Filters








2,317 Hits in 6.4 sec

Constructing pairing-friendly elliptic curves with embedding degree 10 [article]

David Freeman
2006 arXiv   pre-print
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree.  ...  We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham.  ...  A Framework for Constructing Pairing-Friendly Elliptic Curves In this section we describe a general framework for constructing elliptic curves of a given embedding degree k.  ... 
arXiv:math/0601487v1 fatcat:36qcuywvbjcxlmml23otvk43ge

Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10 [chapter]

David Freeman
2006 Lecture Notes in Computer Science  
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree.  ...  We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham [6] .  ...  A Framework for Constructing Pairing-Friendly Elliptic Curves In this section we describe a general framework for constructing elliptic curves of a given embedding degree k.  ... 
doi:10.1007/11792086_32 fatcat:2dav6ei6arerfl7det34rtq7ym

Generating Pairing-Friendly Curves with the CM Equation of Degree 1 [chapter]

Hyang-Sook Lee, Cheol-Min Park
2009 Lecture Notes in Computer Science  
Using this classification, we propose a new algorithm to construct Brezing-Weng-like elliptic curves having the CM equation of degree 1, and we present new families of curves with larger discriminants.  ...  We revisit these methods via a change-of-basis matrix and completely classify a basis for a cyclotomic field to produce a family of pairing-friendly curves with a CM equation of degree 1.  ...  Another approach is to use the ordinary elliptic curves with small embedding degree.  ... 
doi:10.1007/978-3-642-03298-1_5 fatcat:xc7djfd5rrecnorhn24agvaebi

Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures

Maocai Wang, Guangming Dai, Kim-Kwang Raymond Choo, Prem Prakash Jayaraman, Rajiv Ranjan, Yongtang Shi
2016 PLoS ONE  
In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree  ...  And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of  ...  Pairing-friendly elliptic curves under embedding degree 1 with 160 bits. There are 10 group pairing-friendly elliptic curves under embedding degree 1 with 160 bits.  ... 
doi:10.1371/journal.pone.0161857 pmid:27564373 pmcid:PMC5001717 fatcat:4jm5ekddcjdgvl3jqyhqa6f5ea

On cycles of pairing-friendly elliptic curves [article]

Alessandro Chiesa, Lynn Chua, Matthew Weidner
2018 arXiv   pre-print
We study cycles of elliptic curves in which every curve is pairing-friendly.  ...  We rule out cycles of length 2 for particular choices of small embedding degrees.  ...  We also thank François Morain for informing us about the application of cycles of elliptic curves to primality proving.  ... 
arXiv:1803.02067v3 fatcat:2qbrfajzybhw5l5cy45gzhdoqy

CONSTRUCTING PAIRING-FRIENDLY CURVES WITH VARIABLE CM DISCRIMINANT

Hyang-Sook Lee, Cheol-Min Park
2012 Bulletin of the Korean Mathematical Society  
Using this construction, new families of curves with variable discriminants and embedding degrees of k ∈ {8, 16, 20, 24}, which were not covered by Freeman, Scott, and Teske [9], are presented.  ...  Our result is useful for constructing elliptic curves with larger and more flexible discriminants.  ...  There are a number of methods for constructing pairing-friendly elliptic curves with the prescribed embedding degree k.  ... 
doi:10.4134/bkms.2012.49.1.075 fatcat:j5ss2zvckjcyteljyfudke6rka

Generating pairing-friendly elliptic curves with fixed embedding degrees

Liang Li
2016 Science China Information Sciences  
Barreto and Naehrig [2] successfully constructed a family of elliptic curves with embedding degree k = 12, achieving ρ ∼ 1.  ...  An elliptic curve is called pairing-friendly if it has a suitable small embedding degree k and a large prime-order r subgroup such that r √ q dividing #E(F q ).  ...  We describe pairing-friendly elliptic curves, then provide a method to construct them with a fixed embedding degree in Theorem 1 and provide constructions with various embedding degrees.  ... 
doi:10.1007/s11432-016-0412-0 fatcat:lmdg3k2nqvhz7m4rvuzwqu6pwm

On Constructing Families of Pairing-Friendly Elliptic Curves with Variable Discriminant [chapter]

Robert Dryło
2011 Lecture Notes in Computer Science  
Dryªo () Constructing Pairing-friendly Curves 26 / 27 R. Dryªo () Constructing Pairing-friendly Curves 10 / 27 R. Dryªo () Constructing Pairing-friendly Curves 12 / 27 R.  ...  To construct an ordinary elliptic curve with embedding degree k we rst nd parameters (r , t, q), where r is a prime number and there exists an elliptic curve E/ F q with trace t and embedding degree k  ... 
doi:10.1007/978-3-642-25578-6_22 fatcat:nmko5oaefbaq5hx2yggwroufmi

