphertexts for proper decryption. Our anonymous publickey broadcast encryption scheme can be proven in the adaptive model without random oracle. The key technique used to obtain our result is an elaborate combination of the dual system encryption proposed by Waters and a new approach on bilinear pairings using the notion of dual pairing vector spaces (DPVS) proposed by Okamoto and Takasima.

Efficient threshold public key encryption with full security based on dual pairing vector spaces

SUMMARYMost robust and noninteractive threshold public key encryption (PKE) schemes have only been proven secure against chosen‐ciphertext attacks under the static corruption model; yet, the dynamic corruption model is more reasonable. In this paper, on the basis of bilinear groups of prime order and dual pairing vector spaces, we propose a threshold PKE scheme that is noninteractive, robust and, secure against adaptive chosen‐ciphertext attacks under the dynamic corruption model without random oracles. Moreover, our scheme is shown to be more efficient than currently existing fully secure threshold PKE schemes. Copyright © 2013 John Wiley & Sons, Ltd.

Shorter identity-based encryption via asymmetric pairings

We present efficient identity-based encryption (IBE) under the symmetric external Diffie---Hellman (SXDH) assumption in bilinear groups; our scheme also achieves anonymity. In our IBE scheme, all parameters have constant numbers of group elements, and are shorter than those of previous constructions based on decisional linear (DLIN) assumption. Our construction uses both dual system encryption (Waters, CRYPTO 2009) and dual pairing vector spaces (Okamoto and Takashima, Pairing 2008; ASIACRYPT 2009). Specifically, we show how to adapt the recent DLIN-based instantiation of Lewko (EUROCRYPT 2012) to the SXDH assumption. To our knowledge, this is the first work to instantiate either dual system encryption or dual pairing vector spaces under the SXDH assumption. Furthermore, our work could be extended to many other functional encryption. In Particular, we show how to instantiate our framework to inner product encryption and key-policy functional encryption. All parameters of our constructions are shorter than those of DLIN-based constructions.