Homomorphic Function Research Articles

LWR-based Quantum-Safe Pseudo-Random Number Generator

Learning with Rounding (LWR) is a lattice-based cryptographically hard problem which quantum computers find difficult to solve. LWR problem is a derandomized variant of Learning with Errors (LWE) where deterministic rounding is used to generate errors efficiently. LWR can construct a secure seed for Quantum-Safe Pseudo-Random Number Generator (QSPRNG). This study is an endeavor to construct a QSPRNG to generate a stream of pseudo-random bits through a Linear Feedback Shift Register (LFSR). The proposed QSPRNG uses secure seed as an input and a Homomorphic Function for preserving the security of the internal states of LFSRs. NIST statistical tests, ENT, and DIEHARD tests are performed on constructed PRNG for randomness analysis. Also, security and speed analysis for the proposed QSPRNG has been done to illustrate its possible future utilization in cryptography.

LWE Based Quantum-Resistant Pseudo-Random Number Generator

In the realm of cryptography, computational statistics, gaming, simulation processes, gambling, and other related fields, the design of Cryptographically Secure Pseudo-Random Number Generators (CSPRNGs) poses a significant challenge. With the rapid advancement of quantum computing, the imminent "quantum-threat" looms closer, posing a risk to our current cryptographically secure PRNGs. Consequently, it becomes crucial to address these threats seriously and develop diverse tools and techniques to ensure that cryptographically secure Pseudo-Random Number Generators (PRNGs) remain unbreakable by both classical and quantum computers. this paper presents a novel approach to constructing an effective Quantum-Resistant Pseudo-Random Number Generator (QRPRNG) using the principles of lattice-based Learning with Errors (LWE). LWE is considered quantum-resistant due to its reliance on the hardness of problems like the Shortest Vector Problem and Closest Vector Problem. Our work focuses on developing a QRPRNG that utilizes a Linear Feedback Shift Register (LFSR) to generate a stream of pseudo-random bits. To construct a secure seed for the QRPRNG, LWE is employed. The proposed QRPRNG incorporates a secure seed input to the LFSR, and employs a Homomorphic function to protect the security of the finite states within the LFSR. NIST statistical tests are conducted to evaluate the randomness of the generated output by the constructed QRPRNG. The proposed QRPRNG achieves a throughput of 35.172 Mbit/s.

Design of College English Online Teaching Platform Based on Dual-Server PEKS Framework

To improve the English learning efficiency of college students and improve the performance of network teaching, the research on the college English network teaching platform is carried out under the dual-server PEKS framework. After systematic testing and debugging, deployment and implementation, course migration, personnel training, and other links, the system has successfully completed deployment and implementation, which strongly support the research on the college English network teaching platform. The proposed dual-server PEKS search framework makes the teaching platform more secure by designing a linear homomorphic smooth projection HASH function and solves the security loopholes of traditional PEKS. Relevant research groups have conducted questionnaire surveys and information feedback on some teachers and students and generally have a good evaluation of the online teaching platform, indicating that the system has better realized the predetermined functions and effectively supported the research on the college English online teaching platform.

Certificateless Multisignature Scheme Suitable for Network Coding

Network coding can save the wireless network resources and improve the network throughput by combining the routing with coding. Traditional multisignature from certificateless cryptosystem is not suitable for the network coding environment. In this paper, we propose a certificateless multisignature scheme suitable for network coding (NC-CLMSS) by using the sequential multisignature and homomorphic hash function. NC-CLMSS is based on the CDH and ECDL problems, and its security is detailedly proved in the random oracle (RO) model. In NC-CLMSS, the source node generates a multisignature for the message, and the intermediate node linearly combines the receiving message. NC-CLMSS can resist the pollution and forgery attacks, and it has the fixed signature length and relatively high computation efficiency.

A New Approach to Define Algebraic Structure and Some Homomorphism Functions on Set of Pythagorean Triples and Set of Reciprocal Pythagorean Triples

A New Approach to Define Algebraic Structure and Some Homomorphism Functions on Set of Pythagorean Triples and Set of Reciprocal Pythagorean Triples

Wild boundary behaviour of homomorphic functions in domains of C^N

Wild boundary behaviour of homomorphic functions in domains of C^N

Practical and Provably Secure Distributed Aggregation: Verifiable Additive Homomorphic Secret Sharing

