Provable Security for Public Key Cryptosystems

Since certificateless public key cryptosystem can solve the complex certificate management problem in the traditional public key cryptosystem and the key escrow problem in identity-based cryptosystem and the pairing computation is slower than scalar multiplication over the elliptic curve, how to design certificateless signature (CLS) scheme without bilinear pairings is a challenge. In this paper, we first propose a new pairing-free CLS scheme, and then the security proof is presented in the random oracle model (ROM) under the discrete logarithm assumption. The proposed scheme is more efficient than the previous CLS schemes in terms of computation and communication costs and is more suitable for the applications of low-bandwidth environments.

In traditional public key signature, the public key of a signer is essentially a random string selected from a given set. It is infeasible to prove that a party is indeed the signer for a given signature. In general, the public key of a user needs a management authority to authenticate it. It results in that traditional public key cryptosystem (PKC) requires high maintenance cost for certificate management. Although, identity based cryptosystem (IBC) reduces the overhead of management, it suffers from the drawback of key escrow. Certificate-based cryptosystem combines the advantage of both PKC and IBC as it avoids the usage of certificates and does not suffer from key escrow. Recently, Liu et.al proposed an efficient Certificate-based signature and showed that the scheme was secure in the random oracles. Unfortunately, this paper shows that the scheme is insecure and discusses the flaws in their security proof. Then the corresponding attacks are given. To overcome the flaws, an improved scheme is proposed and the result shows that the scheme is provable secure against two game attacks of certificate-based signature in the random oracle model. The security is closely related to the computational Diffie-Hellman problem.KeywordsSecurity analysisattackimproved schemethe CDH problemcertificate-based signature

Confidentiality and authenticity are two fundamental security requirement of Public key Cryptography. These are achieved by encryption scheme and digital signatures respectively. Wireless sensor networks are commonly used for critical security tasks such as intrusion or tamper detection, and therefore must be protected. The article proposes a provable secure signcryption scheme in Random oracle model for wireless security. It enables nodes to authenticate each other by keeping the information confidential. Also achieve data integrity in the communication. Security of the scheme is based on q-Diffie Hellman Problem. We modify the scheme proposed by Libert et al. and proposed a provably secure scheme with respect to security under assumptions of Strong Diffie-Hellman (SDH) and Diffie-Hellman Inversion (DHI) in the random oracles.

Certificateless public key cryptography (CL-PKC) can solve the problems of certificate management in a public key infrastructure (PKI) and of key escrows in identity-based public key cryptography (ID-PKC). In CL-PKC, the key generation center (KGC) does not know the private keys of all users, and their public keys need not be certificated by certification authority (CA). At present, however, most certificateless encryption schemes are based on large integer factorization and discrete logarithms that are not secure in a quantum environment and the computation complexity is high. To solve these problems, we propose a new certificate-less encryption scheme based on lattices, more precisely, using the hardness of the learning with errors (LWE) problem. Compared with schemes based on large integer factorization and discrete logarithms, the most operations are matrixvector multiplication and inner products in our scheme, our approach has lower computation complexity. Our scheme can be proven to be indistinguishability chosen ciphertext attacks (IND-CPA) secure in the random oracle 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.

In this paper, we study the problem of secure integrating public key encryption with keyword search (PEKS) with public key data encryption (PKE). We argue the previous security model is not complete regarding keyword privacy and the previous constructions are secure only in the random oracle model. We solve these problems by first defining a new security model, then give a generic construction which is secure in the new security model without random oracles. Our construction is based on secure PEKS and tag-KEM/DEM schemes and achieves modular design. We also give some applications and extensions for our construction. For example, instantiate our construction with proper components, we have a concrete scheme without random oracles, whose performance is even competitive to the previous schemes with random oracles.

Traditional public key cryptosystem (PKC) requires high maintenance cost for certificate management. Although, identity based cryptosystem (IBC) reduces the overhead of management, it suffers from the drawback of key escrow. Certificate-based cryptosystem solves certificate revocation problem and eliminate third party queries in the traditional PKI. In addition, it also solves the inherent key escrow problem in the IBC. In this paper, we proposed an efficient certificate-based signature and the result shows that the scheme is provable secure against two game attacks of certificate-based signature in the random oracle model. The security is closely related to the difficulty of solving the discrete logarithm problem.

In 1976 Diffie and Hellman [152] described the framework for public-key cryptography. It was not until 1978 that three designs for public-key cryptosystems were published. Rivest, Shamir, and Adleman [431] showed how the discrete logarithm and factorization problems could be used to construct a public-key cryptosystem. This is the well-known RSA cryptosystem. Merkle and Hellman [339] used the knapsack problem in their construction. McEliece [329] built a system based on error correcting codes. Later in 1985 ElGamal [163] designed a public-key cryptosystem using the discrete logarithm problem. Koblitz [283] and Miller [346] suggested the use of elliptic curves in the design of public-key cryptosystems. Nowadays, there are quite a few more suggestions as to how to design public-key cryptosystems, but none so popular as the RSA and ElGamal cryptosystems.

