151 |
- verify: check that the revealed RNs hashes to right hash in public key - |
- verify: check that the revealed RNs hashes to right hash in public key - |
152 |
calculate `$b$` hashes |
calculate `$b$` hashes |
153 |
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|
154 |
|
Merkle (?) |
155 |
|
---------- |
156 |
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|
157 |
|
This scheme is an improvement over Lamport, needing |
158 |
|
only `$k=b+\\lceiling \\log{2} b \\rceiling$` hashes. |
159 |
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160 |
|
Let `$m_i$` be the `$i$`-th bit of the message. |
161 |
|
|
162 |
|
- private key: A list of `$k$` random numbers `$R_i$`. |
163 |
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164 |
|
- public key: Compute a list of `$k$` hashes `$P_i=H(R_i)$`; |
165 |
|
the hash of this list is the public key. |
166 |
|
|
167 |
|
- sign: Reveal the `$R_i$` for `$i \\le b$` if the |
168 |
|
`$m_i=0$`. Compute the checksum `$c=\\sum{m_i}$`, |
169 |
|
and interpret as a bitstring. Reveal `$R_{b+i}$` |
170 |
|
if the `$i$`-th bit of the bitstring is zero. |
171 |
|
|
172 |
|
- verify: |
173 |
|
|
174 |
Merkle-Winternitz |
Merkle-Winternitz |
175 |
----------------- |
----------------- |
176 |
|
|
405 |
$\frac{b}{n}(2^n-1)+1$ \\ |
$\frac{b}{n}(2^n-1)+1$ \\ |
406 |
\parbox{\sw}{BiBa $(h,b,q,n,t,w)$} |
\parbox{\sw}{BiBa $(h,b,q,n,t,w)$} |
407 |
& $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\ |
& $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\ |
|
\parbox{\sw}{Reyzin 1st $(h,b,t,k)$ } |
|
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& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $?$ (XXX) & $?+k$ (XXX) \\ |
|
408 |
\parbox{\sw}{Reyzin 2nd $(h,b,t,k)$ } |
\parbox{\sw}{Reyzin 2nd $(h,b,t,k)$ } |
409 |
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $1$ (XXX) & $1+k$ (XXX) \\ |
& $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $1$ (XXX) & $1+k$ (XXX) \\ |
410 |
|
|