334 |
$\frac{b}{n}(2^n-1)+1$ \\ |
$\frac{b}{n}(2^n-1)+1$ \\ |
335 |
\parbox{\sw}{BiBa $(h,b,q,n,t,w)$} |
\parbox{\sw}{BiBa $(h,b,q,n,t,w)$} |
336 |
& $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\ |
& $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\ |
337 |
|
\parbox{\sw}{PowerBall $(?)$} |
338 |
|
\\ |
339 |
\parbox{\sw}{Reyzin subset-resilient $(h,b,t,k)$ } |
\parbox{\sw}{Reyzin subset-resilient $(h,b,t,k)$ } |
340 |
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $1$ & $1+k$ \\ |
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $1$ & $1+k$ \\ |
341 |
|
|
510 |
|
|
511 |
Octuplet: `$(q, b, th, wh, h, t, ?+wh, w)$` XXX check |
Octuplet: `$(q, b, th, wh, h, t, ?+wh, w)$` XXX check |
512 |
|
|
513 |
|
Probability for successful forgery at one attempt |
514 |
|
after `$r$` signatures: |
515 |
|
`$ {rk \\over k} (n-1)^{(r-1)k} / n^{rk-1} $` |
516 |
|
|
517 |
|
MERKLE HASH TREE VARIANT!!! REDUCE PUBLIC KEY + SIG SIZE!!! |
518 |
|
|
519 |
Reyzin |
Reyzin |
520 |
------ |
------ |
546 |
|
|
547 |
Octuplet: `$(1, b, kh, th, h, t, 1, 1+k)$` XXX check |
Octuplet: `$(1, b, kh, th, h, t, 1, 1+k)$` XXX check |
548 |
|
|
549 |
|
MERKLE HASH TREE VARIANT!!! REDUCE PUBLIC KEY + SIG SIZE!!! |
550 |
|
|
551 |
Bleichenbacher-Maurer |
Bleichenbacher-Maurer |
552 |
--------------------- |
--------------------- |
648 |
`$t=175$`, `$k=62$` |
`$t=175$`, `$k=62$` |
649 |
|
|
650 |
- Bleichenbacher-Maurer. |
- Bleichenbacher-Maurer. |
651 |
|
To sign 160 bits, we need `$n=29$` |
652 |
|
|
653 |
|
|
654 |
Conclusion |
Conclusion |