Often clients (e.g., sensors, organizations) need to outsource joint computations that are based on some joint inputs to external untrusted servers. These computations often rely on the aggregation of data collected from multiple clients, while the clients want to guarantee that the results are correct and, thus, an output that can be publicly verified is required. However, important security and privacy challenges are raised, since clients may hold sensitive information. In this paper, we propose an approach, called verifiable additive homomorphic secret sharing (VAHSS), to achieve practical and provably secure aggregation of data, while allowing for the clients to protect their secret data and providing public verifiability i.e., everyone should be able to verify the correctness of the computed result. We propose three VAHSS constructions by combining an additive homomorphic secret sharing (HSS) scheme, for computing the sum of the clients’ secret inputs, and three different methods for achieving public verifiability, namely: (i) homomorphic collision-resistant hash functions; (ii) linear homomorphic signatures; as well as (iii) a threshold RSA signature scheme. In all three constructions, we provide a detailed correctness, security, and verifiability analysis and detailed experimental evaluations. Our results demonstrate the efficiency of our proposed constructions, especially from the client side.

Privacy preserving cloud based secure digital locker using Paillier based difference function and chaos based cryptosystem

In this paper, a cloud based digital image locker system along with secure user authentication and novel image cryptosystem for preserving privacy of user images is proposed. Images require more storage space as compared to text. So, it is not feasible to store images locally in digital locker for everyone. By taking advantage of high speed Internet, it is feasible to use cloud for efficient storage of images. However, so many researchers feel that cloud technology is ‘honest-but-curious’. Cloud service follows the specified protocol completely, but it traces and analyzes the data to get the user’s important information. To overcome from such challenges, privacy of user’s identity and data should be preserved. The proposed authentication protocol is designed using Paillier based difference function which is based on Homomorphic cryptosystem. The speciality of homomorphic function is that computation on encrypted data is possible without decrypting the cipher text. Because of this, authentication process is done in encrypted environment. A novel image cryptosystem is designed based on Fridrich model. In this cryptosystem, confusion is performed at bit-level and diffusion is performed at pixel-level. Keys are modified in each round of confusion to achieve more security. Simulation and cryptanalysis prove the effectiveness of the proposed system.

HEAWS: An Accelerator for Homomorphic Encryption on the Amazon AWS FPGA

Homomorphic Encryption makes privacy preserving computing possible in a third party owned cloud by enabling computation on the encrypted data of users. However, software implementations of homomorphic encryption are very slow on general purpose processors. With the emergence of ‘FPGAs as a service’, hardware-acceleration of computationally heavy workloads in the cloud are getting popular. In this article we propose HEAWS, a domain-specific coprocessor architecture for accelerating homomorphic function evaluation on the encrypted data using high-performance FPGAs available in the Amazon AWS cloud. To the best of our knowledge, we are the first to report hardware acceleration of homomorphic encryption using Amazon AWS FPGAs. Utilizing the massive size of the AWS FPGAs, we design a high-performance and parallel coprocessor architecture for the FV homomorphic encryption scheme which has become popular for computing exact arithmetic on the encrypted data. We design parallel building blocks and apply pipeline processing at different levels of the implementation hierarchy, and on top of such optimizations we instantiate multiple parallel coprocessors in the FPGA to execute several homomorphic computations simultaneously. While the absolute computation time can be reduced by deploying more computational resources, efficiency of the HW/SW communication interface plays an important role in homomorphic encryption as it is computation as well as data intensive. Our implementation utilizes state of the art 512-bit XDMA feature of high bandwidth communication available in the AWS Shell to reduce the overhead of HW/SW data transfer. Moreover, we explore the design-space to identify optimal off-chip data transfer strategy for feeding the parallel coprocessors in a time-shared manner. As a result of these optimizations, our AWS-based accelerator can perform 613 homomorphic multiplications per second for a parameter set that enables homomorphic computations of depth 4. Finally, we benchmark an artificial neural network for privacy-preserving forecasting of energy consumption in a Smart Grid application and observe five times speed up.

Formulation of Pruning Maps with Rhythmic Neural Firing

Rhythmic neural firing is thought to underlie the operation of neural function. This triggers the construction of dynamical network models to investigate how the rhythms interact with each other. Recently, an approach concerning neural path pruning has been proposed in a dynamical network system, in which critical neuronal connections are identified and adjusted according to the pruning maps, enabling neurons to produce rhythmic, oscillatory activity in simulation. Here, we construct a sort of homomorphic functions based on different rhythms of neural firing in network dynamics. Armed with the homomorphic functions, the pruning maps can be simply expressed in terms of interactive rhythms of neural firing and allow a concrete analysis of coupling operators to control network dynamics. Such formulation of pruning maps is applied to probe the consolidation of rhythmic patterns between layers of neurons in feedforward neural networks.

