Fault-tolerant data transmission models based on the redundant residue number system are proposed in this paper; they can transmit data correctly between two ends unless the residue errors exceed the error-correction ...Fault-tolerant data transmission models based on the redundant residue number system are proposed in this paper; they can transmit data correctly between two ends unless the residue errors exceed the error-correction capability. The expressions for the probability of error are presented when the channel noise is additive Gaussian noise and each branch is M-ary orthogonal signaling modulation. The expressions of the probabilities of undetected and uncorrected error are also obtained when the redundant residue number system are single error-checking and single error-correcting model, respectively.展开更多
A parallel architecture for efficient hardware implementation of Rivest Shamir Adleman(RSA) cryptography is proposed.Residue number system(RNS) is introduced to realize high parallelism,thus all the elements under the...A parallel architecture for efficient hardware implementation of Rivest Shamir Adleman(RSA) cryptography is proposed.Residue number system(RNS) is introduced to realize high parallelism,thus all the elements under the same base are independent of each other and can be computed in parallel.Moreover,a simple and fast base transformation is used to achieve RNS Montgomery modular multiplication algorithm,which facilitates hardware implementation.Based on transport triggered architecture(TTA),the proposed architecture is designed to evaluate the performance and feasibility of the algorithm.With these optimizations,a decryption rate of 106 kbps can be achieved for 1 024-b RSA at the frequency of 100 MHz.展开更多
Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presen...Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presents a new digital watermarking scheme that combines some operators of the Genetic Algorithm (GA) and the Residue Number (RN) System (RNS) to perform encryption on an image, which is embedded into a cover image for the purposes of watermarking. Thus, an image watermarking scheme uses an encrypted image. The secret image is embedded in decomposed frames of the cover image achieved by applying a three-level Discrete Wavelet Transform (DWT). This is to ensure that the secret information is not exposed even when there is a successful attack on the cover information. Content creators can prove ownership of the multimedia content by unveiling the secret information in a court of law. The proposed scheme was tested with sample data using MATLAB2022 and the results of the simulation show a great deal of imperceptibility and robustness as compared to similar existing schemes.展开更多
Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS M...Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS Montgomery modular multiplication, which enables efficient elliptic curve point multiplication （ECPM）. Meanwhile, the elliptic curve arithmetic with ECPM is performed by mixed coordinates and adjusted for hardware implementation. In addition, the conversion between RNS and the binary number system is also discussed. Compared with the results in the literature, our hardware architecture for ECPM demonstrates high performance. A 256-bit ECPM in Xilinx XC2VP100 field programmable gate array device （FPGA） can be performed in 1.44 ms, costing 22147 slices, 45 dedicated multipliers, and 8.25K bits of random access memories （RAMs）.展开更多
Number Systems are media for representing numbers;the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations. The other category, Un-Weighted Number Syst...Number Systems are media for representing numbers;the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations. The other category, Un-Weighted Number Systems, of which the Residue Number System (RNS) belongs, do not carry weights but have not yet found widespread usage in general purpose computing as a result of some challenges;one of the main challenges of RNS is overflow detection and correction. The presence of errors in calculated values due to such factors as overflow means that systems built on this number system will continue to fail until serious steps are taken to resolve the issue. In this paper, a scheme for detecting and correcting overflow during RNS addition is presented. The proposed scheme used mixed radix digits to evaluate the magnitude of the addends in order to detect the occurrence of overflow in their sum. The scheme also demonstrated a simplified technique of correcting the overflow in the event that it occurs. An analysis of the hardware requirements and speed limitations of the scheme showed that it performs considerably better in relation to similar state of art schemes.展开更多
In this paper, we present two new algorithms in residue number systems for scaling and error correction. The first algorithm is the Cyclic Property of Residue-Digit Difference (CPRDD). It is used to speed up the resid...In this paper, we present two new algorithms in residue number systems for scaling and error correction. The first algorithm is the Cyclic Property of Residue-Digit Difference (CPRDD). It is used to speed up the residue multiple error correction due to its parallel processes. The second is called the Target Race Distance (TRD). It is used to speed up residue scaling. Both of these two algorithms are used without the need for Mixed Radix Conversion (MRC) or Chinese Residue Theorem (CRT) techniques, which are time consuming and require hardware complexity. Furthermore, the residue scaling can be performed in parallel for any combination of moduli set members without using lookup tables.展开更多
This paper presents a comparative study of the performances of arithmetic units, based on different number systems like Residue Number System (RNS), Double Base Number System (DBNS), Triple Base Number System (TBNS) a...This paper presents a comparative study of the performances of arithmetic units, based on different number systems like Residue Number System (RNS), Double Base Number System (DBNS), Triple Base Number System (TBNS) and Mixed Number System (MNS) for DSP applications. The performance analysis is carried out in terms of the hardware utilization, timing complexity and efficiency. The arithmetic units based on these number systems were employed in designing various modulation schemes like Binary Frequency Shift Keying (BFSK) modulator/demodulator. The analysis of the performance of the proposed modulator on above mentioned number systems indicates the superiority of other number systems over binary number system.展开更多
基金Supported by the National Natural Science Foundation of China
文摘Fault-tolerant data transmission models based on the redundant residue number system are proposed in this paper; they can transmit data correctly between two ends unless the residue errors exceed the error-correction capability. The expressions for the probability of error are presented when the channel noise is additive Gaussian noise and each branch is M-ary orthogonal signaling modulation. The expressions of the probabilities of undetected and uncorrected error are also obtained when the redundant residue number system are single error-checking and single error-correcting model, respectively.
