Cryptography Reference
In-Depth Information
Let A be a set of N pairwise relatively prime numbers from
Z
p
−
1
which are smaller
than B. We pick n pairwise different numbers a
1
,...,
a
n
in A. We define
r
a
1
1
r
a
n
n
R
=
...
mod
p
a
1
H
(
M
1
)
s
1
a
n
H
(
M
n
)
s
n
=
+···+
−
G
mod (
p
1)
a
1
r
1
a
n
r
n
s
n
Y
=
s
1
+···+
mod (
p
−
1)
.
Show that y
Y
R
g
G
(mod
p
)
if all signatures are correct. What is the complexity of
this computation in terms of n,
≡
, and B? Show that if one signature is incorrect, then
this property holds only with a probability at most N
−
2
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