25 |
set without using a trapdoor function, i.e. without |
set without using a trapdoor function, i.e. without |
26 |
relying on |
relying on |
27 |
number-theoretic assumptions such as the hardness |
number-theoretic assumptions such as the hardness |
28 |
of factoring or discrete logs. |
of factoring or discrete logs. |
29 |
|
|
30 |
|
This scheme is existentially |
31 |
|
unforgeable with an adaptive chosen message attack. |
32 |
As long as the random oracle, used to generate the new private keys |
As long as the random oracle, used to generate the new private keys |
33 |
and to implement the one-time signatures, |
and to implement the one-time signatures, |
34 |
isn't broken, an exhaustive |
isn't broken, an exhaustive |
238 |
Bleichenbacher-Maurer |
Bleichenbacher-Maurer |
239 |
--------------------- |
--------------------- |
240 |
|
|
241 |
ASIACRYPTO construction |
ASIACRPTO construction |
242 |
|
|
243 |
- Construction for `$H_n$`: a binary tree, |
- Construction for `$H_n$`: a binary tree, |
244 |
at each node 2 hashes combined into one |
at each node 2 hashes combined into one |
298 |
and the public key is the corresponding one-time-signature |
and the public key is the corresponding one-time-signature |
299 |
public key. |
public key. |
300 |
|
|
301 |
To generate a signature for the message $m$, |
To generate a signature for the message `$m$`, |
302 |
we start by setting `$p$` to the |
we start by setting `$p$` to the |
303 |
private key. |
private key. |
304 |
Then, we iterate over the following steps `$N$` times: |
Then, we iterate over the following steps `$N$` times: |
320 |
4. `$p \\leftarrow p_x$` |
4. `$p \\leftarrow p_x$` |
321 |
|
|
322 |
After the last iteration, `$p$` contains the private key to be used to sign |
After the last iteration, `$p$` contains the private key to be used to sign |
323 |
the actual message $m$ using the one-time-signature primitive. |
the actual message `$m$` using the one-time-signature primitive. |
324 |
The signature consists of this signature and the whole chain |
The signature consists of this signature and the whole chain |
325 |
of signatures connecting this to the original public key. |
of signatures connecting this to the original public key. |
326 |
|
|
385 |
$\frac{b}{n}(2^n-1)+1$ \\ |
$\frac{b}{n}(2^n-1)+1$ \\ |
386 |
\parbox{\sw}{BiBa $(h,b,q,n,t,w)$} |
\parbox{\sw}{BiBa $(h,b,q,n,t,w)$} |
387 |
& $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\ |
& $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\ |
388 |
\parbox{\sw}{Reyzin one-way\cite{XXX} $(h,b,t,k)$ } |
\parbox{\sw}{Reyzin 1st $(h,b,t,k)$ } |
389 |
|
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $?$ (XXX) & $?+k$ (XXX) \\ |
390 |
|
\parbox{\sw}{Reyzin 2nd $(h,b,t,k)$ } |
391 |
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $1$ (XXX) & $1+k$ (XXX) \\ |
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $1$ (XXX) & $1+k$ (XXX) \\ |
|
olean mouseClickHit(MouseEvent e, VobScene oldVobScene, float[] zout); |
|
392 |
|
|
393 |
\parbox{\sw}{Bleichenbacher-Maurer\cite{XXX (ASIACRYPT)} |
\parbox{\sw}{Bleichenbacher-Maurer\cite{XXX(ASIACRYPT)} |
394 |
(h, n) |
(h, n) |
395 |
} |
} |
396 |
& $1$ & $\lfloor\eta n\rfloor$ |
& $1$ & $\lfloor\eta n\rfloor$ |