Iterative DNA Coding Scheme With GC Balance and Run-Length Constraints Using a Greedy Algorithm

In this paper, we propose a novel iterative encoding algorithm for DNA storage to satisfy both the GC balance and run-length constraints using a greedy algorithm. DNA strands with run-length more than three and the GC balance ratio far from 50\% are known to be prone to errors. The proposed encoding algorithm stores data at high information density with high flexibility of run-length at most $m$ and GC balance between $0.5\pm\alpha$ for arbitrary $m$ and $\alpha$. More importantly, we propose a novel mapping method to reduce the average bit error compared to the randomly generated mapping method, using a greedy algorithm. The proposed algorithm is implemented through iterative encoding, consisting of three main steps: randomization, M-ary mapping, and verification. It has an information density of 1.8616 bits/nt in the case of $m=3$, which approaches the theoretical upper bound of 1.98 bits/nt, while satisfying two constraints. Also, the average bit error caused by the one nt error is 2.3455 bits, which is reduced by $20.5\%$, compared to the randomized mapping.Comment: 19 page

A Modified pqsigRM: RM Code-Based Signature Scheme

We propose a novel signature scheme based on a modified Reed--Muller (RM) code, which reduces the signing complexity and key size compared to existing code-based signature schemes. This cheme is called as the modified pqsigRM, and corresponds to an improvement of pqsigRM, the proposal submitted to NIST. Courtois, Finiasz, and Sendrier (CFS) proposed a code-based signature scheme using the Goppa codes based on a full domain hash approach. However, owing to the properties of Goppa codes, the CFS signature scheme has drawbacks such as signing complexity and large key size. We overcome these disadvantages of the CFS signature scheme using partially permuted RM code and its decoding, which finds a near codeword for any received vector. Using a partially permuted RM code, the signature scheme resists various known attacks on the RM code-based cryptography. Additionally, we further modify the RM codes by row insertion/deletion of the generator matrix and thereafter resolve the problems reported in the post-quantum cryptography forum by NIST, such as the Hamming weight distribution of the public code

Near-optimal Polynomial for Modulus Reduction Using L2-norm for Approximate Homomorphic Encryption

Since Cheon et al. introduced an approximate homomorphic encryption scheme for complex numbers called Cheon-Kim-Kim-Song (CKKS) scheme, it has been widely used and applied in real-life situations, such as privacy-preserving machine learning. The polynomial approximation of a modulus reduction is the most difficult part of the bootstrapping for the CKKS scheme. In this paper, we cast the problem of finding an approximate polynomial for a modulus reduction into an L2-norm minimization problem. As a result, we find an approximate polynomial for the modulus reduction without using the sine function, which is the upper bound for the approximation of the modulus reduction. With the proposed method, we can reduce the degree of the polynomial required for an approximate modulus reduction, while also reducing the error compared with the most recent result reported by Han et al. (CT-RSA\u27 20). Consequently, we can achieve a low-error approximation, such that the maximum error is less than $2^{-40}$ for the size of the message $m/q\approx 2^{-10}$. By using the proposed method, the constraint of $q = O(m^{3/2})$ is relaxed as $O(m)$, and thus the level loss in bootstrapping can be reduced. The solution of the cast problem is determined in an efficient manner without iteration

Efficient Error Control for Scalable Media Transmission over 3G Broadcast Networks

Abstract. Broadcast and mobile phone technologies have now combined to provide wireless multimedia services. 3GPP2 has introduced the Broadcast and Multicast Services (BCMCS) architecture in a 3G wireless network. BCMCS are capable of supplying multimedia content, which requires successive frames to arrive within a specific time interval. We analyze the execution time of Reed-Solomon decoding, which is the MAC-layer forward error correction scheme used in cdma2000 1xEV-DO BCMCS, under different air channel conditions. The results show that the time constraints of MPEG-4 cannot be guaranteed by Reed-Solomon decoding when the packet loss rate (PLR) is high, due to its long computation time on current hardware. To alleviate this problem, we propose three error control schemes. Our static scheme bypasses Reed-Solomon decoding at the mobile node to satisfy the MPEG-4 time constraint when the PLR exceeds a given boundary. Our second, dynamic scheme corrects errors in a best-effort manner within the time constraint, instead of giving up altogether when the PLR is high. The third, video-aware dynamic scheme fixes errors in a similar way to the dynamic scheme, but in a priority-driven manner which improves the quality of the final video. Extensive simulation results show the effectiveness of our schemes compared to the original FEC scheme

Compensative microstepping based position control with passive nonlinear adaptive observer for permanent magnet stepper motors

