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- An efficient scalable RNS architecture for large dynamic rangesPublication . Miguens Matutino, Pedro; Chaves, Ricardo; Sousa, LeonelThis paper proposes an efficient scalable Residue Number System (RNS) architecture supporting moduli sets with an arbitrary number of channels, allowing to achieve larger dynamic range and a higher level of parallelism. The proposed architecture allows the forward and reverse RNS conversion, by reusing the arithmetic channel units. The arithmetic operations supported at the channel level include addition, subtraction, and multiplication with accumulation capability. For the reverse conversion two algorithms are considered, one based on the Chinese Remainder Theorem and the other one on Mixed-Radix-Conversion, leading to implementations optimized for delay and required circuit area. With the proposed architecture a complete and compact RNS platform is achieved. Experimental results suggest gains of 17 % in the delay in the arithmetic operations, with an area reduction of 23 % regarding the RNS state of the art. When compared with a binary system the proposed architecture allows to perform the same computation 20 times faster alongside with only 10 % of the circuit area resources.
- Arithmetic-based binary-to-RNS converter modulo {2(n)+/- k} for jn-Bit dynamic rangePublication . Miguens Matutino, Pedro; Chaves, Ricardo; Sousa, LeonelIn this brief, a read-only-memoryless structure for binary-to-residue number system (RNS) conversion modulo {2(n) +/- k} is proposed. This structure is based only on adders and constant multipliers. This brief is motivated by the existing {2(n) +/- k} binary-to-RNS converters, which are particular inefficient for larger values of n. The experimental results obtained for 4n and 8n bits of dynamic range suggest that the proposed conversion structures are able to significantly improve the forward conversion efficiency, with an AT metric improvement above 100%, regarding the related state of the art. Delay improvements of 2.17 times with only 5% area increase can be achieved if a proper selection of the {2(n) +/- k} moduli is performed.
- ROM-less RNS-to-binary converter moduli {22N − 1, 22N + 1, 2N − 3, 2N + 3}Publication . Miguens Matutino, Pedro; Chaves, Ricardo; Sousa, LeonelIn this paper, a novel ROM-less RNS-to-binary converter is proposed, using a new balanced moduli set {22n-1, 22n + 1, 2n-3, 2n + 3} for n even. The proposed converter is implemented with a two stage ROM-less approach, which computes the value of X based only in arithmetic operations, without using lookup tables. Experimental results for 24 to 120 bits of Dynamic Range, show that the proposed converter structure allows a balanced system with 20% faster arithmetic channels regarding the related state of the art, while requiring similar area resources. This improvement in the channel's performance is enough to offset the higher conversion costs of the proposed converter. Furthermore, up to 20% better Power-Delay-Product efficiency metric can be achieved for the full RNS architecture using the proposed moduli set. © 2014 IEEE.
- A Compact and Scalable RNS ArchitecturePublication . Miguens Matutino, Pedro; Chaves, Ricardo; Sousa, LeonelThis paper proposes a unified architecture for designing Residue Number System (RNS) based processors for moduli sets with an arbitrary number of channels. Recently, new RNS moduli sets have been proposed in order to increase the dynamic range and reduce the width of the channels. The proposed architecture allows designing forward and reverse RNS converters, as well as the arithmetic operators of each modulo channel. The forward and reverse conversions are implemented using channel arithmetic units, resulting in a very compact architecture. Moreover, the arithmetic operations supported at the channel level include addition, subtraction, and multiplication with accumulation capability. The presented results suggest that the proposed RNS architecture leads to compact and scalable implementations, with competitive, or even better, performance when compared with the related state of the art, considering fixed moduli sets. Experimental results suggest gains of 17% in the delay of arithmetic operations, with an area reduction of 23% regarding the state of the art.
- Pipelined FPGA coprocessor for elliptic curve cryptography based on residue number systemPublication . Miguens Matutino, Pedro; Araújo, Juvenal; Sousa, Leonel; Chaves, RicardoIn this paper a novel pipelined FPGA coprocessor for ECC is proposed, exploiting the parallelism capabilities of RNS to the computation of large operand algorithms. This intrinsic characteristic of representing large integer numbers as a set of smaller and independent values allows for the parallelization of the computationally heavy large operand multiplications, required in asymmetrical cryptographic algorithms. Towards a compact and performance efficient design, the RNS coprocessor supports a single highly pipelined multi-modulo arithmetic unit. Implementation results, on FPGA of this RNS based ECC coprocessor, suggest one of the smallest programmable designs with a proportional performance when compared with related state of the art. Additionally, the resulting architecture allows for the computation of varying key sizes without changing the design or its implementation.