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Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Optimal ate pairing twists of elliptic curves jacobian coordinates
2019/5/27
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a pa...
Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation
NFS optimal ate pairing computation
2019/4/28
Recent algorithmic improvements of discrete logarithm computation in special extension fields threaten the security of pairing-friendly curves used in practice. A possible answer to this delicate situ...
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
TNFS-secure optimal pairing twisted Ate pairing
2018/11/6
In this paper we give a comprehensive comparison between pairing-friendly elliptic curves in Jacobi Quartic and Edwards form with quadratic, quartic, and sextic twists. Our comparison looks at the bes...
Embedding Multiplications at a Linear Rate and its Applications
algebraic function fields Embedding Multiplications
2018/5/2
Although the study of this embedding problem is of independent theoretical interest, we present a few representative applications to secure computation. We construct a linear number of oblivious trans...
In Praise of Twisted Canonical Embedding
Lattice techniques number theory canonical embedding
2018/4/19
In ideal-lattice cryptography, lattices are generated by defining a bijective map between an ideal of a ring of integers and a subset of Cn. This map can be taken to be the coefficient embedding and, ...
Contract signing protocols have been proposed and analyzed for more than three decades now. One of the main problems that appeared while studying such schemes is the impossibility of achieving both fa...
Optimal Ate Pairing on Elliptic Curves with Embedding Degree 9,15 and 27
Elliptic Curves Optimal Pairings Miller's algorithm
2017/1/3
Since the advent of pairing based cryptography, much attention has been given to efficient computation of pairings on elliptic curves with even embedding degrees. The few works that exist in the case ...
On Implementing Pairing-Based Protocols with Elliptic Curves of Embedding Degree One
public-key cryptography implement pairing-based protocols
2016/4/26
We observe that the conventional classification of pairings into Types 1, 2, 3 and 4 is not applicable to pairings from elliptic curves with embedding degree one. We define three kinds of pairings fro...
On near prime-order elliptic curves with small embedding degrees
Pairing Friendly Elliptic Curve MNT curves Complex Multiplication
2015/12/23
In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to
generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all fa...
Self-pairings on supersingular elliptic curves with embedding degree $three$
Tate pairing Weil pairing
2014/3/10
Self-pairings are a special subclass of pairings and have interesting applications in cryptographic schemes and protocols. In this paper, we explore the computation of the self-pairings on supersingul...
By embedding a Toeplitz matrix-vector product (MVP) of dimension $n$ into a circulant MVP of dimension $N=2n+\delta -1$, where $\delta $ can be any nonnegative integer, we present a $GF(2^n)$ multipli...
Pairing computation on curves with efficiently computable endomorphism and small embedding degree
elliptic curves pairings isogenies
2010/7/14
Scott uses an efficiently computable isomorphism in order to optimize pairing computation on a particular class of curves with embedding degree 2. He pointed out that pairing implementation becomes th...
A study of pairing computation for curves with embedding degree 15
Pairing based cryptography Pairing computation Arithmetic Interpolation
2009/8/7
This paper presents the first study of pairing computation on curves with embedding
degree 15. We compute the Ate and the twisted Ate pairing for a family of curves with parameter
1.5 and embeddin...
Embedding in Two Least Significant Bits with Wet Paper Coding
Two Least Significant Bits Wet Paper Coding steganalytic attacks
2009/6/5
In this paper, we present three embedding schemes for extensions of least significant bit overwriting to both of the two lowest bit planes in digital images. Our approaches are inspired by the work of...
Abelian varieties with prescribed embedding degree
Abelian varieties prescribed embedding degree
2009/6/2
We present an algorithm that, on input of a CM-field K, an
integer k 1, and a prime r 1 mod k, constructs a q-Weil number
2 OK corresponding to an ordinary, simple abelian variety A over
the f...