Fully homomorphic encryption: a general framework and implementations

ABSTRACT Two data items a and b are stored on an untrusted database in their encrypted forms and , respectively. It is required that the encryption function be fully homomorphic, that is, E must satisfy the conditions and . This would allow the owner of the data, as well as an untrusted party operating the database on behalf of the owner, to perform operations directly on the encrypted data without the need for decryption. We propose a general framework that allows the derivation of such fully homomorphic functions. Two implementations of the general framework are then described that, in addition to being secure, enjoy the property of being efficient to compute.

Towards a rational bidding process of initial public offerings: a proposed model for secure auction based on homomorphic computation and secure hash functions

Towards a rational bidding process of initial public offerings: a proposed model for secure auction based on homomorphic computation and secure hash functions

Secure Hash Algorithm based Multiple Tenant User Security over Green Cloud Environment

This paper proposes a green cloud multi-tenant trust authentication with secure hash algorithm-3 (GreenCloud-MTASHA3) scheme to eliminate the unauthorised tenant access. GreenCloud-MTASHA3 scheme provide security over the multiple tenant requests by referring the confidentiality, integrity and availability rate. Confidentiality refers to limiting the unauthorised tenant's green cloud data access using the additive homomorphic privacy property in proposed scheme. Additive homomorphic privacy property-based encryption function is developed to improve the privacy preserving level. To attain the integrity level between the tenant requests and green cloud server machine in GreenCloud-MTASHA3 scheme an encrypted trust data management process is carried out. Trustworthiness of tenant request is measured to maintain the consistency level on security with minimal computational time. The proposed scheme attains the confidentiality, integrity and availability rate on communicating task. Experiment is conducted on factors such as secure computation confidence, authorised tenant computational time and space taken on storing encrypted data.

HEPCloud: An FPGA-based Multicore Processor for FV Somewhat Homomorphic Function Evaluation

In this paper, we present an FPGA based hardware accelerator ‘ $\mathsf{HEPCloud}$ ’ for homomorphic evaluations of medium depth functions which has applications in cloud computing. Our $\mathsf{HEPCloud}$ architecture supports the polynomial ring based homomorphic encryption scheme FV for a ring-LWE parameter set of dimension $2^{15}$ , modulus size 1,228-bit, and a standard deviation 50. This parameter-set offers a multiplicative depth 36 and at least 85 bit security. The processor of $\mathsf{HEPCloud}$ is composed of multiple parallel cores. To achieve fast computation time for such a large parameter-set, various optimizations in both algorithm and architecture levels are performed. For fast polynomial multiplications, we use CRT with NTT and achieve two dimensional parallelism in $\mathsf{HEPCloud}$ . We optimize the BRAM access, use a fast Barrett like polynomial reduction method, optimize the cost of CRT, and design a fast divide-and-round unit. Beside parallel processing, we apply pipelining strategy in several of the sequential building blocks to reduce the impact of sequential computations. Finally, we implement $\mathsf{HEPCloud}$ on a medium-size Xilinx Virtex 6 FPGA board ML605 board and measure its on-board performance. To store the ciphertexts during a homomorphic function evaluation, we use the large DDR3 memory of the ML605 board. Our FPGA-based implementation of $\mathsf{HEPCloud}$ computes a homomorphic multiplication in 26.67 s, of which the actual computation takes only 3.36 s and the rest is spent for off-chip memory access. It requires about 37,551 s to evaluate the SIMON-64/128 block cipher, but the per-block timing is only about 18 s because $\mathsf{HEPCloud}$ processes 2,048 blocks simultaneously. The results show that FPGA-based acceleration of homomorphic function evaluations is feasible, but fast memory interface is crucial for the performance.

Hardware Assisted Fully Homomorphic Function Evaluation and Encrypted Search

In this paper we propose a scheme to perform homomorphic evaluations of arbitrary depth with the assistance of a special module recryption box . Existing somewhat homomorphic encryption schemes can only perform homomorphic operations until the noise in the ciphertexts reaches a critical bound depending on the parameters of the homomorphic encryption scheme. The classical approach of bootstrapping also allows for arbitrary depth evaluations, but has a detrimental impact on the size of the parameters, making the whole setup inefficient. We describe two different instantiations of our recryption box for assisting homomorphic evaluations of arbitrary depth. The recryption box refreshes the ciphertexts by lowering the inherent noise and can be used with any instantiation of the parameters, i.e. there is no minimum size unlike bootstrapping. To demonstrate the practicality of the proposal, we design the recryption box on a Xilinx Virtex 6 FPGA board ML605 to support the FV somewhat homomorphic encryption scheme. The recryption box requires 0.43 ms to refresh one ciphertext. Further, we use this recryption box to boost the performance of encrypted search operation. On a 40 core Intel server, we can perform encrypted search in a table of $2^{16}$ entries in around 20 seconds. This is roughly 20 times faster than the implementation without recryption box.

