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
本文对不同偏置下的NPN输入双极运算放大器LM108分别在1.8 Me V和1 Me V两种电子能量下、不同束流电子辐照环境中的损伤特性及变化规律进行了研究,分析了不同偏置状态下其辐照敏感参数在辐照后三种温度(室温,100℃,125℃)下随时间变化...本文对不同偏置下的NPN输入双极运算放大器LM108分别在1.8 Me V和1 Me V两种电子能量下、不同束流电子辐照环境中的损伤特性及变化规律进行了研究,分析了不同偏置状态下其辐照敏感参数在辐照后三种温度(室温,100℃,125℃)下随时间变化的关系,讨论了引起电参数失效的机理,并且分析了器件在室温和高温的退火效应以讨论引起器件电参数失效的机理.结果表明,1.8 Me V和1 Me V电子对运算放大器LM108主要产生电离损伤,相同束流下1.8 Me V电子造成的损伤比1 Me V电子更大,相同能量下0.32Gy(Si)/s束流电子产生的损伤大于1.53 Gy(Si)/s束流电子.对于相同能量和束流的电子辐照,器件零偏时的损伤大于正偏时的损伤.器件辐照后的退火行为都与温度有较大的依赖关系,而这种关系与辐照感生的界面态密度增长直接相关.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.
文摘本文对不同偏置下的NPN输入双极运算放大器LM108分别在1.8 Me V和1 Me V两种电子能量下、不同束流电子辐照环境中的损伤特性及变化规律进行了研究,分析了不同偏置状态下其辐照敏感参数在辐照后三种温度(室温,100℃,125℃)下随时间变化的关系,讨论了引起电参数失效的机理,并且分析了器件在室温和高温的退火效应以讨论引起器件电参数失效的机理.结果表明,1.8 Me V和1 Me V电子对运算放大器LM108主要产生电离损伤,相同束流下1.8 Me V电子造成的损伤比1 Me V电子更大,相同能量下0.32Gy(Si)/s束流电子产生的损伤大于1.53 Gy(Si)/s束流电子.对于相同能量和束流的电子辐照,器件零偏时的损伤大于正偏时的损伤.器件辐照后的退火行为都与温度有较大的依赖关系,而这种关系与辐照感生的界面态密度增长直接相关.
