Efficient and Secure Delegation of Exponentiation in General Groups to a Single Malicious Server

Group exponentiation is an important and relatively expensive operation used in many public-key cryptosystems and, more generally, cryptographic protocols. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that this operation is delegated from a computationally weaker client to a computationally stronger server. Solving this problem in the case of a single, possibly malicious, server, has remained open since the introduction of a formal model. In previous work we have proposed practical and secure solutions applicable to two classes of specific groups, related to well-known cryptosystems. In this paper, we investigate this problem in a general class of multiplicative groups, possibly going beyond groups currently subject to quantum cryptanalysis attacks. Our main results are efficient delegation protocols for exponentiation in these general groups. The main technique in our results is a reduction of the protocol's security probability (i.e., the probability that a malicious server convinces a client of an incorrect exponentiation output) that is more efficient than by standard parallel repetition. The resulting protocols satisfy natural requirements such as correctness, security, privacy and efficiency, even if the adversary uses the full power of quantum computers. In particular, in our protocols the client performs a number of online group multiplications smaller by 1 to 2 orders of magnitude than in a non-delegated computation

Secure and Efficient Delegation of Elliptic-Curve Pairing

Many public-key cryptosystems and, more generally, cryp- tographic protocols, use pairings as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client del- egates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client's pairing inputs and security of the client's output, in the sense of detecting, except for very small probability, any malicious server's at- tempt to convince the client of an incorrect pairing result. In this paper we show that the computation of bilinear pairings in all known pairing-based cryptographic protocols can be eciently, privately and securely delegated to a single, possibly malicious, server. Our tech- niques provides eciency improvements over past work in all input sce- narios, regardless on whether inputs are available to the parties in an oine phase or only in the online phase, and on whether they are public or have privacy requirements. The client's online runtime improvement is, for some of our protocols almost 1 order of magnitude, no matter which practical elliptic curve, among recently recommended ones, is used for the pairing realization

Cryptanalysis of Server-Aided RSA Protocols with Private-Key Splitting

International audienceWe analyze the security and the efficiency of interactive protocols where a client wants to delegate the computation of an RSA signature given a public key, a public message and the secret signing exponent. We consider several protocols where the secret exponent is splitted using some algebraic decomposition. We first provide an exhaustive analysis of the delegation protocols in which the client outsources a single RSA exponentiation to the server. We then revisit the security of the protocols RSA-S1 and RSA-S2 that were proposed by Matsumoto, Kato and Imai in 1988. We present an improved lattice-based attack on RSA-S1 and we propose a simple variant of this protocol that provides better efficiency for the same security level. Eventually, we present the first attacks on the protocol RSA-S2 that employs the Chinese Remainder Theorem to speed up the client's computation. The efficiency of our (heuristic) attacks has been validated experimentally

Delegating a Product of Group Exponentiations with Application to Signature Schemes

Many public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client's input exponent and security of the client's output, in the sense of detecting, except for very small probability, any malicious server's attempt to convince the client of an incorrect exponentiation result. Only recently, ecient protocols for the delegation of a xed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements. In this paper we show that a product of many xed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client's online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the rst delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q-order subgroup in Zp, for p; q primes, as well as their variants based on elliptic curves. Previous ecient delegation results seem limited to the delegation of single algorithms within cryptographic schemes

Delegated Time-Lock Puzzle

Time-Lock Puzzles (TLPs) are cryptographic protocols that enable a client to lock a message in such a way that a server can only unlock it after a specific time period. However, existing TLPs have certain limitations: (i) they assume that both the client and server always possess sufficient computational resources and (ii) they solely focus on the lower time bound for finding a solution, disregarding the upper bound that guarantees a regular server can find a solution within a certain time frame. Additionally, existing TLPs designed to handle multiple puzzles either (a) entail high verification costs or (b) lack generality, requiring identical time intervals between consecutive solutions. To address these limitations, this paper introduces, for the first time, the concept of a "Delegated Time-Lock Puzzle" and presents a protocol called "Efficient Delegated Time-Lock Puzzle" (ED-TLP) that realises this concept. ED-TLP allows the client and server to delegate their resource-demanding tasks to third-party helpers. It facilitates real-time verification of solution correctness and efficiently handles multiple puzzles with varying time intervals. ED-TLP ensures the delivery of solutions within predefined time limits by incorporating both an upper bound and a fair payment algorithm. We have implemented ED-TLP and conducted a comprehensive analysis of its overheads, demonstrating the efficiency of the construction

CONSTRUCTION OF EFFICIENT AUTHENTICATION SCHEMES USING TRAPDOOR HASH FUNCTIONS

In large-scale distributed systems, where adversarial attacks can have widespread impact, authentication provides protection from threats involving impersonation of entities and tampering of data. Practical solutions to authentication problems in distributed systems must meet specific constraints of the target system, and provide a reasonable balance between security and cost. The goal of this dissertation is to address the problem of building practical and efficient authentication mechanisms to secure distributed applications. This dissertation presents techniques to construct efficient digital signature schemes using trapdoor hash functions for various distributed applications. Trapdoor hash functions are collision-resistant hash functions associated with a secret trapdoor key that allows the key-holder to find collisions between hashes of different messages. The main contributions of this dissertation are as follows: 1. A common problem with conventional trapdoor hash functions is that revealing a collision producing message pair allows an entity to compute additional collisions without knowledge of the trapdoor key. To overcome this problem, we design an efficient trapdoor hash function that prevents all entities except the trapdoor key-holder from computing collisions regardless of whether collision producing message pairs are revealed by the key-holder. 2. We design a technique to construct efficient proxy signatures using trapdoor hash functions to authenticate and authorize agents acting on behalf of users in agent-based computing systems. Our technique provides agent authentication, assurance of agreement between delegator and agent, security without relying on secure communication channels and control over an agent’s capabilities. 3. We develop a trapdoor hash-based signature amortization technique for authenticating real-time, delay-sensitive streams. Our technique provides independent verifiability of blocks comprising a stream, minimizes sender-side and receiver-side delays, minimizes communication overhead, and avoids transmission of redundant information. 4. We demonstrate the practical efficacy of our trapdoor hash-based techniques for signature amortization and proxy signature construction by presenting discrete log-based instantiations of the generic techniques that are efficient to compute, and produce short signatures. Our detailed performance analyses demonstrate that the proposed schemes outperform existing schemes in computation cost and signature size. We also present proofs for security of the proposed discrete-log based instantiations against forgery attacks under the discrete-log assumption

Secure data sharing in cloud and IoT by leveraging attribute-based encryption and blockchain

“Data sharing is very important to enable different types of cloud and IoT-based services. For example, organizations migrate their data to the cloud and share it with employees and customers in order to enjoy better fault-tolerance, high-availability, and scalability offered by the cloud. Wearable devices such as smart watch share user’s activity, location, and health data (e.g., heart rate, ECG) with the service provider for smart analytic. However, data can be sensitive, and the cloud and IoT service providers cannot be fully trusted with maintaining the security, privacy, and confidentiality of the data. Hence, new schemes and protocols are required to enable secure data sharing in the cloud and IoT. This work outlines our research contribution towards secure data sharing in the cloud and IoT. For secure data sharing in the cloud, this work proposes several novel attribute-based encryption schemes. The core contributions to this end are efficient revocation, prevention of collusion attacks, and multi-group support. On the other hand, for secure data sharing in IoT, a permissioned blockchain-based access control system has been proposed. The system can be used to enforce fine-grained access control on IoT data where the access control decision is made by the blockchain-based on the consensus of the participating nodes”--Abstract, page iv