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Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation
NFS optimal ate pairing computation
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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...
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
Orbit rotation symmetric function Walsh transform
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2015/12/30
In the literature, few constructions of n-variable rotation symmetric bent functions have been presented,
which either have restriction on n or have algebraic degree no more than 4. In this paper, fo...
On near prime-order elliptic curves with small embedding degrees
Pairing Friendly Elliptic Curve MNT curves Complex Multiplication
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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...
Constructing Elliptic Curves with Prescribed Embedding Degrees
Constructing Elliptic Curves Prescribed Embedding Degrees
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2009/4/14
Pairing-based cryptosystems depend on the existence of
groups where the Decision Diffie-Hellman problem is easy to solve,
but the Computational Diffie-Hellman problem is hard. Such is the
case of e...
On prime-order elliptic curves with embedding degrees k = 3, 4 and 6
Elliptic curves pairing-based cryptosystems
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2008/5/22
We further analyze the solutions to the Diophantine equa-
tions from which prime-order elliptic curves of embedding degrees k =
3, 4 or 6 (MNT curves) may be obtained.We give an explicit algorithm t...
Implementing Cryptographic Pairings Over Curves of Embedding Degrees 8 and 10
bilinear pairings cryptography pairing-friendly curves
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2008/5/22
In this paper, we will describe efficient implementations of
the Tate and Ate pairings over ordinary elliptic curves of embedding degrees
8 and 10. We will discuss the possible curve-dependent optim...