Constructing Pairing-Friendly Genus 2 Curves with Split Jacobian [chapter]

Robert Dryło
2012 Lecture Notes in Computer Science  
.3 Originally sparse families for elliptic curves were introduced by Mayaji et al. to characterize elliptic curves of prime order with embedding degrees k = 3, 4, 6.  ...  In general, we construct ordinary pairing-friendly elliptic curves as follows: Given k, we nd parameters r, t, q of an elliptic curve E, where q is the size of the eld of denition of E, t is the trace  ... 
doi:10.1007/978-3-642-34931-7_25 fatcat:ulnrab55a5h2vbxnix5vl6bs6m

A Taxonomy of Pairing-Friendly Elliptic Curves

David Freeman, Michael Scott, Edlyn Teske
2009 Journal of Cryptology  
We also include new constructions of pairing-friendly curves that improve on the previously known constructions for certain embedding degrees.  ...  Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairingbased cryptographic systems.  ...  elliptic curves with embedding degree 10 and discriminant 1.  ... 
doi:10.1007/s00145-009-9048-z fatcat:gwawq4j23refpe74ucw4oqjfsy

Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9

X. LIN, C.-A. ZHAO, F. ZHANG, Y. WANG
2008 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k = 9 or curves with k = 12.  ...  In this paper, we present efficient methods for the k = 9 case, including generation of elliptic curves with the shorter Miller loop, the denominator elimination and speed up of the final exponentiation  ...  curves with even embedding degrees.  ... 
doi:10.1093/ietfec/e91-a.9.2387 fatcat:5i6clm46dbcsrggsqgugqr7wuy

Faster Ate Pairing Computation over Pairing-Friendly Elliptic Curves Using GLV Decomposition

Soo Kyung Eom
2013 ETRI Journal  
Elliptic curves with small embedding degrees only allow a few of these pairings. In such cases, efficiently computable endomorphisms can be used, as in [11] and [12].  ...  To construct more pairing-friendly curves, we consider μ-expansion using the Gallant-Lambert-Vanstone (GLV) decomposition method, where μ is an arbitrary integer.  ...  Conclusion In this paper, we constructed pairing-friendly curves with small embedding degrees using a modified Cocks-Pinch method.  ... 
doi:10.4218/etrij.13.0112.0756 fatcat:n2xt4fvfxbgf7mzi4z5avlbpyu

More constructing pairing-friendly elliptic curves for cryptography [article]

Tanaka Satoru and Nakamula Ken (Department of Mathematics and Information Sciences, Tokyo Metropolitan University)
2007 arXiv   pre-print
We produce new families of parameters using our algorithm for pairing-friendly elliptic curves of embedding degree 8, and we actually compute some explicit curves as numerical examples.  ...  The problem of constructing elliptic curves suitable for pairing applications has received a lot of attention. To solve this, we propose a variant algorithm of a known method by Brezing and Weng.  ...  Our framework of pairing-friendly curves A survey on the construction of pairing-friendly elliptic curves is given by Freeman et al. [7] .  ... 
arXiv:0711.1942v1 fatcat:22mqdgevhnfmfoviyw3zwwubzi

A New Family of Pairing-Friendly Elliptic Curves [chapter]

Michael Scott, Aurore Guillevic
2018 Lecture Notes in Computer Science  
In this note we announce the discovery of a new family of pairing friendly elliptic curves which includes a new construction for a curve with an embedding degree of 54.  ...  The well known taxonomy of Freeman, Scott and Teske only considered curves with embedding degrees up to 50.  ...  For k = 12 Algorithm 1: Aurifeuillean construction of pairing-friendly curves Input: embedding degree k, small discriminant D Output: family (r, t, y, p) of a pairing-friendly elliptic curve of embedding  ... 
doi:10.1007/978-3-030-05153-2_2 fatcat:fcr3p5jyifbrlhapo5252dppne

Pairing-Friendly Curves with Minimal Security Loss by Cheon's Algorithm

Cheol-Min Park
2011 ETRI Journal  
This paper proposes a method for searching parameters of pairing-friendly elliptic curves that induces minimal security loss by Cheon's algorithm.  ...  In ICISC 2007, Comuta and others showed that among the methods for constructing pairing-friendly curves, those using cyclotomic polynomials, that is, the Brezing-Weng method and the Freeman-Scott-Teske  ...  Main Algorithm We call an elliptic curve with a small embedding degree and a large prime-order subgroup a pairing-friendly curve.  ... 
doi:10.4218/etrij.11.0210.0338 fatcat:6ipixamcajbejebvcqmzb5lmnq
« Previous Showing results 1 — 15 out of 2,317 results