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Elliptic curve cryptography: Algorithms and implementation analysis over coordinate systems
Setiadi I.a, Kistijantoro A.I.a, Miyaji A.b
a School of Electrical Engineering and Informatics, Institut Teknologi Bandung, Bandung, Indonesia
b School of Informatics Science, Japan Advanced Institute of Science and Technology, Nomi, Japan
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2015 IEEE.Since the last decade, the growth of computing power and parallel computing has resulted in significant needs of efficient cryptosystem. Elliptic Curve Cryptography (ECC) offers faster computation and stronger security over other asymmetric cryptosystems such as RSA. ECC can be used for several cryptography activities: secret key sharing, message encryption, and digital signature. This paper gives step-by-step tutorial to transform ECC over prime field GF(p) from mathematical concept to the software implementation. This paper also gives several alternatives and tradeoffs between different coordinate systems in the computational process. The implementation result is quite interesting since several computational costs have been optimized in latest instruction sets. For the study case, we provides the implementation result in C language with GNU GMP library on Intel i3 CPU M350 2.27GHz (1 Core, 2 GB RAM, 32-bit architecture).[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Asymmetric cryptosystems,Co-ordinate system,ECC algorithms,Elliptic curve,Elliptic curve cryptography,Elliptic Curve Cryptography(ECC),Implementation analysis,Software implementation[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Coordinate System,Cryptography,ECC Algorithm,Elliptic Curve[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1109/ICAICTA.2015.7335349[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]