A generic construction of CCA-secure deterministic encryption

Lossy trapdoor functions (LTFs), introduced by Peikert and Waters (STOC’08), have already been found to be a very useful tool in constructing complex cryptographic primitives in a black-box manner, such as one-way trapdoor functions, deterministic public-key encryption, CCA-secure public-key encryption, etc. Due to the existence of the side-channel attack, the leakage of trapdoor information in lossy trapdoor function systems can lead to the impossibility of provable security. Recently, Zhang et al. introduced a model of consecutive and continual leakage-resilient and updatable lossy trapdoor functions (ULTFs) and provided a concrete construction to achieve the security. Meanwhile, they proposed a consecutive and continual leakage-resilient public-key encryption scheme. However, in this paper, we demonstrate that the correctness of injective function can not be satisfied. Furthermore, the attacker can easily distinguish the evaluation key of ULTFs generated by the challenger according to the security model. Finally, we show two new constructions based on the continual leakage-resilient public-key encryption scheme of Brakerski et al. (FOCS 2010) and demonstrate the security of our scheme in the consecutive and continual leakage model.

Kakvi and Kiltz (EUROCRYPT'12) proposed the first tight security reduction for RSA full domain hash signature scheme (RSA-FDH) with public exponent e < N1/4 in the random oracle (RO) model, and they left an open problem which called for a tightly secure RSA-FDH for N1/4 < e < N. In this paper, we consider the improved RSA (iRSA) trapdoor functions, introduced by Cao (Science in China'01), are functions that the security can be strictly proved to be equivalent to the factoring. We show that iRSA-FDH has a tight security reduction for e < N. Technically we construct iRSA lossy trapdoor functions, and then we apply the lossiness of the iRSA trapdoor functions to obtain tight security reductions for iRSA-FDH in the RO model. Finally, we propose a tightly secure blind signature scheme based on our iRSA lossy trapdoor functions in the RO model.

Leakage of private information including private key has become a threat to the security of computing systems. It has become a common security requirement that a cryptographic scheme should withstand various leakage attacks, including continuous leakage attacks. In order to obtain an Identity-based encryption (IBE) scheme which can keep its original security in the continuous leakage setting, we propose a new construction method of IBE scheme with Chosen-ciphertext attacks (CCA) security, which can tolerate continuous leakage attacks on many private keys of each identity, and whose security is proved based on the hardness of the classical Decisional bilinear Diffie-Hellman (DBDH) assumption in the standard model. The leakage parameter is independent of the plaintext space and has the constant size.

Injective one-way trapdoor functions are one of the most fundamental cryptographic primitives. In this work we show how to derandomize lossy encryption (with long messages) to obtain lossy trapdoor functions, and hence injective one-way trapdoor functions.Bellare, Halevi, Sahai and Vadhan (CRYPTO ’98) showed that if Enc is an IND-CPA secure cryptosystem, and H is a random oracle, then x ↦ Enc(x,H(x)) is an injective trapdoor function. In this work, we show that if Enc is a lossy encryption with messages at least 1-bit longer than randomness, and h is a pairwise independent hash function, then x ↦ Enc(x,h(x)) is a lossy trapdoor function, and hence also an injective trapdoor function.The works of Peikert, Vaikuntanathan and Waters and Hemenway, Libert, Ostrovsky and Vergnaud showed that statistically-hiding 2-round Oblivious Transfer (OT) is equivalent to Lossy Encryption. In their construction, if the sender randomness is shorter than the message in the OT, it will also be shorter than the message in the lossy encryption. This gives an alternate interpretation of our main result. In this language, we show that any 2-message statistically sender-private semi-honest oblivious transfer (OT) for strings longer than the sender randomness implies the existence of injective one-way trapdoor functions. This is in contrast to the black box separation of injective trapdoor functions from many common cryptographic protocols, e.g. IND-CCA encryption.

Lossy trapdoor functions (LTDF) and all-but-one trapdoor functions (ABO-TDF) are fundamental cryptographic primitives. And given the recent advances in quantum computing, it would be much desirable to develop new and improved lattice-based LTDF and ABO-TDF. In this work, we provide more compact constructions of LTDF and ABO-TDF based on the learning with errors (LWE) problem. In addition, our LWE-based ABO-TDF can allow smaller system parameters to support super-polynomially many injective branches in the construction of CCA secure public key encryption. As a core building tool, we provide a more compact homomorphic symmetric encryption schemes based on LWE, which might be of independent interest. To further optimize the ABO-TDF construction, we employ the full rank difference encoding technique. As a consequence, the results presented in this work can substantially improve the performance of all the previous LWE-based cryptographic constructions based upon LTDF and ABO-TDF.