Certificateless threshold signature scheme from bilinear maps

Security proof is a key criterion to judge the satisfaction of the security requirements in a protocol. Recently, Chang et al. proposed a password-based three-party key exchange protocol without server's public key. The security goal of the proposed protocol is to eliminate various security threats. In this paper, we show that the proposed protocol is still suffered from the denial of service and the man-in-the-middle attacks. We also prove that the probability of an adversary breaking the AKE security of the protocol is non-negligible in the random oracle model.

From the birth of the blockchain technology, multisignatures attract much attention as a tool for handling blockchain transactions. Concerning the application to the blockchain, multisignatures with public-key aggregation, which can compress public keys of signers to a single public key, is preferable to the standard multisignature because the public keys and the signature used in a transaction are stored to verify the transaction later. Several multisignature schemes with public key aggregation are proposed, however, there are no known schemes having a tight security reduction.We propose a first multisignature with public-key aggregation whose security is proven to be tightly secure under the DDH assumption in the random oracle model. Our multisignature is based on the DDH-based multisignature by Le, Yang, and Ghorbani, however, our security proof is different from theirs. The idea of our security proof originates from another DDH-based multisignature by Le, Bonnecaze, and Gabillon whose security proof is tightly one. By tailoring their security proof to a setting which admits the public-key aggregation, we can prove the tight security of our multisignature.

From the birth of the blockchain technology, multisignatures attract much attention as a tool for handling blockchain transactions. Concerning the application to the blockchain, multisignatures with public-key aggregation, which can compress public keys of signers to a single public key, is preferable to the standard multisignature because the public keys and the signature used in a transaction are stored to verify the transaction later. Several multisignature schemes with public key aggregation are proposed, however, there are no known schemes having a tight security reduction. We propose a first multisignature with public-key aggregation whose security is proven to be tightly secure under the DDH assumption in the random oracle model. Our multisignature is based on the DDH-based multisignature by Le, Yang, and Ghorbani, however, our security proof is different from theirs. The idea of our security proof originates from another DDH-based multisignature by Le, Bonnecaze, and Gabillon whose security proof is tightly one. By tailoring their security proof to a setting which admits the public-key aggregation, we can prove the tight security of our multisignature.

The invention of public-key cryptography was of central importance to the field of cryptography and provided answers to many key management problems for large scale networks. For all its benefits, however, public-key cryptography did not provide a comprehensive solution to the key management problem. Indeed, the possibilities brought forth by public-key cryptography heightened the need for sophisticated key management systems to answer questions such as the following:"How can I easily encrypt a file once for a number of different people using public-key cryptography?""If I lose my keys, how can I decrypt all of my files that were encrypted with those keys?""How do I know that I really have Alice’s public key and not the public key of someone pretending to be Alice?""How can I know that a public key is still trustworthy?"The paper discusses public key cryptography and its use in applications such as Key Agreement, Data Encryption and Digital Signature. The paper discusses some public key algorithms such as DH, RSA, and DSA and also gives working explanations of these algorithms.KeywordsShared SecretCertificate AuthorityCipher TextHash CodeDigital CertificateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The security of public-key cryptography relies on well-studied hard problems, problems for which we do not have efficient algorithms. Factorization and discrete logarithm are the two most known and used hard problems. Unfortunately, they can be easily solved on a quantum computer by Shor's algorithm. Also, the research area of cryptography demands for crypto-diversity which says that we should offer a range of hard problems for public-key cryptography. If one hard problem proves to be easy, we should be able to provide alternative solutions. Some of the candidates for post-quantum hard problems, i.e. problems which are believed to be hard even on a quantum computer, are the Learning Parity with Noise (LPN), the Learning with Errors (LWE) and the Shortest Vector Problem (SVP). A thorough study of these problems is needed in order to assess their hardness. In this thesis we focus on the algorithmic study of LPN. LPN is a hard problem that is attractive, as it is believed to be post-quantum resistant and suitable for lightweight devices. In practice, it has been employed in several encryption schemes and authentication protocols. At the beginning of this thesis, we take a look at the existing LPN solving algorithms. We provide the theoretical analysis that assesses their complexity. We compare the theoretical results with practice by implementing these algorithms. We study the efficiency of all LPN solving algorithms which allow us to provide secure parameters that can be used in practice. We push further the state of the art by improving the existing algorithms with the help of two new frameworks. In the first framework, we split an LPN solving algorithm into atomic steps. We study their complexity, how they impact the other steps and we construct an algorithm that optimises their use. Given an LPN instance that is characterized by the noise level and the secret size, our algorithm provides the steps to follow in order to solve the instance with optimal complexity. In this way, we can assess if an LPN instance provides the security we require and we show what are the secure instances for the applications that rely on LPN. The second framework handles problems that can be decomposed into steps of equal complexity. Here, we assume that we have an adversary that has access to a finite or infinite number of instances of the same problem. The goal of the adversary is to succeed in just one instance as soon as possible. Our framework provides the strategy that achieves this. We characterize an LPN solving algorithm in this framework and show that we can improve its complexity in the scenario where the adversary is restricted. We show that other problems, like password guessing, can be modeled in the same framework.

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.