基金Supported by the Natural Science Foundation of Tianjin (No. 11JCZDJC15800)the National Natural Science Foundation of China(No. 61003306)
文摘A parallel architecture for efficient hardware implementation of Rivest Shamir Adleman(RSA) cryptography is proposed.Residue number system(RNS) is introduced to realize high parallelism,thus all the elements under the same base are independent of each other and can be computed in parallel.Moreover,a simple and fast base transformation is used to achieve RNS Montgomery modular multiplication algorithm,which facilitates hardware implementation.Based on transport triggered architecture(TTA),the proposed architecture is designed to evaluate the performance and feasibility of the algorithm.With these optimizations,a decryption rate of 106 kbps can be achieved for 1 024-b RSA at the frequency of 100 MHz.
文摘Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presents a new digital watermarking scheme that combines some operators of the Genetic Algorithm (GA) and the Residue Number (RN) System (RNS) to perform encryption on an image, which is embedded into a cover image for the purposes of watermarking. Thus, an image watermarking scheme uses an encrypted image. The secret image is embedded in decomposed frames of the cover image achieved by applying a three-level Discrete Wavelet Transform (DWT). This is to ensure that the secret information is not exposed even when there is a successful attack on the cover information. Content creators can prove ownership of the multimedia content by unveiling the secret information in a court of law. The proposed scheme was tested with sample data using MATLAB2022 and the results of the simulation show a great deal of imperceptibility and robustness as compared to similar existing schemes.
基金supported by the National Natural Science Foundation of China under Grant No. 61073173
文摘Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS Montgomery modular multiplication, which enables efficient elliptic curve point multiplication （ECPM）. Meanwhile, the elliptic curve arithmetic with ECPM is performed by mixed coordinates and adjusted for hardware implementation. In addition, the conversion between RNS and the binary number system is also discussed. Compared with the results in the literature, our hardware architecture for ECPM demonstrates high performance. A 256-bit ECPM in Xilinx XC2VP100 field programmable gate array device （FPGA） can be performed in 1.44 ms, costing 22147 slices, 45 dedicated multipliers, and 8.25K bits of random access memories （RAMs）.
文摘Number Systems are media for representing numbers;the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations. The other category, Un-Weighted Number Systems, of which the Residue Number System (RNS) belongs, do not carry weights but have not yet found widespread usage in general purpose computing as a result of some challenges;one of the main challenges of RNS is overflow detection and correction. The presence of errors in calculated values due to such factors as overflow means that systems built on this number system will continue to fail until serious steps are taken to resolve the issue. In this paper, a scheme for detecting and correcting overflow during RNS addition is presented. The proposed scheme used mixed radix digits to evaluate the magnitude of the addends in order to detect the occurrence of overflow in their sum. The scheme also demonstrated a simplified technique of correcting the overflow in the event that it occurs. An analysis of the hardware requirements and speed limitations of the scheme showed that it performs considerably better in relation to similar state of art schemes.
文摘In this paper, we present two new algorithms in residue number systems for scaling and error correction. The first algorithm is the Cyclic Property of Residue-Digit Difference (CPRDD). It is used to speed up the residue multiple error correction due to its parallel processes. The second is called the Target Race Distance (TRD). It is used to speed up residue scaling. Both of these two algorithms are used without the need for Mixed Radix Conversion (MRC) or Chinese Residue Theorem (CRT) techniques, which are time consuming and require hardware complexity. Furthermore, the residue scaling can be performed in parallel for any combination of moduli set members without using lookup tables.
文摘This paper presents a comparative study of the performances of arithmetic units, based on different number systems like Residue Number System (RNS), Double Base Number System (DBNS), Triple Base Number System (TBNS) and Mixed Number System (MNS) for DSP applications. The performance analysis is carried out in terms of the hardware utilization, timing complexity and efficiency. The arithmetic units based on these number systems were employed in designing various modulation schemes like Binary Frequency Shift Keying (BFSK) modulator/demodulator. The analysis of the performance of the proposed modulator on above mentioned number systems indicates the superiority of other number systems over binary number system.
