/[gzz]/manuscripts/Sigs/article.rst
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revision 1.79 by benja, Sun May 18 16:35:05 2003 UTC revision 1.80 by benja, Sun May 18 16:50:02 2003 UTC
# Line 151  Lamport Line 151  Lamport
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    
154    Merkle (?)
155    ----------
156    
157    This scheme is an improvement over Lamport, needing
158    only `$k=b+\\lceiling \\log{2} b \\rceiling$` hashes.
159    
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    
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    
# Line 385  and Line 405  and
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 $(h,b,t,k)$ }  
             & $1$ & $b$ & $kh$ & $th$ & $h$ & $t$ & $?$ (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    

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