mirror of https://github.com/zcash/zips.git
Add references for BLS and BN curves.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
parent
34714e064c
commit
b086930d5a
|
@ -6220,8 +6220,8 @@ Let $\ParamG{b} := 3$.
|
||||||
|
|
||||||
(\hairspace $\ParamG{q}$ and $\ParamG{r}$ are prime.)
|
(\hairspace $\ParamG{q}$ and $\ParamG{r}$ are prime.)
|
||||||
|
|
||||||
Let $\GroupG{1}$ be the group of points on a Barreto--Naehrig curve $\CurveG{1}$ over
|
Let $\GroupG{1}$ be the group of points on a Barreto--Naehrig (\cite{BN2005})
|
||||||
$\GF{\ParamG{q}}$ with equation $y^2 = x^3 + \ParamG{b}$.
|
curve $\CurveG{1}$ over $\GF{\ParamG{q}}$ with equation $y^2 = x^3 + \ParamG{b}$.
|
||||||
This curve has embedding degree 12 with respect to $\ParamG{r}$.
|
This curve has embedding degree 12 with respect to $\ParamG{r}$.
|
||||||
|
|
||||||
Let $\GroupG{2}$ be the subgroup of order $r$ in the sextic twist $\CurveG{2}$ of
|
Let $\GroupG{2}$ be the subgroup of order $r$ in the sextic twist $\CurveG{2}$ of
|
||||||
|
@ -6386,8 +6386,8 @@ Let $\ParamS{b} := 4$.
|
||||||
|
|
||||||
(\hairspace $\ParamS{q}$ and $\ParamS{r}$ are prime.)
|
(\hairspace $\ParamS{q}$ and $\ParamS{r}$ are prime.)
|
||||||
|
|
||||||
Let $\GroupS{1}$ be the group of points on a Barreto--Lynn--Scott curve $\CurveS{1}$ over
|
Let $\GroupS{1}$ be the group of points on a Barreto--Lynn--Scott (\cite{BLS2002})
|
||||||
$\GF{\ParamS{q}}$ with equation $y^2 = x^3 + \ParamS{b}$.
|
curve $\CurveS{1}$ over $\GF{\ParamS{q}}$ with equation $y^2 = x^3 + \ParamS{b}$.
|
||||||
This curve has embedding degree 12 with respect to $\ParamS{r}$.
|
This curve has embedding degree 12 with respect to $\ParamS{r}$.
|
||||||
|
|
||||||
Let $\GroupS{2}$ be the subgroup of order $\ParamS{r}$ in the sextic twist $\CurveS{2}$ of
|
Let $\GroupS{2}$ be the subgroup of order $\ParamS{r}$ in the sextic twist $\CurveS{2}$ of
|
||||||
|
@ -8855,6 +8855,7 @@ found by Brian Warner.
|
||||||
\item Specify support for \cite{BIP-111} (the \texttt{NODE\_BLOOM} service bit)
|
\item Specify support for \cite{BIP-111} (the \texttt{NODE\_BLOOM} service bit)
|
||||||
in network protocol version $170004$.
|
in network protocol version $170004$.
|
||||||
\item Give references \cite{Vercauter2009} and \cite{AKLGL2010} for the optimal ate pairing.
|
\item Give references \cite{Vercauter2009} and \cite{AKLGL2010} for the optimal ate pairing.
|
||||||
|
\item Give references for BLS \cite{BLS2002} and BN \cite{BN2005} curves.
|
||||||
\item Define $\KASproutDerivePublic$ for $\KASproutCurve$.
|
\item Define $\KASproutDerivePublic$ for $\KASproutCurve$.
|
||||||
\item Caveat the claim about \noteTraceabilitySet in \crossref{overview} and link to
|
\item Caveat the claim about \noteTraceabilitySet in \crossref{overview} and link to
|
||||||
\cite{Peterson2017} and \cite{Quesnelle2017}.
|
\cite{Peterson2017} and \cite{Quesnelle2017}.
|
||||||
|
|
|
@ -75,6 +75,26 @@ Lecture Notes in Computer Science; Springer, 2013.},
|
||||||
Last revised September~12, 2011.}
|
Last revised September~12, 2011.}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
@misc{BLS2002,
|
||||||
|
presort={BLS2002},
|
||||||
|
author={Paulo Barreto and Ben Lynn and Michael Scott},
|
||||||
|
title={Constructing {E}lliptic {C}urves with {P}rescribed {E}mbedding {D}egrees},
|
||||||
|
url={https://eprint.iacr.org/2002/088},
|
||||||
|
urldate={2018-04-20},
|
||||||
|
howpublished={Cryptology ePrint Archive: Report 2002/088.
|
||||||
|
Last revised February~22, 2005.}
|
||||||
|
}
|
||||||
|
|
||||||
|
@misc{BN2005,
|
||||||
|
presort={BN2005},
|
||||||
|
author={Paulo Barreto and Michael Naehrig},
|
||||||
|
title={Pairing-{F}riendly {E}lliptic {C}urves of {P}rime {O}rder},
|
||||||
|
url={https://eprint.iacr.org/2005/133},
|
||||||
|
urldate={2018-04-20},
|
||||||
|
howpublished={Cryptology ePrint Archive: Report 2005/133.
|
||||||
|
Last revised February~28, 2006.}
|
||||||
|
}
|
||||||
|
|
||||||
@misc{Vercauter2009,
|
@misc{Vercauter2009,
|
||||||
presort={Vercauter2009},
|
presort={Vercauter2009},
|
||||||
author={Frederik Vercauteren},
|
author={Frederik Vercauteren},
|
||||||
|
|
Loading…
Reference in New Issue