This paper presents a compensative microstepping based position control with passive nonlinear adaptive observer for permanent magnet stepper motor. Due to the resistance uncertainties, a position error exists in the steady-state, and a ripple of position error appears during operation. The compensative microstepping is proposed to remedy this problem. The nonlinear controller guarantees the desired currents. The passive nonlinear adaptive observer is designed to estimate the phase resistances and the velocity. The closed-loop stability is proven using input to state stability. Simulation results show that the position error in the steady-state is removed by the proposed method if the persistent excitation conditions are satisfied. Furthermore, the position ripple is reduced, and the Lissajou curve of the phase currents is a circle

Amortized Large Look-up Table Evaluation with Multivariate Polynomials for Homomorphic Encryption

We present a new method for efficient look-up table (LUT) evaluation in homomorphic encryption (HE), based on Ring-LWE-based HE schemes, including both integer-message schemes such as Brakerski-Gentry-Vaikuntanathan (BGV) and Brakerski/Fan-Vercauteren (BFV), and complex-number-message schemes like the Cheon-Kim-Kim-Song (CKKS) scheme. Our approach encodes bit streams into codewords and translates LUTs into low-degree multivariate polynomials, allowing for the simultaneous evaluation of multiple independent LUTs with minimal overhead. To mitigate noise accumulation in the CKKS scheme, we propose a novel noise-reduction technique, accompanied by proof demonstrating its effectiveness in asymptotically decreasing noise levels. We demonstrate our algorithm\u27s effectiveness through a proof-of-concept implementation, showcasing significant efficiency gains, including a 0.029ms per slot evaluation for 8-input, 8-output LUTs and a 280ms amortized decryption time for AES-128 using CKKS on a single GPU. This work not only advances LUT evaluation in HE but also introduces a transciphering method for the CKKS scheme utilizing standard symmetric-key encryption, bridging the gap between discrete bit strings and numerical data

Privacy-Preserving Machine Learning with Fully Homomorphic Encryption for Deep Neural Network

Fully homomorphic encryption (FHE) is one of the prospective tools for privacypreserving machine learning (PPML), and several PPML models have been proposed based on various FHE schemes and approaches. Although the FHE schemes are known as suitable tools to implement PPML models, previous PPML models on FHE encrypted data are limited to only simple and non-standard types of machine learning models. These non-standard machine learning models are not proven efficient and accurate with more practical and advanced datasets. Previous PPML schemes replace non-arithmetic activation functions with simple arithmetic functions instead of adopting approximation methods and do not use bootstrapping, which enables continuous homomorphic evaluations. Thus, they could not use standard activation functions and could not employ a large number of layers. The maximum classification accuracy of the existing PPML model with the FHE for the CIFAR-10 dataset was only 77% until now. In this work, we firstly implement the standard ResNet-20 model with the RNS-CKKS FHE with bootstrapping and verify the implemented model with the CIFAR-10 dataset and the plaintext model parameters. Instead of replacing the non-arithmetic functions with the simple arithmetic function, we use state-of-the-art approximation methods to evaluate these non-arithmetic functions, such as the ReLU, with sufficient precision [1]. Further, for the first time, we use the bootstrapping technique of the RNS-CKKS scheme in the proposed model, which enables us to evaluate a deep learning model on the encrypted data. We numerically verify that the proposed model with the CIFAR-10 dataset shows 98.67% identical results to the original ResNet-20 model with non-encrypted data. The classification accuracy of the proposed model is 90.67%, which is pretty close to that of the original ResNet-20 CNN model...Comment: 12 pages, 4 figure

Bootstrapping on SEAL

We implement bootstrapping of RNS-CKKS on SEAL, a homomorphic encryption library released by Microsoft. And we measure the accuracy of encrypted data after bootstrapping for various parameters, which allows us to do more than thousands of homomorphic operations

Improved Reduction Between SIS Problems over Structured Lattices

Lattice-based cryptographic scheme is constructed based on hard problems on an algebraic structured lattice such as the short integer solution (SIS) problems. These problems are called ring-SIS (R-SIS) and its generalized version, module-SIS (M-SIS). Generally, it has been considered that problems defined on the module-lattice are more difficult than the problems defined on the ideal-lattice. However, Koo, No, and Kim showed that R-SIS is more difficult than M-SIS under some norm constraints of R-SIS. However, this reduction has problems that the rank of the module is limited to about half of the instances of R-SIS, and the comparison is not performed through the same modulus of R-SIS and M-SIS. In this paper, we propose that R-SIS is more difficult than M-SIS with the same modulus under some constraint of R-SIS. Also, we show that R-SIS with the modulus prime $q$ is more difficult than M-SIS with the composite modulus $c$ such that $c$ is divided by $q$. In particular, it shows that through the reduction from M-SIS to R-SIS with the same modulus, the rank of the module is extended as much as the number of instances of R-SIS from half of the number of instances of R-SIS. Finally, this paper shows that R-SIS is more difficult than M-SIS under some constraint, which is tighter than the M-SIS in the previous work