Condition proxy re-encryption is a promising security primitive for pervasive data sharing in such settings as cloud-based social networks and collaborations. However, it is challenging to create a secure condition proxy re-encryption scheme that is applicable for circumstances with multiple conditions. Based on secret sharing, Lan et al. proposed a conditional proxy re-encryption scheme that can support "AND" and "OR" gates over multiple conditions, and claimed that the scheme is secure against Chosen-Ciphertext Attack (CCA) in the random oracle model. However, by giving two concrete attacks, we show that their scheme is not CCA secure and even not secure against Chosen-Plaintext Attack (CPA) under their defined security model. Furthermore, we analyze why the scheme cannot satisfy the security mentioned above.

In 2011, Chris Peikert and Brent Waters proposed the concept of lossy trapdoor functions, which is an inherent and powerful cryptographic concept. Lossy trapdoor functions can be used for simple black-box constructing CCA encryption schemes, collision-resistent hash functions and oblivious transfer schemes. Chris Peikert and Brent Waters constructed lossy trapdoor functions based on decisional Diffie–Hellman assumption and learning with errors problem separately, which can be generalized to all-but-one trapdoor functions. In this paper, we generalize the lossy trapdoor functions and all-but-one trapdoor functions based on the polynomial ring separately, and we construct two types of trapdoor functions based on polynomial learning with errors assumption, which have more throughput and efficiency.

The goal of this paper is to design an id-based encryption (IBE) scheme that can flexibly tolerate leakage bounds, by only increasing the size of secret key proportionally, and the security level can be achieved to be against chosen-ciphertext attacks (CCA). As our main technical tool for CCA security, we introduce an initiation of all-but-one lossy filter, which is a simple version of all-but-many lossy filter to the leakage resilient settings. As our main result, we use the all-but-one lossy filter to construct an IBE scheme that is secure against leakage resilient chosen-ciphertext attacks (CCA), and the leakage rate is 1/2 &minus; ο(1).

Lossy trapdoor functions, introduced by Peikert and Waters (STOC’08), have received a lot of attention in the last years, because of their wide range of applications. The notion has been recently extended to the identity-based setting by Bellare et al. (Eurocrypt’12). An identity-based trapdoor function (IB-TDF) satisfying the lossy property introduced by Bellare et al. can be used to construct other cryptographic primitives in the identity-based setting: encryption schemes with semantic security under chosen-plaintext attacks, deterministic encryption schemes, and hedged encryption schemes that maintain some security when messages are encrypted using randomness of poor quality. However, the constructed primitives can be proved secure only against selective adversaries who select the target identity upfront.Our first contribution is an alternative definition for the lossiness of an identity-based trapdoor function. We prove that an IB-TDF satisfying the new property can be used to construct all the aforementioned primitives, in the identity-based setting, with security against adaptive adversaries. We further consider the new definition and its implications in the more general scenario of hierarchical identity-based cryptography, which has proved very useful both for practical applications and to establish theoretical relations with other cryptographic primitives (including encryption with chosen-ciphertext security or with forward-security).As a second contribution, we describe a pairing-based hierarchical IB-TDF satisfying the new definition of lossiness against either selective or, for hierarchies of constant depth, adaptive adversaries. This is also the first example of hierarchical trapdoor functions based on traditional (i.e., non-lattice-related) number theoretic assumptions. As a direct consequence of our two contributions, we obtain a hierarchical identity-based (HIB) encryption scheme with chosen-plaintext security, a HIB deterministic encryption scheme and a HIB hedged encryption scheme, all of them with security against adaptive adversaries.

We define new algorithmic problems and discuss their properties (in particular, we present a careful study of their computational complexity). We apply the new problems to design public key encryption protocols with semantic security relative to their decisional variants. We then show how to provide efficient schemes that are semantically secure under adaptive chosen ciphertext attacks in the random oracle model. Finally, we show that the ideas developed in this extended abstract can be used to design the most efficient known cryptosystem with semantic security under non-adaptive chosen ciphertext attacks in the standard security model.

