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New Point Addition Formulae for ECC Applications [chapter]

Nicolas Meloni
Lecture Notes in Computer Science  
It is based on new point addition formulae that suit very well to exponentiation algorithms based on Euclidean addition chains.  ...  In this paper we propose a new approach to point scalar multiplication on elliptic curves defined over fields of characteristic greater than 3.  ...  First we will propose new point addition formulae in a specific case.  ... 
doi:10.1007/978-3-540-73074-3_15 fatcat:xsf4ferxvrbrnayxp7bh7fqxna

New Quintupling Point Arithmetic 5P Formulas for Lopez-Dahab Coordinate over Binary Elliptic Curve Cryptography

Waleed K AbdulRaheem, Sharifah Bte, Nur Izura, Muhammad Rezal
2019 International Journal of Advanced Computer Science and Applications  
Two formulas are introduced for the point quintupling which and , the cost of the two formulas are and respectively. The two formulas are proven as valid points.  ...  This paper introduces new quintupling point (5P) formulas which can be precomputed once and can be reused at the scalar multiplication level.  ...  Algorithm 2: The projective form of two points adding formula in LD coordinate where is: A new formula for point addition using mixed addition in affine LD coordinate is proposed by [13] , with cost of  ... 
doi:10.14569/ijacsa.2019.0100754 fatcat:4aj4qchzwbf4jatcbrahcavdrm

On Reduced Computation Cost for Edwards and Extended Twisted Edwards Curves

Gautam Kumar, Hemraj Saini
2016 Indian Journal of Science and Technology  
Scalar multiplication is having the scope for gaining the computational efficiency for Elliptic Curve Cryptography (ECC).  ...  Applications: The operation is performing on input scalar which multiplies with point-coordinates on curve, which has accumulated on reduced clock cycles with resistance to the simple side channel attack  ...  The following terms such as unified refers to addition formula remain valid when two input points are identical and it can also be used for point doubling, and the term complete refers the addition formula  ... 
doi:10.17485/ijst/2016/v9i44/105071 fatcat:d5c3jhv27zcchl65ae5ds2cuym

Public-Key Cryptography on the Top of a Needle

Lejla Batina, Nele Mentens, Kazuo Sakiyama, Bart Preneel, Ingrid Verbauwhede
2007 2007 IEEE International Symposium on Circuits and Systems  
This work describes the smallest known hardware implementation for Elliptic/Hyperelliptic Curve Cryptography (ECC/HECC).  ...  This implies the same arithmetic unit for both cases which supports arithmetic in a field F2p .  ...  Operation in F (2 p ) 2 Addition Multiplication F 2 p 2ADD 3MUL+4ADD From the formulae for point operations for projective coordinates [2] it is evident that we need to implement only multiplications  ... 
doi:10.1109/iscas.2007.378270 dblp:conf/iscas/BatinaMSPV07 fatcat:lqkwkw2z75dh7dnann5z55mykq

High-speed implementation of an ECC-based wireless authentication protocol on an ARM microprocessor

M. Aydos, T. Yanık, Ç.K. Koç
2001 IEE Proceedings - Communications  
With these timings, the execution of the ECC-based wireless authentication protocol takes around 140ms on the ARM7TDMI processor, which is a widely used, low-power core processor for wireless applications  ...  The ECDSA and a recently proposed ECC-based wireless authentication protocol are implemented using the library.  ...  The addition formulae for the Jacobian and the modified Jacobian coordinates are given in [15] .  ... 
doi:10.1049/ip-com:20010511 fatcat:4vplnqaynnfoxk57lxwfnezjei

Low-Cost Elliptic Curve Cryptography for Wireless Sensor Networks [chapter]

Lejla Batina, Nele Mentens, Kazuo Sakiyama, Bart Preneel, Ingrid Verbauwhede
2006 Lecture Notes in Computer Science  
Our compact and low-power ECC processor contains a Modular Arithmetic Logic Unit (MALU) for ECC field arithmetic.  ...  This work describes a low-cost Public-Key Cryptography (PKC) based solution for security services such as key-distribution and authentication as required for wireless sensor networks.  ...  At the next (lower) level are the point group operations i.e. addition and doubling. The point addition in affine coordinates is performed according to the following formulae.  ... 
doi:10.1007/11964254_3 fatcat:juu3aespxzgcfai4aynr2bj5sq

Comprehensive Efficient Implementations of ECC on C54xx Family of Low-cost Digital Signal Processors [article]

Yasir Malik
2015 arXiv   pre-print
These are the best known results for fixed-point low power digital signal processor to date.  ...  We present comprehensive yet efficient implementations of ECC on fixed-point TMS54xx series of digital signal processors (DSP). 160-bit prime field GF(p) ECC is implemented over a wide range of coordinate  ...  using the same formula as that of addition.  ... 
arXiv:1502.01872v1 fatcat:usg2gzrnxfakvm5a5j3o5d2c2m

