• Journal of IKEEE
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• v.25 no.4
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• pp.625-633
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• 2021

This paper describes a scalable architecture for flexible hardware implementation of Montgomery modular multiplication. Our scalable modular multiplier architecture, which is based on a one-dimensional array of processing elements (PEs), performs word parallel operation and allows us to adjust computational performance and hardware complexity depending on the number of PEs used, N_PE. Based on the proposed architecture, we designed a scalable Montgomery modular multiplier (sMM) core supporting eight field sizes defined in SEC2. Synthesized with 180-nm CMOS cell library, our sMM core was implemented with 38,317 gate equivalents (GEs) and 139,390 GEs for N_PE=1 and N_PE=8, respectively. When operating with a 100 MHz clock, it was evaluated that 256-bit modular multiplications of 0.57 million times/sec for N_PE=1 and 3.5 million times/sec for N_PE=8 can be computed. Our sMM core has the advantage of enabling an optimized implementation by determining the number of PEs to be used in consideration of computational performance and hardware resources required in application fields, and it can be used as an IP (intellectual property) in scalable hardware design of elliptic curve cryptography (ECC).

• The Journal of Korean Society for Radiation Therapy
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• v.26 no.1
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• pp.137-147
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• 2014

Purpose : The purpose of this study is to verify the accuracy of dose delivery according to the patient's breathing cycle in Gated Volumetric Modulated Arc Therapy Materials and Methods : TrueBeam STxTM(Varian Medical System, Palo Alto, CA) was used in this experiment. The Computed tomography(CT) images that were acquired with RANDO Phantom(Alderson Research Laboratories Inc. Stamford. CT, USA), using Computerized treatment planning system(Eclipse 10.0, Varian, USA), were used to create VMAT plans using 10MV FFF with 1500 cGy/fx (case 1, 2, 3) and 220 cGy/fx(case 4, 5, 6) of doserate of 1200 MU/min. The regular respiratory period of 1.5, 2.5, 3.5 and 4.5 sec and the patients respiratory period of 2.2 and 3.5 sec were reproduced with the $QUASAR^{TM}$ Respiratory Motion Phantom(Modus Medical Devices Inc), and it was set up to deliver radiation at the phase mode between the ranges of 30 to 70%. The results were measured at respective respiratory conditions by a 2-Dimensional ion chamber array detector(I'mRT Matrixx, IBA Dosimetry, Germany) and a MultiCube Phantom(IBA Dosimetry, Germany), and the Gamma pass rate(3 mm, 3%) were compared by the IMRT analysis program(OmniPro I'mRT system software Version 1.7b, IBA Dosimetry, Germany) Results : The gamma pass rates of Case 1, 2, 3, 4, 5 and 6 were the results of 100.0, 97.6, 98.1, 96.3, 93.0, 94.8% at a regular respiratory period of 1.5 sec and 98.8, 99.5, 97.5, 99.5, 98.3, 99.6% at 2.5 sec, 99.6, 96.6, 97.5, 99.2, 97.8, 99.1% at 3.5 sec and 99.4, 96.3, 97.2, 99.0, 98.0, 99.3% at 4.5 sec, respectively. When a patient's respiration was reproduced, 97.7, 95.4, 96.2, 98.9, 96.2, 98.4% at average respiratory period of 2.2 sec, and 97.3, 97.5, 96.8, 100.0, 99.3, 99.8% at 3.5 sec, respectively. Conclusion : The experiment showed clinically reliable results of a Gamma pass rate of 95% or more when 2.5 sec or more of a regular breathing period and the patient's breathing were reproduced. While it showed the results of 93.0% and 94.8% at a regular breathing period of 1.5 sec of Case 5 and 6, it could be confirmed that the accurate dose delivery could be possible on the most respiratory conditions because based on the results of 100 patients's respiratory period analysis as no one sustained a respiration of 1.5 sec. But, pretreatment dose verification should be precede because we can't exclude the possibility of error occurrence due to extremely short respiratory period, also a training at the simulation and careful monitoring are necessary for a patient to maintain stable breathing. Consequently, more reliable and accurate treatments can be administered.