Blockchain Papers

Yu Cao, Xuehui Du, Lulu Zhang, Shihao Wang

With the continuous development of blockchain technology, an increasing number of scholars have begun to consider the harm of data leakage during on-chain transactions and the requirement for privacy data protection. Zero-knowledge range proof, as a cryptographic technology, can perform legitimacy verification of data while hiding private data, effectively realizing the protection of private data on the blockchain, so it is increasingly used to protect blockchain privacy. The mainstream construction methods for range proofs can be mainly divided into two categories: n-ary decomposition and square decomposition. This paper introduces and analyzes the advantages and disadvantages of these construction methods in detail. Then, based on these two methods, a zero-knowledge range proof scheme based on multibit split square decomposition (ZKRPMSSD) is proposed, which requires no trusted third-party setting and can achieve range proofs for arbitrary ranges. The proposed ZKRPMSSD scheme processes the original data based on the multibit split idea, and the acquisition method of secret value components is optimized so that the acquisition of components does not depend on the scale of the original problem. Additionally, the algorithms for proof generation and verification in the ZKRPMSSD scheme are redesigned based on the \(\Sigma\) protocol and Pedersen commitments, effectively reducing the computational cost of the proof generation and verification process. Finally, typical n-ary decomposition and square decomposition zero-knowledge range proof construction schemes are taken for comparative analysis. Under 256-bit security and the same problem scale, experimental results indicate that ZKRPMSSD has advantages in proof and verification time costs.

Timothy Peter Hulick

For an oscillator that is periodically swept in frequency between some upper and lower bound, the output amplitude may easily be made constant and therefore known with a high degree of certainty. The instantaneous frequency exists only at a point in time and therefore possesses a zero probability of existing at any point. This thesis deals with the development of a method for interchanging the probability density functions of amplitude and frequency so that the latter becomes known with certainty while the former is known only to the extent that it is within a certain range. The method developed makes practical the use of the fast tuned voltage controlled oscillator as the local oscillator in a frequency scanning superheterodyne receiver. Exact frequency is expressed by a digital word of finite bit length that, in actuality, expresses the value of a quantized amplitude variable whose quantized value represents a precise frequency. Because of the interrelationship of amplitude, frequency, and time through the Fourier Transform, functions of these variables are also interrelated suggesting the possibility that the original certainty of amplitude information may be traded with the original uncertainty of frequency information. The success of the method presented makes use of the precise knowledge of the frequencies of the sidebands generated by the angle modulation process rather than make direct use of the instantaneous frequency. After mathematical development, a design example addresses the actual frequency range in the microwave region where the scanning superheterodyne receiver finds military application. To demonstrate the concept of precise frequency control with words of finite length, a practical frequency model is designed and constructed by scaling megahertz to hertz. Extensive use is made of monolithic waveform generators, balanced mixers, and operational amplifiers used as active filters and time domain summers. All assemblies within the model have practical microwave counterparts. Time and frequency domain waveforms are observed at virtually every major point of the model corresponding to the functional block interfaces and are compared with the mathematical predictions. The ultimate goal of precise frequency selection as a function of an imprecise independent variable is also obtained with the aid of a spectrum analyzer and dual trace oscilloscope. The causes of less than optimum signal level separation of adjacent discrete frequencies are analyzed in a qualitative manner. Reasons for the ineffectiveness of a quantitative critique are also presented. Experimental results, however, are demonstrated proof of the feasibility of the concept of exchanging probability density functions of related variables and that refinement is the only ingredient missing to render the fast scan VCO a useful local oscillator.