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Faster Homomorphic Trace-Type Function Evaluation

IEEE ACCESS 2021年 9卷 53061-53077页

作者： Ishimaki, Yu Yamana, Hayato Waseda Univ Tokyo 1698555 Japan Waseda Univ Fac Sci & Engn Tokyo 1698555 Japan

Homomorphic encryption enables computations over encrypted data without decryption, and can be used for outsourcing computations to some untrusted source. In homomorphic encryption based on the hardness of ring-learning with errors, offering promising security and functionality, a plaintext is represented by a polynomial. A plaintext is treated as a vector whose homomorphic evaluation enables component-wise addition and multiplication, as well as rotation across the components. We focus on a commonly used and time-consuming subroutine that enables homomorphically summing-up the components of the vector or homomorphically extracting the coefficients of the polynomial, and call it homomorphic trace-type function. We improve the efficiency of the homomorphic trace-type function evaluation. The homomorphic trace-type function evaluation is performed by repeating homomorphic rotation followed by addition (rotations-and-sums). To correctly add up a rotated ciphertext and an unrotated one, a special operation called key-switching should be performed on the rotated one. As key-switching is computationally expensive, the rotations-and-sums is inherently inefficient. We propose a more efficient trace-type function evaluation by using loop-unrolling, which is compatible with other optimization techniques such as hoisting, and can exploit multi-threading. We show that the rotations-and-sums is not the optimal solution in terms of runtime complexity and that a trade-off exists between time and space. Experimental results demonstrate that our proposed method works 1.32-2.12 times faster than the previous method.

关键词： Switches Encryption Runtime Complexity theory Outsourcing Optimization Licenses Homomorphic encryption secure outsourcing ring-learning with errors

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Design and analysis of pairing protocol for bluetooth enabled devices using R-LWEL attice-based cryptography

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JOURNAL OF INFORMATION SECURITY AND APPLICATIONS 2017年第Aug.期35卷 44-50页

作者： Gajbhiye, Samta Karmakar, Sanjeev Sharma, Monisha Sharma, Sanjay CSVTU SSGI SSTC Comp Sci & Engn DeptFET Bhilai Chhattisgarh India CSVTU BIT Comp Applicat Bhilai Chhattisgarh India CSVTU SSTC SSGI Elect & Telecommun DeptFET Bhilai Chhattisgarh India CSVTU BIT Dept Math Bhilai Chhattisgarh India

Secure Simple Pairing protocol of Bluetooth introduced in Bluetooth version 2.1 + EDR has security issues. Shared secret key using Elliptic Curve Diffie-Hellman algorithm generated in public key exchange phase, is subsequently used for authentication of devices and for computing Link key. The stability of Elliptic-Curve-Diffie-Hellman is based on the determination of order and structure of a finite Abelian group and computation of Elliptic Curve Discrete Logarithm (ECDLP) in a cyclic group. An algorithm for a quantum computers exists, that can figure out the inverse of Elliptic Curve Discrete Logarithm in polynomial time. Therefore, it demands a safe and sound cryptosystem for quantum computers. A revision to boost the security of pairing and authentication process in the Secure Simple Pairing (SSP) protocol of Bluetooth intended for classical and quantum computers is proposed called as Classiquantum Resistance Secure Simple Pairing protocol. On simulating the proposed protocol, it is studied that the proposed protocol is superior over SSP, as far as security performance by enhancement of key strength and by wrapping link key with two R-LWE secret key, is concerned. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Secure Simple Pairing Elliptic curve Diffie-Hellman Numeric comparison Quantum computers Lattice-based cryptography ring-learning with errors

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cuFE: High Performance Privacy Preserving Support Vector Machine With Inner-Product Functional Encryption

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTING 2024年第1期12卷 328-343页

作者： Han, Kyung Hyun Lee, Wai-Kong Karmakar, Angshuman Mera, Jose Maria Bermudo Hwang, Seong Oun Hongik Univ Dept Elect & Comp Engn Sejong 04066 South Korea Gachon Univ Dept Comp Engn Seongnam 13120 South Korea Katholieke Univ Leuven COSIC B-3000 Leuven Belgium

Privacy preservation is a sensitive issue in our modern society. It is becoming increasingly important in many applications in this ever-growing and highly connected digital era. Functional encryption is a computation on encrypted data paradigm that allows users to retrieve the evaluation of a function on encrypted data without revealing the data, thus effectively protecting users' privacy. However, existing functional encryption implementations are still very time-consuming for practical deployment, especially when applied to machine learning applications that involve a huge amount of data. In this paper, we present a high-performance implementation of inner-product functional encryption (IPFE) based on ring-learning with errors on graphics processing units. We propose novel techniques to parallelize the Gaussian sampling, which is one of the most time-consuming operations in the IPFE scheme. We further execute a systematic investigation to select the best strategy for implementing number theoretic transform and inverse number theoretic transform for different security levels. Compared to the existing AVX2 implementation of IPFE, our implementation on a RTX 2060 GPU device can achieve 34.24x, 40.02x, 156.30x, and 18.76x speed-up for Setup, Encrypt, KeyGen, and Decrypt respectively. Finally, we propose a fast privacy-preserving Support Vector Machine (SVM) application to classify data securely using our GPU-accelerated IPFE scheme. Experimental results show that our implementation can classify 100 inputs with 591 support vectors in 688 ms (less than a second), which is 33.12x faster than the AVX2.

