ICS 180: Introduction to Cryptography
4/23/2004
Homework 3
Due
Tuesday
, 5/04/2004
[[ you get more than a week! ]]
1
Authentication Scheme from OneWay Permutations
Let PPT algorithms (
Gen,Sample,Eval
) defne a OWF (or OWP)
{
f
i
}
i
∈I
. Suppose that
players
U
and
B
use the ±ollowing authentication scheme. For example, say that
B
is a
bank’s web portal and
C
is a web applet run by the bank’s client. The scheme is designed
to last ±or one year, and needs to be reinitialized a±ter that:
•
Initialization Protocol:
Let
n
= 365.
B
runs
Gen
(1
τ
) to pick a oneway ±unction
f
i
with security parameter
τ
and runs
Sample
(
i
) to pick a random element
x
(
n
)
in the domain
D
i
o±
f
i
. Then
B
computes, ±or
k
going ±rom
n
down to 1, values
x
(
k
−
1)
=
f
i
(
x
(
k
)
) =
Eval
(
i,x
(
k
)
). (You’ll see in a second why we are computing them
backward rather than ±orward.)
B
keeps ±or himsel±
x
(0)
as the “verifcation value” ±or
C
, and gives to
C
(over some secure channel) the “root authentication secret”
x
(365)
.
C
then regenerates all the
x
(
k
)
values ±or
k
= 0
,...,
364 by consecutive applications o±
f
i
. Let’s denote
k
times repeated application o±
f
i
as a ±unction (
f
i
)
(
k
)
:
D
i
→ {
0
,
1
}
∗
.
With this notation we have
x
(
n
−
k
)
= (
f
i
)
(
k
)
(
x
(
n
)
) ±or every
k
.
•
Authentication Protocol:
To authenticate himsel± to
B
on day
t
,
C
sends to
B
value
x
=
x
(
t
)
and announces that he is “
C
”.
B
then picks the yesterday’s verifcation
value
x
(
t
−
1)
±or that client, and authenticates this client as indeed “
C
” i±
f
i
(
x
) =
x
(
t
−
1)
.
I± the equation holds
B
stores
x
as
x
(
t
)
. (It’s easy to generalize this to the case when
C
contacted
B
last on any day
t
′
< t
: Just compute (
f
i
)
(
t
−
t
′
)
on
x
(
t
)
and compare
with
x
(
t
′
)
.)
Assume that the adversary
E
, who tries to authenticate himsel± as “
C
” to
B
too, can
eavesdrop
on all instances o± the (
C,B
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 Spring '04
 Jarecki

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