[Gzz-commits] manuscripts/Sigs article.rst

[Benja Fallenstein]

CVSROOT:        /cvsroot/gzz
Module name:    manuscripts
Changes by:     Benja Fallenstein <address@hidden>      03/05/19 18:24:32

Modified files:
        Sigs           : article.rst 

Log message:
        twid

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/manuscripts/Sigs/article.rst.diff?tr1=1.153&tr2=1.154&r1=text&r2=text

Patches:
Index: manuscripts/Sigs/article.rst
diff -u manuscripts/Sigs/article.rst:1.153 manuscripts/Sigs/article.rst:1.154
--- manuscripts/Sigs/article.rst:1.153  Mon May 19 18:05:53 2003
+++ manuscripts/Sigs/article.rst        Mon May 19 18:24:32 2003
@@ -63,7 +63,7 @@
 their operation does not rely on
 trapdoor functions, whose strength is based on
 unproven number-theoretic assumptions such as the
-difficulty of factoring large integers [XXX].
+difficulty of factoring large integers.
 
 Unlike signature schemes based on trapdoor functions,
 one-time signatures can withstand a long-time
@@ -278,13 +278,22 @@
     }
     \end{table*}
 
-For example, using the Merkle signature scheme [XXX],
-with X long sigs and X ...
+To sign `$b$` bits, the Merkle signature scheme uses 
+`$k=(b+\\lfloor \\log{2} b \\rfloor+1)$` numbers of length
+`$h$` as the private key. Therefore, `$k$` calls 
+to the oracle are needed to generate a new private key.
+To generate a public key from a private key,
+the Merkle scheme needs `$k$` calls to the hash function.
+Signing only consists of revealing random numbers
+from the private key and doesn't use the hash function.
+Verification needs at most `$k$` hash function
+invocations. Therefore, we get `$t_s'=0$` and
+`$t_v'=k$`; for the generation of the key pair,
+we get `$t_0'=2k$`.
 
-
-with `$N=32$` and `$n=5$` and a 160-bit hash,
+With `$N=32$` and `$n=5$` and a 160-bit hash,
 we obtain a signature scheme
-with 110.0KB signatures and uses
+with 110 KB signatures and uses
 `$2.1\\cdot 10^{5}$`
 hash invocations for signing and `$5.6\\cdot 10^3$` 
 hash invocations for verification. 
@@ -299,8 +308,8 @@
     ts=2.02e+05 [~1009.76ms], 
     tv=5.57e+03 [~27.84ms])
 
-The private keys in these schemes is only 160 bits long;
-the random oracle is used to generate all the other private keys.
+The private keys in these schemes need only be 160 bits long;
+the random oracle can be used to generate all the other private keys.
 
 
 Practical Variants