关键词： Graphics processing units Encryption Cryptography Iron Machine learning Transforms Public key inner-product functional encryption privacy-preserving ring-learning with errors support vector machines

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Analysis of Error Dependencies on Newhope

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IEEE ACCESS 2020年 8卷 45443-45456页

作者： Song, Minki Lee, Seunghwan Shin, Dong-Joon Lee, Eunsang Kim, Young-Sik No, Jong-Seon Hanyang Univ Dept Elect & Comp Engn Seoul 04763 South Korea Seoul Natl Univ INMC Dept Elect & Comp Engn Seoul 08826 South Korea Chosun Univ Dept Informat & Commun Engn Gwangju 61452 South Korea

Among many submissions to NIST post-quantum cryptography (PQC) project, NewHope is a promising key encapsulation mechanism (KEM) based on the ring-learning with errors (ring-LWE) problem. Since NewHope is an indistinguishability (IND)-chosen ciphertext attack secure KEM by applying the Fujisaki-Okamoto transform to an IND-chosen plaintext attack secure public-key encryption, accurate calculation of decryption failure rate (DFR) is required to guarantee resilience against attacks that exploit decryption failures. However, the current upper bound (UB) on DFR of NewHope is rather loose because the compression noise, the effect of encoding/decoding of NewHope, and the approximation effect of centered binomial distribution are not fully considered. Furthermore, since NewHope is a ring-LWE based cryptography, there is a problem of error dependency among error coefficients, which makes accurate DFR calculation difficult. In this paper, we derive much tighter UB on DFR than the current UB by using constraint relaxation and union bound. Especially, the above-mentioned factors are all considered in the derivation of new UB and the centered binomial distribution is not approximated. Since the error dependency is also considered, the new UB is much closer to the real DFR than the current UB. Furthermore, the new UB is parameterized by using Chernoff-Cramer bound to facilitate the calculation of new UB for the parameters of NewHope. Since the new UB is much lower than the DFR requirement of PQC, this DFR margin can be used to improve NewHope. As a result, the security level and bandwidth efficiency of NewHope are improved by 7.2 % and 5.9 %, respectively.

关键词： Bandwidth efficiency Chernoff-Cramer bound decryption failure rate error dependency key encapsulation mechanism lattice-based cryptography NewHope NIST post-quantum cryptography relaxation ring-learning with errors security union bound upper bound

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An efficient and light weight polynomial multiplication for ideal lattice-based cryptography

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MULTIMEDIA TOOLS AND APPLICATIONS 2021年第2期80卷 3089-3120页

作者： Yadav, Vijay Kumar Verma, Shekhar Venkatesan, S. Indian Inst Informat Technol Allahabad Devghat Allahabad 211015 UP India

ring-learning with errors (ring-LWE) based cryptographic schemes such as signature, key exchange, and encryption require polynomial multiplication. This multiplication operation is the most time consuming and computationally rigorous process in ring-LWE. In order to improve the efficiency of the ring-LWE based schemes, most of the existing schemes use Fast Fourier Transform (FFT) based polynomial multiplication algorithm. It is known that Discrete Sine Transformation (DST) and Discrete Cosine Transformation (DCT) are faster than the FFT. The combination of DCT and DST is Discrete Trigonometric Transform (DTT). When we generalize DTT in terms of FFT form, it becomes Generalized Discrete Fourier Transform (GDFT). In this paper, we propose two new polynomial multiplication techniques using DTT and GDFT. When we applycircular convolutionandskew-circular convolutionon DTT or GDFT for the polynomial multiplication, it gives us wrong results. To overcome this issue, we usesymmetric convolutionoperation on DTT and GDFT. We implemented and compared the proposed polynomial multiplication schemes with the current state-of-the-art schemes in terms of computation and communication costs. The implementation results show that the proposed schemes DTT and GDFT perform more efficiently as compared to current state-of-the-art schemes in terms of computation and communication costs.

关键词： Fast fourier transform Discrete cosine transformation Number theoretic transform Lattice-based cryptography ring-learning with errors

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Efficient Reductions in Cyclotomic rings - Application to ring-LWE Based FHE Schemes 24th

Efficient Reductions in Cyclotomic Rings - Application to Ri...