The concept of policy-based cryptography is a promising paradigm for trust establishment and authorization in largescale open environments like the Internet and Mobile Networks. It aims at providing a framework for performing cryptographic operations with respect to policies formalized as monotone Boolean expressions written in standard normal forms. A policy involves conjunctions and disjunctions of conditions where each condition is fulfilled by a digital credential representing the signature of a specific credential issuer on a set of statements about a certain entity. Therefore, an entity fulfills a policy if any only if it has been issued a set of credentials fulfilling the combination of conditions specified by the policy.In this work, we focus on policy-based encryption schemes which allow to encrypt a message according to a policy so that only entities fulfilling the policy are able to decrypt the message. More generally, policy-based encryption belongs to an emerging family of encryption schemes sharing the ability to integrate encryption with access control structures. This ability is mainly enabled by bilinear pairings over elliptic curves and allows for several interesting applications in different contexts.A policy-based encryption scheme has to fulfill two primary requirements: on one hand, provable security under well defined attack models. On the other hand, efficiency, especially when dealing with the conjunctions and disjunctions of credential-based conditions.The contributions of our research work are twofold:1. The standard acceptable notion of security for public-key encryption schemes is indistinguishability against chosen ciphertext attacks. Hence, it is natural to require that a policy-based encryption scheme also satisfies this strong notion of security. However, the definition of this security notion must be adapted to the policy-based setting. Our first contribution is the definition of policy-oriented security model for policy-based encryption schemes as well as the development of an efficient policy-based encryption scheme that is provably secure under our security model in the random oracle model.2. Policy-based encryption schemes may suffer from the key-escrow property i.e. in addition to the legitimate holder of the credentials fulfilling the encryption policy, any collusion of credential issuers who are able to issue a set of credentials fulfilling the policy can decrypt the message. Our second contribution is to address this issue through the notion of policy-based public-key encryption. The latter allows encrypting a message not only with respect to a policy but also according to a public-key so that only an entity fulfilling the policy and having access to the corresponding private-key is able to decrypt the message. We developed a policy-based public-key encryption scheme from bilinear pairings and proved its security under the corresponding security model. Our proposal improves related work in terms of both security and efficiency.

For two years, public key encryption has become an essential topic in cryptography, namely with security against chosen-ciphertext attacks. This paper presents a generic technique to make a highly secure cryptosystem from any partially trapdoor one-way function, in the random oracle model. More concretely, any suitable problem providing a one-way cryptosystem can be efficiently derived into a chosen-ciphertext secure encryption scheme. Indeed, the overhead only consists of two hashing and a XOR. As application, we provide the most efficient El Gamal encryption variant, therefore secure relative to the computational Diffie-Hellman problem. Furthermore, we present the first scheme whose security is relative to the factorization of large integers, with a perfect reduction (factorization is performed within the same time and with identical probability of success as the security break).

Non-malleability is an important and intensively studied security notion for many cryptographic primitives. In the context of public key encryption, this notion means it is infeasible for an adversary to transform an encryption of some message m into one of a related message m' under the given public key. Although it has provided a strong security property for many applications, it still does not suffice for some scenarios like the system where the users could issue keys on-the-fly. In such settings, the adversary may have the power to transform the given public key and the ciphertext. To withstand such attacks, Fischlin introduced a stronger notion, known as complete non-malleability, which requires that the non-malleability property be preserved even for the adversaries attempting to produce a ciphertext of some related message under the transformed public key. To date, many schemes satisfying this stronger security have been proposed, but they are either inefficient or proved secure in the random oracle model. In this work, we put forward a new encryption scheme in the common reference string model. Based on the standard DBDH assumption, the proposed scheme is proved completely non-malleable secure against adaptive chosen ciphertext attacks in the standard model. In our scheme, the well-formed public keys and ciphertexts could be publicly recognized without drawing support from unwieldy techniques like non-interactive zero knowledge proofs or one-time signatures, thus achieving a better performance.

In public-key encryption (PKE), ciphertexts received by a receiver may be possibly correlated and the security of a PKE relies on honestly generated system parameters. Security against selective opening attacks (SOA) for PKE guarantees that even when an attacker has broken into a subset of honestly generated ciphertexts and opened them (i.e., seeing plaintexts and random bits), the unopened ciphertexts remain secure. While security against parameter subversion attacks (PSA) for PKE requires that even when the public system parameters are maliciously generated, a PKE scheme should be secure. In this paper, we initiate the study of PKE secure against both SOA and PSA. To capture SOA and PSA simultaneously, we formulate a new security notion called indistinguishability under selective opening attacks and parameter subversion attacks (IND-SO-PSA). Further, we define the lossy trapdoor function and all-but-many lossy trapdoor function in the presence of PSA (LTF-PSA and ABM-LTF-PSA correspondingly) and propose an instantiation with the efficiently-embeddable group (EG). Applying these new primitives, we construct a PKE scheme that is proven to be IND-SO-PSA secure.

Notes on a provably-secure certificate-based encryption against malicious CA attacks