Power Analysis Attacks on ECC: A Major Security Threat

Hilal Houssain, Mohamad Badra, Turki F.
2012 International Journal of Advanced Computer Science and Applications  
In addition, this paper describes critical concerns to be considered in designing PAAs on ECC particular for WSNs, and illustrates the need to conduct, in the near future, intensive researches for the  ...  Wireless sensor networks (WSNs) are largely deployed in different sectors and applications, and Elliptic Curve Cryptography (ECC) is proven to be the most feasible PKC for WSN security.  ...  The additive inverse of a point P = (x, y) is the point (x, x + y) for curves defined over the GF(2 m )fields.  ... 
doi:10.14569/ijacsa.2012.030615 fatcat:hppzbbla2jdajindgcktv4lf5q

Application of Montgomery's Trick to Scalar Multiplication for Elliptic and Hyperelliptic Curves Using a Fixed Base Point [chapter]

Pradeep Kumar Mishra, Palash Sarkar
2004 Lecture Notes in Computer Science  
The increase in speed is due to a proper application of Montgomery's trick to efficiently perform the simultaneous inversion of several field elements.  ...  The algorithm uses Montgomery's trick and a precomputed table consisting of multiples of the base point.  ...  This memory requirement might be costly for memory constrained applications (as in smart card applications). In such situations our algorithm cannot be used.  ... 
doi:10.1007/978-3-540-24632-9_4 fatcat:lhg7wqhot5gqje7y6ogfaoj5mq

Power Analysis to ECC Using Differential Power Between Multiplication and Squaring [chapter]

Toru Akishita, Tsuyoshi Takagi
2006 Lecture Notes in Computer Science  
The proposed attack is applicable to two efficient power analysis countermeasures based on unified addition formulae and elliptic curves with Montgomery form.  ...  Power analysis is a serious attack to implementation of elliptic curve cryptosystems (ECC) on smart cards. For ECC, many power analysis attacks and countermeasures have been proposed.  ...  We applied this bias to unified addition formulae and Montgomery ladder on a Montgomery-form elliptic curve.  ... 
doi:10.1007/11733447_11 fatcat:3mpu5s4yovfdpmbjth4opeer6e

Software Implementation of Curve based Cryptography for Constrained Devices

Kakali Chatterjee, Asok De, Daya Gupta
2011 International Journal of Computer Applications  
of ECC / HECC.  ...  Curve based cryptography are preferred for embedded hardware since they require shorter operand size than RSA to attain the same security level.  ...  Some efficient and innovative methodology for accelerating the elliptic curve point formulae over prime fields are proposed in [8] [9] .  ... 
doi:10.5120/2942-3914 fatcat:6cuca7q2ivdhrnkzclwjfly54y

Implementing Elliptic Curve Cryptography [chapter]

Wolfgang Bauer
2002 IFIP Advances in Information and Communication Technology  
Properties like short keys and efficient algorithms make elliptic curve cryptography (EOO) more and more interesting for future oriented applications.  ...  Furthermore, we discuss aspects of the standardized encoding, and point out where interoperability problems could occur.  ...  As the formulas of table 1 show, one simple point addition requires many operations in the underlying finite field.  ... 
doi:10.1007/978-0-387-35612-9_3 fatcat:ejfc3maf3za5jcey6zhwljro5i

Low-Resource and Fast Binary Edwards Curves Cryptography [chapter]

Brian Koziel, Reza Azarderakhsh, Mehran Mozaffari-Kermani
2015 Lecture Notes in Computer Science  
The recently presented formulas for mixed point addition in [1] were found to be invalid, but were corrected such that the speed and register usage were maintained.  ...  We utilize corrected mixed point addition and doubling formulas to achieve a secure, but still fast implementation of a point multiplication on binary Edwards curves.  ...  The authors would like to thank the reviewers for their constructive comments. This material is based upon work supported by the National Science Foundation under Award No.  ... 
doi:10.1007/978-3-319-26617-6_19 fatcat:rqg4dkjr3jd7dhv5pxygs6ulu4

Completing the Complete ECC Formulae with Countermeasures

Łukasz Chmielewski, Pedro Massolino, Jo Vliegen, Lejla Batina, Nele Mentens
2017 Journal of Low Power Electronics and Applications  
This work implements and evaluates the recent complete addition formulae for the prime order elliptic curves of Renes, Costello and Batina on an FPGA platform.  ...  This is the first work looking into side-channel security issues of hardware implementations of the complete formulae.  ...  Author Contributions: For this work, the authors of KU Leuven were mainly responsible for the low-level architecture, i.e.  ... 
doi:10.3390/jlpea7010003 fatcat:gujyt7mbsvdcnoqd4qfctnbfd4

Elliptic Curve Cryptoprocessor Implementation on a Nano FPGA: Interesting for Resource-Constrained Devices

Hilal Houssain, Turki F. Al-Somani
2012 International Journal of RFID Security and Cryptography  
This is because of the limited number of resources available on Nano FPGAs, which opens a new challenging opportunity for future Nano FPGAs to satisfy the needs of critical portable applications and resource-constrained  ...  This paper presents an implementation of an Elliptic Curve Cryptography (ECC) cryptoprocessor on a Nano Field Programmable Gate Array (FPGA), that maybe be interesting for resource-constrained devices  ...  For elliptic curve defined over GF(2 m ), many different forms of formulas are found [19] for point addition and doubling.  ... 
doi:10.20533/ijrfidsc.2046.3715.2012.0006 fatcat:fvfezzjofng6tmpsp326g6abtm
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