Reference : Efficient Implementation of Pedersen Commitments Using Twisted Edwards Curves

	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Engineering, computing & technology : Computer science
	Focus Areas :	Security, Reliability and Trust
	To cite this reference:	http://hdl.handle.net/10993/33705

Title :	Efficient Implementation of Pedersen Commitments Using Twisted Edwards Curves
Language :	English
Author, co-author :	Franck, Christian [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
	Groszschädl, Johann [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Publication date :	Jun-2017
Main document title :	Mobile, Secure, and Programmable Networking - Third International Conference, MSPN 2017, Paris, France, June 29-30, 2017, Revised Selected Papers
Author, co-author :	Bouzefrane, Samia
	Banerjee, Soumya
	Sailhan, Françoise
	Boumerdassi, Selma
	Renault, Eric
Publisher :	Springer Verlag
Collection and collection volume :	Lecture Notes in Computer Science, volume 10566
Pages :	1-17
Peer reviewed :	Yes
Audience :	International
ISBN :	978-3-319-67806-1
Event name :	3rd International Conference on Mobile, Secure, and Programmable Networking (MSPN 2017)
Event date :	from 29-06-2017 to 30-06-2017
Event place (city) :	Paris
Event country :	France
Keywords :	[en] Pedersen Commitments ; Elliptic Curve Cryptography ; Twisted Edwards Curves ; Pseudo-Mersenne Prime Fields ; Efficient Implementation ; x86 Assembler
Abstract :	[en] Cryptographic commitment schemes are used in many contexts, whereby the size of the secret data and the security requirements depend on the target application. Using a software library that has been designed for other purposes (e.g., key-exchange or digital signatures) to compute commitments can be complicated or inefficient. We present in this paper a flexible implementation of Pedersen commitments based on elliptic curves in twisted Edwards form. The implementation supports a set of five curves of varying cryptographic strength, which are defined over 127, 159, 191, 223, and 255-bit pseudo-Mersenne prime fields. One can dynamically (i.e., at runtime) choose one of the curves according to the required level of security, and it is also possible to adapt to the size of the data to be committed by varying the number of base points. The point arithmetic is performed with optimized formulas using extended coordinates and dynamically pre-computed tables are utilized to speed up the scalar multiplication. Our implementation is written in ANSI C (with optional x86 assembler optimizations for the field arithmetic) and was compiled and tested successfully with Visual C on Windows, gcc on Linux, and clang on macOS. We present detailed benchmarking results for the field and point arithmetic on all five curves. When using an Intel Core i7 processor clocked at 2.7 GHz as test platform, we can compute more than 38,000 commitments per second on a twisted Edwards curve over a 127-bit field.
Permalink :	http://hdl.handle.net/10993/33705
DOI :	10.1007/978-3-319-67807-8
Other URL :	http://link.springer.com/chapter/10.1007/978-3-319-67807-8_1

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