/[gzz]/manuscripts/Sigs/article.rst
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revision 1.92 by benja, Sun May 18 19:16:52 2003 UTC revision 1.93 by benja, Sun May 18 19:37:41 2003 UTC
# Line 412  Lamport Line 412  Lamport
412  - 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 -
413    calculate `$b$` hashes    calculate `$b$` hashes
414    
415    Octuplet: `$(1, b, bh, 2bh, h, 2b, 0, b)$`
416    
417    
418  Merkle (?)  Merkle (?)
419  ----------  ----------
420    
# Line 432  Let `$m_i$` be the `$i$`-th bit of the m Line 435  Let `$m_i$` be the `$i$`-th bit of the m
435    
436  - verify:  - verify:
437    
438    Octuplet: `$(1, b, h(b+\\lceil \\log{2} b \\rceil), h, h,
439    b+\\lceil \\log{2} b \\rceil + 1, 0,
440    \\le b+\\lceil \\log{2} b \\rceil$`
441    
442    
443  Merkle-Winternitz  Merkle-Winternitz
444  -----------------  -----------------
445    
# Line 466  Let `$H$` donate the hash function, with Line 474  Let `$H$` donate the hash function, with
474    Verification requires `$k2^n + 1$` invocations    Verification requires `$k2^n + 1$` invocations
475    of the hash function.    of the hash function.
476    
477    Octuplet: `$(1, b, \\frac{bh}{n}+h, h, h,
478    2\\frac{b}{n}(2^n-1)+1, \\frac{b}{n}(2^n-1)+1,
479    \\frac{b}{n}(2^n-1)+1)$`
480    
481    
482  BiBa  BiBa
483  ----  ----
484    
# Line 489  until a '`$w$`-time collision' is found. Line 502  until a '`$w$`-time collision' is found.
502    into the same bin; verify that the balls match the public key    into the same bin; verify that the balls match the public key
503    (i.e., that the public key contains their hashes).    (i.e., that the public key contains their hashes).
504    
505    Octuplet: `$(q, b, th, wh, h, t, ?+wh, w)$`
506    
507    
508  Reyzin  Reyzin
509  ------  ------
# Line 516  Probability for successful forgery after Line 531  Probability for successful forgery after
531    
532  ?  ?
533    
534    Octuplet: `$(1, b, kh, th, h, t, 1, 1+k)$`
535    
536    
537  Bleichenbacher-Maurer  Bleichenbacher-Maurer
538  ---------------------  ---------------------
539    
# Line 537  ASIACRPTO construction Line 555  ASIACRPTO construction
555  - verify: check that right nodes revealed, and that tree computes right  - verify: check that right nodes revealed, and that tree computes right
556    public key - calculate some less than `$9n+2$` hashes    public key - calculate some less than `$9n+2$` hashes
557    
558    Octuplet: `$(1, \\lfloor\\eta n\\rfloor,
559    3(n+1)h, h, h, 9n+2, 0, 9n+2)$`
560    
561    
562  Merkle hash trees  Merkle hash trees
563  -----------------  -----------------
564    
# Line 565  all the public keys, just path through t Line 587  all the public keys, just path through t
587    
588  - verify: verify signature with new public key, verify hash chain.  - verify: verify signature with new public key, verify hash chain.
589    
590    Octuplet: `$({2^n}q', b, 2s'+r'+hn, h, h,
591    ({2^n}+1)c_0'+c_s' + 2^{n+1}-1, c_s', 2c_v'+n$`
592    
593  Efficiency of key boosting  Efficiency of key boosting
594  ==========================  ==========================
# Line 576  Efficiency of key boosting Line 600  Efficiency of key boosting
600    
601  - maybe recommendations  - maybe recommendations
602    
603    Octuplet: `${q'}^N, b, N(r'+s'), r', h,
604    c_0', N(c_0'+c_s'), Nc_v)$`
605    
606    
607  Tradeoffs in deterministic key boosting  Tradeoffs in deterministic key boosting
608  ---------------------------------------  ---------------------------------------
609    

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