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Efficient Implementation of Elliptic Curve Cryptography
, Ph.D. Dissertation Sharif University of Technology ; Bayat-Sarmadi, Siavash (Supervisor)
Abstract
Elliptic curve cryptography (ECC) has received attention because it can achieve the same security level as other classical asymmetric methods while using a key with smaller length. Although ECC is more efficient compared to AlGemal and RSA cryptosystems, fast computation of ECC is always desirable. Point multiplication is an essential operation in cryptographic computations. Low-latency and low-complexity multiplication architectures lead to more efficient cryptosystems.In this thesis, a fixed-base comb point multiplication method has been used to perform regular point multiplication. Additionally, two low-complexity (LC) and low-latency (LL) architectures for the regular point...
Efficient Implementation of Elliptic Curve Scalar Multiplication without Division and Inversion Operations
, M.Sc. Thesis Sharif University of Technology ; Bayat-Sarmadi, Siavash (Supervisor)
Abstract
Elliptic curve cryptography (ECC) has received attention because it can achieve a security level similar to other asymmetric methods while using a key with smaller length. Although ECC is more efficient compared to other asymmetric methods, fast computation of ECC is always desirable. In this thesis,a fixed-base comb point multiplication method has been modified to perform regular point multiplication. Additionally, two low-complexity and lowlatency architectures for the modified point multiplication algorithm has been proposed. In order to achieve these architectures, a low-latency pipelined digit-level field multiplier for all national institute of standards and technology (NIST)...
Efficient Implementation of Elliptic Curve Cryptography on Curve-25519
, M.Sc. Thesis Sharif University of Technology ; Bayat Sarmadi, Siavash (Supervisor)
Abstract
Elliptic curve cryptography (ECC) has received attention because it can achieve a security level similar to other asymmetric methods while using a key with smaller length. Although ECC is more efficient compared to other asymmetric methods, fast computation of ECC is always desirable. In this thesis, a fixed-base comb point multiplication method has been modified to perform regular point multiplication. Additionally, two low-complexity and lowlatency architectures for the modified point multiplication algorithm has been proposed. In order to achieve these architectures, a low-latency pipelined digit-level field multiplier for all national institute of standards and technology (NIST)...
A low-latency and low-complexity point-multiplication in ECC
, Article IEEE Transactions on Circuits and Systems I: Regular Papers ; Volume 65, Issue 9 , 2018 , Pages 2869-2877 ; 15498328 (ISSN) ; Bayat Sarmadi, S ; Mosanaei Boorani, H ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
Elliptic curve cryptography (ECC) has received attention, because it can achieve the same security level as other asymmetric methods while using a key with smaller length. Although ECC is more efficient compared with other asymmetric methods, the fast computation of ECC is always desirable. In this paper, a fixed-base comb point multiplication method has been used to perform regular point multiplication. In addition, two low-complexity (LC) and low-latency (LL) architectures for the regular point multiplication using fixed-base comb method have been proposed. The point multiplication architectures have been implemented using field-programmable gate array and application-specific integrated...