/[gzz]/manuscripts/Sigs/article.rst
ViewVC logotype

Diff of /manuscripts/Sigs/article.rst

Parent Directory Parent Directory | Revision Log Revision Log | View Patch Patch

revision 1.97 by benja, Sun May 18 19:50:56 2003 UTC revision 1.98 by benja, Sun May 18 20:06:17 2003 UTC
# Line 329  and Line 329  and
329                  $b+\lceil \log{2} b \rceil + 1$ & $0$ &                  $b+\lceil \log{2} b \rceil + 1$ & $0$ &
330                  $\le b$ \\                  $\le b$ \\
331          \parbox{\sw}{Merkle-Winternitz\cite{XXX} $(h,b,n)$ }          \parbox{\sw}{Merkle-Winternitz\cite{XXX} $(h,b,n)$ }
332              & $1$ & $b$ & $\frac{bh}{n}+h$ & $h$ & $h$ &              & $1$ & $b$ & $\frac{b}{n}h+h$ & $h$ & $h$ &
333                  $2\frac{b}{n}(2^n-1)+1$ & $\frac{b}{n}(2^n-1)+1$ &                  $2\frac{b}{n}(2^n-1)+1$ & $\frac{b}{n}(2^n-1)$ &
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              & $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\              & $q$ & $b$ & $th$ & $wh$ & $h$ & $t$ & $?+wh$ & $w$ \\
# Line 454  Let `$H$` donate the hash function, with Line 454  Let `$H$` donate the hash function, with
454    
455  - private key: A list of random numbers `$(R_0,...,R_k)$`.  - private key: A list of random numbers `$(R_0,...,R_k)$`.
456    
457  - public key: Compute `$P_0=H^{k2^n}(R_0)$`, and  - public key: Compute `$P_0=H^{k(2^n-1)}(R_0)$`, and
458    `$P_i=H^{2^n}(R_i)$` for `$i>0$`. The hash of    `$P_i=H^{2^n-1}(R_i)$` for `$i>0$`. The hash of
459    `$(P_0,...,P_k)$` is the public key.    `$(P_0,...,P_k)$` is the public key.
460    
461    Needs `$2k2^n + 1$` hash function invocations.    Needs `$2k(2^n-1) + 1$` hash function invocations.
462    
463  - signature: Split the `$b$`-bit message into `$k$`  - signature: Split the `$b$`-bit message into `$k$`
464    parts of `$n$` bits each. Interpreted each part    parts of `$n$` bits each. Interpreted each part
465    as an integer `$k_i$` for `$0 < i \\le k$`.    as an integer `$k_i$` for `$0 < i \\le k$`.
466    Compute `$S_i=H^{k_i}(R_i)$` for `$i>0$`    Compute `$S_i=H^{k_i}(R_i)$` for `$i>0$`
467    and `$S_0=H^{2^nk-\\sum{k_i}}(R_0)$`. The tuple    and `$S_0=H^{(2^n-1)k-\\sum{k_i}}(R_0)$`. The tuple
468    `$(S_0,...,S_k)$` is the signature.    `$(S_0,...,S_k)$` is the signature.
469    
470    Signing requires `$k2^n$` invocations    Signing requires `$k(2^n-1)$` invocations
471    of the hash function.    of the hash function.
472    
473  - verification: Compute `$k_i$` as above.  - verification: Compute `$k_i$` as above.
474    Compute `$V_0=H^{\\sum{k_i}}(S_0)$`    Compute `$V_0=H^{\\sum{k_i}}(S_0)$`
475    and `$V_i=H^{2^n-k_i}(S_i)$` for `$i>0$`.    and `$V_i=H^{2^n-1-k_i}(S_i)$` for `$i>0$`.
476    Check that the hash of `$(V_0,...,V_i)$`    Check that the hash of `$(V_0,...,V_i)$`
477    equals the public key.    equals the public key.
478    
479    Verification requires `$k2^n + 1$` invocations    Verification requires `$k(2^n-1) + 1$` invocations
480    of the hash function.    of the hash function.
481    
482  Octuplet: `$(1, b, \\frac{bh}{n}+h, h, h,  Octuplet: `$(1, b, kh + h, h, h,
483  2\\frac{b}{n}(2^n-1)+1, \\frac{b}{n}(2^n-1)+1,  2k(2^n-1)+1, k(2^n-1)+1, k(2^n-1)+1)$`
 \\frac{b}{n}(2^n-1)+1)$`  
484    
485    
486  BiBa  BiBa

Legend:
Removed from v.1.97  
changed lines
  Added in v.1.98

savannah-hackers-public@gnu.org
ViewVC Help
Powered by ViewVC 1.1.26