scholarly journals Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1507 ◽  
Author(s):  
Utku Gulen ◽  
Selcuk Baktir
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Wireless Sensor ◽  
Network Nodes ◽  
Point Multiplication ◽  
Speed Up ◽  
Field Multiplication ◽  
First Time ◽  
Efficient Realization ◽  
Scalar Point Multiplication

We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve scalar point multiplication. We take advantage of the fast Fourier transform for the first time in the literature to speed up the number theoretic transform for an efficient realization of elliptic curve cryptography. Our implementation achieves elliptic curve scalar point multiplication in only 0.65 s and 1.31 s for multiplication of fixed and random points, respectively, and has similar or better timing performance compared to previous works in the literature.

scholarly journals Comparative analysis of the scalar point multiplication algorithms in the NIST FIPS 186 elliptic curve cryptography

2021 ◽  
Author(s):  
M. Babenko ◽  
A. Tchernykh ◽  
A. Redvanov ◽  
A. Djurabaev
Keyword(s):  
Comparative Analysis ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Execution Time ◽  
Elliptic Curve Cryptosystem ◽  
Coordinate Systems ◽  
Point Multiplication ◽  
Window Method ◽  
Scalar Point Multiplication

In today's world, the problem of information security is becoming critical. One of the most common cryptographic approaches is the elliptic curve cryptosystem. However, in elliptic curve arithmetic, the scalar point multiplication is the most expensive compared to the others. In this paper, we analyze the efficiency of the scalar multiplication on elliptic curves comparing Affine, Projective, Jacobian, Jacobi-Chudnovsky, and Modified Jacobian representations of an elliptic curve. For each coordinate system, we compare Fast exponentiation, Nonadjacent form (NAF), and Window methods. We show that the Window method is the best providing lower execution time on considered coordinate systems.

Elliptic Curve Cryptography with Security System in Wireless Sensor Networks

2010 ◽  
Author(s):  
Xu Huang ◽  
Dharmendra Sharma ◽  
Sio-Iong Ao ◽  
Hideki Katagir ◽  
Li Xu ◽  
...  
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Security System ◽  
Wireless Sensor

Elliptic Curve Cryptography on WISPs

2013 ◽  
pp. 562-583
Author(s):  
Michael Hutter ◽  
Erich Wenger ◽  
Markus Pelnar ◽  
Christian Pendl
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Public Key ◽  
Wireless Sensor ◽  
Binary Field ◽  
Montgomery Ladder ◽  
Sensing Platforms ◽  
Cryptographic Primitive ◽  
Prime Fields ◽  
Dedicated Hardware

In this chapter, the authors explore the feasibility of Elliptic Curve Cryptography (ECC) on Wireless Identification and Sensing Platforms (WISPs). ECC is a public-key based cryptographic primitive that has been widely adopted in embedded systems and Wireless Sensor Networks (WSNs). In order to demonstrate the practicability of ECC on such platforms, the authors make use of the passively powered WISP4.1DL UHF tag from Intel Research Seattle. They implemented ECC over 192-bit prime fields and over 191-bit binary extension fields and performed a Montgomery ladder scalar multiplication on WISPs with and without a dedicated hardware multiplier. The investigations show that when running at a frequency of 6.7 MHz, WISP tags that do not support a hardware multiplier need 8.3 seconds and only 1.6 seconds when a hardware multiplier is supported. The binary-field implementation needs about 2 seconds without support of a hardware multiplier. For the WISP, ECC over prime fields provides best performance when a hardware multiplier is available; binary-field based implementations are recommended otherwise. The use of ECC on WISPs allows the realization of different public-key based protocols in order to provide various cryptographic services such as confidentiality, data integrity, non-repudiation, and authentication.

Elliptic Curve Cryptography on WISPs

2013 ◽  
pp. 120-143
Author(s):  
Michael Hutter ◽  
Erich Wenger ◽  
Markus Pelnar ◽  
Christian Pendl
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Public Key ◽  
Wireless Sensor ◽  
Binary Field ◽  
Montgomery Ladder ◽  
Sensing Platforms ◽  
Cryptographic Primitive ◽  
Prime Fields ◽  
Dedicated Hardware

In this chapter, the authors explore the feasibility of Elliptic Curve Cryptography (ECC) on Wireless Identification and Sensing Platforms (WISPs). ECC is a public-key based cryptographic primitive that has been widely adopted in embedded systems and Wireless Sensor Networks (WSNs). In order to demonstrate the practicability of ECC on such platforms, the authors make use of the passively powered WISP4.1DL UHF tag from Intel Research Seattle. They implemented ECC over 192-bit prime fields and over 191-bit binary extension fields and performed a Montgomery ladder scalar multiplication on WISPs with and without a dedicated hardware multiplier. The investigations show that when running at a frequency of 6.7 MHz, WISP tags that do not support a hardware multiplier need 8.3 seconds and only 1.6 seconds when a hardware multiplier is supported. The binary-field implementation needs about 2 seconds without support of a hardware multiplier. For the WISP, ECC over prime fields provides best performance when a hardware multiplier is available; binary-field based implementations are recommended otherwise. The use of ECC on WISPs allows the realization of different public-key based protocols in order to provide various cryptographic services such as confidentiality, data integrity, non-repudiation, and authentication.

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