Properties of two-layer FHE and their applications

Homomorphic equality test is a process, which was present in CRYPTO'2014 as a tool of refresh in a FHE (Alperin-Sheriff and Peikert, 2014), and has been used to test whether the plaintext of a given ciphertext is equal to a certain number. In fact, this powerful function induced many new applications about homomorphic encryption, in theory and practice, especially when homomorphic comparison and arithmetic functions are needed. Firstly, this paper extended three useful processes to Alperin-Sheriff and Peikert (2014), HTG, FDDec and negative, which are essential to many applications. HTG can transform a HEPerm ciphertext, a ciphertext of permutation matrix in Alperin-Sheriff and Peikert (2014), to a small GSW ciphertext. FDDec can decrypt a HEPerm ciphertext directly. Secondly, this paper concluded the rules of application about our scheme and constructed an efficiency l' bits comparator as an example of application. Lastly, this paper finds a solution, based on the equality test, for the problem of password leakage, which can protect the password and preserve the bypass function, when the database of password was compromised.

A Collusion-Resistant and Privacy-Preserving Data Aggregation Protocol in Crowdsensing System

With the pervasiveness and increasing capability of smart devices, mobile crowdsensing has been applied in more and more practical scenarios and provides a more convenient solution with low costs for existing problems. In this paper, we consider an untrusted aggregator collecting a group of users’ data, in which personal private information may be contained. Most previous work either focuses on computing particular functions based on the sensing data or ignores the collusion attack between users and the aggregator. We design a new protocol to help the aggregator collect all the users’ raw data while resisting collusion attacks. Specifically, the bitwise XOR homomorphic functions and aggregate signature are explored, and a novel key system is designed to achieve collusion resistance. In our system, only the aggregator can decrypt the ciphertext. Theoretical analysis shows that our protocol can capture k-source anonymity. In addition, extensive experiments are conducted to demonstrate the feasibility and efficiency of our algorithms.

Elliptic Curve Multiset Hash

A homomorphic, or incremental, multiset hash function, associates a hash value to arbitrary collections of objects (with possible repetitions) in such a way that the hash of the union of two collections is easy to compute from the hashes of the two collections themselves: it is simply their sum under a suitable group operation. In particular, hash values of large collections can be computed incrementally and/or in parallel. Homomorphic hashing is thus a very useful primitive with applications ranging from database integrity verification to streaming set/multiset comparison and network coding. Unfortunately, constructions of homomorphic hash functions in the literature are hampered by two main drawbacks: they tend to be much longer than usual hash functions at the same security level (e.g. to achieve a collision resistance of 2^128, they are several thousand bits long, as opposed to 256 bits for usual hash functions), and they are also quite slow. In this paper, we introduce the Elliptic Curve Multiset Hash (ECMH), which combines a usual bit string-valued hash function like BLAKE2 with an efficient encoding into binary elliptic curves to overcome both difficulties. On the one hand, the size of ECMH digests is essentially optimal: 2m-bit hash values provide O(2^m) collision resistance. On the other hand, we demonstrate a highly-efficient software implementation of ECMH, which our thorough empirical evaluation shows to be capable of processing over 3 million set elements per second on a 4 GHz Intel Haswell machine at the 128-bit security level---many times faster than previous practical methods.

Enhanced authentication for WLAN–EPS interworking systems

Novel authentication procedures for interworking wireless local area networks and evolved packet system are proposed for the 3GPP TS 33.402 (released 12 September 2014) standard. The novel solutions mainly exploit public-key fully homomorphic encryption schemes and one-way functions. This not only mitigates potential security threats, but significantly reduces the authentication load of the standard, especially in the case of 3GPP-IP access.

Aggregated-Proof Based Hierarchical Authentication Scheme for the Internet of Things

The Internet of Things (IoT) is becoming an attractive system paradigm to realize interconnections through the physical, cyber, and social spaces. During the interactions among the ubiquitous things, security issues become noteworthy, and it is significant to establish enhanced solutions for security protection. In this work, we focus on an existing U2IoT architecture (i.e., unit IoT and ubiquitous IoT), to design an aggregated-proof based hierarchical authentication scheme (APHA) for the layered networks. Concretely, 1) the aggregated-proofs are established for multiple targets to achieve backward and forward anonymous data transmission; 2) the directed path descriptors, homomorphism functions, and Chebyshev chaotic maps are jointly applied for mutual authentication; 3) different access authorities are assigned to achieve hierarchical access control. Meanwhile, the BAN logic formal analysis is performed to prove that the proposed APHA has no obvious security defects, and it is potentially available for the U2IoT architecture and other IoT applications.