This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions.Unlike traditional Merkle trees,the Verkle tree sig...This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions.Unlike traditional Merkle trees,the Verkle tree significantly reduces signature size by utilizing polynomial and vector commitments.Compact proofs also accelerate the verification process,reducing computational overhead,which makes Verkle trees particularly useful.The study proposes a new approach based on a non-positional polynomial notation(NPN)employing the Chinese Remainder Theorem(CRT).CRT enables efficient data representation and verification by decomposing data into smaller,indepen-dent components,simplifying computations,reducing overhead,and enhancing scalability.This technique facilitates parallel data processing,which is especially advantageous in cryptographic applications such as commitment and proof construction in Verkle trees,as well as in systems with constrained computational resources.Theoretical foundations of the approach,its advantages,and practical implementation aspects are explored,including resistance to potential attacks,application domains,and a comparative analysis with existing methods based on well-known parameters and characteristics.An analysis of potential attacks and vulnerabilities,including greatest common divisor(GCD)attacks,approximate multiple attacks(LLL lattice-based),brute-force search for irreducible polynomials,and the estimation of their total number,indicates that no vulnerabilities have been identified in the proposed method thus far.Furthermore,the study demonstrates that integrating CRT with Verkle trees ensures high scalability,making this approach promising for blockchain systems and other distributed systems requiring compact and efficient proofs.展开更多
The use of formal specification in software development is becoming increasingly prevalent. The Z notation is a formal method, a language, and a style for expressing formal specification of software systems. This pape...The use of formal specification in software development is becoming increasingly prevalent. The Z notation is a formal method, a language, and a style for expressing formal specification of software systems. This paper presents a part of the specification work on a hotel viproom reservation system.展开更多
Guqin music is a precious cultural heritage of China. The notation of Guqin is very special, which records its playing methods and techniques. For the purpose of preserving the guqin art, the digitalization of guqin n...Guqin music is a precious cultural heritage of China. The notation of Guqin is very special, which records its playing methods and techniques. For the purpose of preserving the guqin art, the digitalization of guqin notation and an interpretation method of guqin notation were conducted. By using this interpretation method, raw images of handwritten notations are transformed into structural data that can be processed and analyzed by computers easily. The method decomposes each single complex character of guqin notations into simple radicals and finds the structure of the character. According to the radicals and the structure, the character is interpreted into meaningful codes. The experimental results show our method is effective.展开更多
A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presente...A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presented at the beginning of the transformation.展开更多
This paper introduces the base-X notation and discusses the conversion between numbers of different bases. It also introduces the tri-value logic that is associated with the base-3 system.
DP enhanced notations are the new technical application on traditional DP system in order to adapt to higher requirements on offshore unit. But they are very complicated to apply. This article introduces the general o...DP enhanced notations are the new technical application on traditional DP system in order to adapt to higher requirements on offshore unit. But they are very complicated to apply. This article introduces the general of DP enhanced notations. At the same time, it provides a case, based on 145 m DSV built in a yard located at Shanghai, China. This case shows main settings for control systems and auxiliary systems of DNV ＂DYNPOS-ER＂. DP analysis and FMEA reports show all these setting can fulfill the requirements of Rules and diving operations.展开更多
While Bronze Age Proto-Sinaic and Proto-Canaanite syllabic inscriptions were found engraved on fragments of pottery and stone,evidence of early alphabetic script was also inscribed in ink onto a massive parchment scro...While Bronze Age Proto-Sinaic and Proto-Canaanite syllabic inscriptions were found engraved on fragments of pottery and stone,evidence of early alphabetic script was also inscribed in ink onto a massive parchment scroll,known as the Torah.Albeit the contours of those original characters transformed over time,it took the clairvoyant genius of Moses,and later the scribes of Ancient Israel,to configure and adapt ancient semitic prototypes into phonetic letters,producing the greatest literary document in the history of the world,the Bible.This article summarizes the acoustic properties of that alphabet,with further historical considerations.展开更多
Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual con...Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.展开更多
In Chin.Phys.B 34114704(2025),Eq.(7)and the associated unit notation were incorrect.The correct ones are present here.Since Eq.(7)is an in-built expression in the simulation package,the correction is purely typographi...In Chin.Phys.B 34114704(2025),Eq.(7)and the associated unit notation were incorrect.The correct ones are present here.Since Eq.(7)is an in-built expression in the simulation package,the correction is purely typographical and does not affect the simulation procedure,numerical results,or the conclusions.展开更多
基金funded by the Ministry of Science and Higher Education of Kazakhstan and carried out within the framework of the project AP23488112“Development and study of a quantum-resistant digital signature scheme based on a Verkle tree”at the Institute of Information and Computational Technologies.