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24th International Conference on Selected Areas in Cryptography (SAC)

作者： Bajard, Jean-Claude Eynard, Julien Hasan, Anwar Martins, Paulo Sousa, Leonel Zucca, Vincent Sorbonne Univ LIP6 CNRS UPMC Paris France Univ Waterloo Dept Elect & Comp Engn Waterloo ON Canada Univ Lisbon Inst Super Tecn INESC ID Lisbon Portugal

ISBN: (纸本)9783319725659;9783319725642

With Fully Homomorphic Encryption (FHE), it is possible to process encrypted data without having an access to the private-key. This has a wide range of applications, most notably the offloading of sensitive data processing. Most research on FHE has focused on the improvement of its efficiency, namely by introducing schemes based on ring-learning with errors (RLWE), and techniques such as batching, which allows for the encryption of multiple messages in the same ciphertext. Much of the related research has focused on RLWE relying on power-of-two cyclotomic polynomials. While it is possible to achieve efficient arithmetic with such polynomials, one cannot exploit batching. Herein, the efficiency of ring arithmetic underpinned by non-power-of-two cyclomotic polynomials is analyzed and improved. Two methods for polynomial reduction are proposed, one based on the Barrett reduction and the other on a Montgomery representation. Speed-ups up to 2.66 are obtained for the reduction operation using an i7-5960X processor when compared with a straightforward implementation of the Barrett reduction. Moreover, the proposed methods are exploited to enhance homomorphic multiplication of Fan-Vercauteren (FV) and Brakerski-Gentry-Vaikuntantahan (BGV) encryption schemes, producing experimental speed-ups up to 1.37.

关键词： Polynomial reduction Number Theoretic Transform Residue Number Systems ring-learning with errors Homomorphic encryption

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Lattice-Based Fine-grained Data Access Control and Sharing Scheme in Fog and Cloud Computing Environments for the 6G Systems 18

Lattice-Based Fine-grained Data Access Control and Sharing S...

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18th IEEE International Conference on Mobility, Sensing and Networking (MSN)

作者： Pei, Bei Zhou, Xianbin Jiang, Rui Minist Publ Secur Res Inst 3 Shanghai 200031 Peoples R China Southeast Univ Sch Cyber Sci & Engn Nanjing 210096 Peoples R China

ISBN: (纸本)9781665464574

The 6G (the sixth generation mobile communication) network is a heterogeneous network, which includes the cloud computing and the fog computing environment. And, the data securities in the 6G Systems may face great challenges. On the one hand, fine-grained data access control in fog and cloud computing environments is essential to the 6G network. On the other hand, quantum computing attacks may cause great security threats for the 6G network. In order to solve the above problems, we propose a lattice-based fine-grained data access control and sharing scheme in fog and cloud computing environments (LB-DACSS) for the 6G network. Firstly, our LB-DACSS scheme can achieve secure data sharing and fine-grained access control in fog and cloud computing environments. Secondly, we apply a lattice encryption algorithm to ensure our LB-DACSS scheme can withstand quantum computing attacks. Thirdly, our LB-DACSS scheme can achieve secure attribute revocation. Fourthly, we bind a unique secret value related to the user's attribute to construct the user's secret key. Finally, both formal security analysis and performance analysis show that our LB-DACSS scheme is efficient and secure.

关键词： Fine-grained Access Control Fog and Cloud Computing Environments Quantum computing attacks Lattice-Based Encryption ring-learning with errors Attribute Revocation

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Lattice-based lightweight cryptosystem

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INTERNATIONAL JOURNAL OF AD HOC AND UBIQUITOUS COMPUTING 2022年第3期41卷 135-146页

作者： Jain, Shivani Padmavathy, R. NIT Warangal Dept Comp Sci & Engn Warangal 506004 Telangana India

The lattice-based cryptographic constructions are emerging as a major contender of post quantum cryptography. The power-of-2 cyclotomic rings are widely used in lattice-based solutions but these rings have limitations in choice and are scarce. In the proposed work, prime cyclotomic rings are considered for investigation as they enjoy the same security and benefits as power-of-2 rings. In today's world of resource constraint devices, cryptographic constructions are expected to be simpler and lightweight, compared to conventional cryptography. The major concern in the deployment of lattice-based constructions is the size of the payloads. The byte modulus, which is an adaption of the LAC scheme, is used to overcome this problem. Our results show that the proposed scheme is more compact but reasonably secure and relatively efficient in comparison to other popular solutions such as LAC. Further, to withstand decryption failure, the popular BCH and Turbo code are used as error correction with the proposed scheme. The performance of BCH and Turbo code along with prime cyclotomic rings with or without byte modulus is studied and reported.

关键词： prime cyclotomic rings ring-learning with errors byte modulus lattice-based cryptography

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