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revision 1.109 by tjl, Mon May 19 15:05:59 2003 UTC revision 1.110 by tjl, Mon May 19 15:40:31 2003 UTC
# Line 185  In order to be able to sign 160-bit hash Line 185  In order to be able to sign 160-bit hash
185  a unique private key for each 160-bit hash.  a unique private key for each 160-bit hash.
186  This is done by requiring that `$q^N > 2^{160}$` and choosing  This is done by requiring that `$q^N > 2^{160}$` and choosing
187  `$x$` based on the bits of the hash to be signed.  `$x$` based on the bits of the hash to be signed.
188  - however, we *can* use OTS algorithms with chosen-message attacks since final pubkey  If we use Merkle hash trees to obtain the underlying `$q$`-time scheme
189    not known  from a one-time scheme, we have for the parameters of the two algorithms
190    the inequality `$ nN \ge 160 $`.
191  we want the full deterministic  Obtaining the minimal integral solutions of this inequality
192  algorithm, for 160-bit hashes  gives us a tradeoff where the length of the signature is approximately
193  that, which requires `$ nN = 160 $`.  linear with `$N$` and the time to sign grows exponentially with `$n$`.
194    
195  All choices produce a *linear* operation from the characteristics  All choices produce a *linear* operation from the characteristics
196  of a scheme to the characteristics of the other scheme.  of a scheme to the characteristics of the other scheme.
# Line 198  Particularly, the signature length incre Line 198  Particularly, the signature length incre
198  and the time to sign grows exponentially with `$n$` and  and the time to sign grows exponentially with `$n$` and
199  linearly (in the opposite direction!) with `$N$`.  linearly (in the opposite direction!) with `$N$`.
200    
201    For example,
202    
203      - feasible      - feasible
204    

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