diff options
author  Florian Dold <florian.dold@gmail.com>  20180925 16:47:18 +0200 

committer  Florian Dold <florian.dold@gmail.com>  20180925 16:53:42 +0200 
commit  74f745bb854ad16f10b1f9dc9b3bef55236e32e8 (patch)  
tree  176a411ffb6ed278e3ea117c92898e7e94c66641 /talerfc19/paper.tex  
parent  d0716421b852348ddec12a20267fa25518189b5e (diff)  
download  papers74f745bb854ad16f10b1f9dc9b3bef55236e32e8.tar.gz papers74f745bb854ad16f10b1f9dc9b3bef55236e32e8.tar.bz2 papers74f745bb854ad16f10b1f9dc9b3bef55236e32e8.zip 
proof stuff
Diffstat (limited to 'talerfc19/paper.tex')
rwrr  talerfc19/paper.tex  59 
1 files changed, 20 insertions, 39 deletions
diff git a/talerfc19/paper.tex b/talerfc19/paper.tex index ba4cd28..3778c63 100644  a/talerfc19/paper.tex +++ b/talerfc19/paper.tex @@ 818,16 +818,7 @@ We require the following security properties to hold for $\textsc{CoinSignKx}$: \end{itemize}
Let $\textsc{Sign} = (\algo{KeyGen}_{S}, \algo{Sign}_{S}, \algo{Verify}_{S})$ be a signature
<<<<<<< HEAD
scheme that satisfies SUFCMA.

Let $(\algo{Setup}_C, H_{pk})$ be a computationally binding commitment
scheme, where $\algo{Setup}$ generates the public commitment key $pk$
and $H_{pk} : \{0,1\}^* \rightarrow \{0,1\}^\lambda$ deterministically
commits to a bitstring.
=======
scheme that satisfies selective unforgeability under chosen message attacks (SUFCMA).
>>>>>>> 534bdbc8e54e678e799cdfb96cfb534fe52f8998
Let $\V{PRF}$ be a pseudorandom function family and $H : \{0,1\}^* \rightarrow \{0,1\}^\lambda$
a collisionresistant hash function.
@@ 837,15 +828,8 @@ Using these primitives, we now instantiate the syntax of our incometransparent \begin{itemize}
\item $\algo{ExchangeKeygen}(1^{\lambda}, 1^{\kappa}, \mathfrak{D})$:
<<<<<<< HEAD
 Generate the exchange's signing key pair
 $\V{skESign} \leftarrow \algo{KeyGen}_{S}(1^\lambda)$ and
 public commitment key $\V{CK} \leftarrow \algo{Setup}_C(1^\lambda)$.

=======
Generate the exchange's signing key pair $\V{skESign} \leftarrow \algo{KeyGen}_{S}(1^\lambda)$.
>>>>>>> 534bdbc8e54e678e799cdfb96cfb534fe52f8998
For each element in the sequence $\mathfrak{D} = d_1,\dots,d_n$, generate
denomination key pair $(\V{skD}_i, \V{pkD}_i) \leftarrow \algo{KeyGen}_{BS}(1^\lambda)$.
\item $\algo{CustomerKeygen}(1^\lambda,1^\kappa)$:
@@ 1250,27 +1234,25 @@ Our instantiation satisfies {weak income transparency}. \begin{enumerate}
\item the execution of the refresh protocol is incomplete,
\item the commitment for the $\gamma$th blinded coin and transfer
 public key does not match the revealed value,
+ public key is dishonest,
\item a commitment for a blinded coin and transfer public key other
 than the $\gamma$th does not match the revealed value,
+ than the $\gamma$th is dishonest,
\end{enumerate}
 We show these to be exhaustive by assuming their converses all hold:
 As the commitment is signed by $\V{skCoin}_0$, our honest key generation
 assumption of $\textsc{CoinSignKx}$ applies to the coin public key.
 Any commitments that match were computed honestly, thanks to our
 commitment scheme $(\algo{Setup}_C, H_{pk})$ being computationally
 binding.
 We assumed the $\gamma$th transfer public key is honest, so
 our key exchange completeness assumption of $\textsc{CoinSignKx}$
 yields $\algo{Kex}_{CSK}(t,C') = \algo{Kex}_{CSK}(c',T)$ where
 $T = \algo{KeyGenPub}_{CSK}(t)$ is the transfer key.
 It follows our customer obtains the correct transfer secret and
 derives the correct coins.
 We assumed the refresh concluded and all submissions besides the
 $\gamma$th were honest, so the exchange correctly reveals the signed
 blinded coin. We assumed the $\gamma$th blinded coin is correct too,
 so customer now recompute the new coin correctly, violating $R_i \in F$.
+ We show these to be exhaustive by assuming their converses all hold: As the
+ commitment is signed by $\V{skCoin}_0$, our key exchange completeness
+ assumption of $\textsc{CoinSignKx}$ applies to the coin public key. Any
+ commitments that match were computed honestly, thanks to our commitment
+ scheme $(\algo{Setup}_C, H_{pk})$ being computationally binding. We assumed
+ the revealed $\gamma$th transfer public key is honest. Hence our key
+ exchange completeness assumption of $\textsc{CoinSignKx}$ yields
+ $\algo{Kex}_{CSK}(t,C') = \algo{Kex}_{CSK}(c',T)$ where $T =
+ \algo{KeyGenPub}_{CSK}(t)$ is the transfer key, thus the customer obtains the
+ correct transfer secret. We assumed the refresh concluded and all
+ submissions besides the $\gamma$th were honest, so the exchange correctly
+ reveals the signed blinded coin. We assumed the $\gamma$th blinded coin is
+ correct too, so customer now recompute the new coin correctly, violating
+ $R_i \in F$.
We shall prove
\begin{equation}\label{eq:incometransparencyproof}
@@ 1279,11 +1261,10 @@ Our instantiation satisfies {weak income transparency}. where the expectation runs over
any probability space used by the adversary and challenger.
 We shall optimize our adversary in ways that maximize $p \over b + p$ by
 proving the optimised adversary exists. We may then restrict our analysis
 to these optimised adversaries, which suffices for our game result, but
 note that reductions would not permit this trick.
 %TODO: Improve??
+ We shall now consider executions of the income transparency game with an
+ optimal adversary with respect to maximizing $p \over b + p$. Note that this
+ is permissible since we are not carring out a reduction, but are interested
+ in the expectation of the game's return value.
As a reminder, if a refresh operation is initiated using a false commitment
that is detected by the exchange, then the new coin cannot be obtained, and
