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Add references for BLS and BN curves. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2018-04-21 07:11:00 +01:00
parent 34714e064c
commit b086930d5a
2 changed files with 25 additions and 4 deletions
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9
protocol/protocol.tex
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@ -6220,8 +6220,8 @@ Let $\ParamG{b} := 3$.
(\hairspace $\ParamG{q}$ and $\ParamG{r}$ are prime.)
Let $\GroupG{1}$ be the group of points on a Barreto--Naehrig curve $\CurveG{1}$ over
$\GF{\ParamG{q}}$ with equation $y^2 = x^3 + \ParamG{b}$.
Let $\GroupG{1}$ be the group of points on a Barreto--Naehrig (\cite{BN2005})
curve $\CurveG{1}$ over $\GF{\ParamG{q}}$ with equation $y^2 = x^3 + \ParamG{b}$.
This curve has embedding degree 12 with respect to $\ParamG{r}$.
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.)
Let $\GroupS{1}$ be the group of points on a Barreto--Lynn--Scott curve $\CurveS{1}$ over
$\GF{\ParamS{q}}$ with equation $y^2 = x^3 + \ParamS{b}$.
Let $\GroupS{1}$ be the group of points on a Barreto--Lynn--Scott (\cite{BLS2002})
curve $\CurveS{1}$ over $\GF{\ParamS{q}}$ with equation $y^2 = x^3 + \ParamS{b}$.
This curve has embedding degree 12 with respect to $\ParamS{r}$.
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)
in network protocol version $170004$.
\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 Caveat the claim about \noteTraceabilitySet in \crossref{overview} and link to
\cite{Peterson2017} and \cite{Quesnelle2017}.

20
protocol/zcash.bib
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@ -75,6 +75,26 @@ Lecture Notes in Computer Science; Springer, 2013.},
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,
presort={Vercauter2009},
author={Frederik Vercauteren},