文摘This paper examines the application of the Verkle tree—an efficient data structure that leverages commitments and a novel proof technique in cryptographic solutions.Unlike traditional Merkle trees,the Verkle tree significantly reduces signature size by utilizing polynomial and vector commitments.Compact proofs also accelerate the verification process,reducing computational overhead,which makes Verkle trees particularly useful.The study proposes a new approach based on a non-positional polynomial notation(NPN)employing the Chinese Remainder Theorem(CRT).CRT enables efficient data representation and verification by decomposing data into smaller,indepen-dent components,simplifying computations,reducing overhead,and enhancing scalability.This technique facilitates parallel data processing,which is especially advantageous in cryptographic applications such as commitment and proof construction in Verkle trees,as well as in systems with constrained computational resources.Theoretical foundations of the approach,its advantages,and practical implementation aspects are explored,including resistance to potential attacks,application domains,and a comparative analysis with existing methods based on well-known parameters and characteristics.An analysis of potential attacks and vulnerabilities,including greatest common divisor(GCD)attacks,approximate multiple attacks(LLL lattice-based),brute-force search for irreducible polynomials,and the estimation of their total number,indicates that no vulnerabilities have been identified in the proposed method thus far.Furthermore,the study demonstrates that integrating CRT with Verkle trees ensures high scalability,making this approach promising for blockchain systems and other distributed systems requiring compact and efficient proofs.
文摘The use of formal specification in software development is becoming increasingly prevalent. The Z notation is a formal method, a language, and a style for expressing formal specification of software systems. This paper presents a part of the specification work on a hotel viproom reservation system.
基金National Natural Science Foundation of China(No.6097507)
文摘Guqin music is a precious cultural heritage of China. The notation of Guqin is very special, which records its playing methods and techniques. For the purpose of preserving the guqin art, the digitalization of guqin notation and an interpretation method of guqin notation were conducted. By using this interpretation method, raw images of handwritten notations are transformed into structural data that can be processed and analyzed by computers easily. The method decomposes each single complex character of guqin notations into simple radicals and finds the structure of the character. According to the radicals and the structure, the character is interpreted into meaningful codes. The experimental results show our method is effective.
文摘A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presented at the beginning of the transformation.
文摘This paper introduces the base-X notation and discusses the conversion between numbers of different bases. It also introduces the tri-value logic that is associated with the base-3 system.
文摘DP enhanced notations are the new technical application on traditional DP system in order to adapt to higher requirements on offshore unit. But they are very complicated to apply. This article introduces the general of DP enhanced notations. At the same time, it provides a case, based on 145 m DSV built in a yard located at Shanghai, China. This case shows main settings for control systems and auxiliary systems of DNV ＂DYNPOS-ER＂. DP analysis and FMEA reports show all these setting can fulfill the requirements of Rules and diving operations.
文摘While Bronze Age Proto-Sinaic and Proto-Canaanite syllabic inscriptions were found engraved on fragments of pottery and stone,evidence of early alphabetic script was also inscribed in ink onto a massive parchment scroll,known as the Torah.Albeit the contours of those original characters transformed over time,it took the clairvoyant genius of Moses,and later the scribes of Ancient Israel,to configure and adapt ancient semitic prototypes into phonetic letters,producing the greatest literary document in the history of the world,the Bible.This article summarizes the acoustic properties of that alphabet,with further historical considerations.
基金National Natural Science Foundation of China(Grant Number:11304126)College Students' Innovation Training Program(Grant Number:202110299696X)。
文摘Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.
文摘In Chin.Phys.B 34114704(2025),Eq.(7)and the associated unit notation were incorrect.The correct ones are present here.Since Eq.(7)is an in-built expression in the simulation package,the correction is purely typographical and does not affect the simulation procedure,numerical results,or the conclusions.
