Lecture 3.1: Handling Remote Access: RADIUS Motivation
Lecture 3.1: Handling Remote Access: RADIUS Motivation
Lecture 3.1: Handling Remote Access: RADIUS Motivation
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Properties of a good hash function<br />
Preimage resistance<br />
Given Y = result of a hash, it is hard to find X such<br />
as H(X)=Y<br />
Second preimage resistance<br />
Given X, it is hard to find another X’ such that<br />
H(X) = H(X’)<br />
Collision resistance<br />
It is hard to find two generic X1 and X2 such that<br />
H(X1) = H(X2)<br />
Giuseppe Bianchi<br />
1. What is the<br />
probability that<br />
none of you N=22<br />
is born in my<br />
same day?<br />
2. What is the<br />
probability that<br />
no two+ of us<br />
N=23 are born the<br />
same day?<br />
Giuseppe Bianchi<br />
Birthday paradox<br />
H<br />
Human being X birthday<br />
⎛<br />
⎜1−<br />
⎝<br />
1<br />
365<br />
⎞<br />
⎟<br />
⎠<br />
22<br />
⎛ 364 ⎞<br />
= ⎜ ⎟<br />
⎝ 365 ⎠<br />
22<br />
=<br />
94.<br />
1%<br />
⎛ 1 ⎞ ⎛ 2 ⎞ ⎛ 22 ⎞<br />
1⋅⎜1<br />
− ⎟⋅<br />
⎜1−<br />
⎟⋅<br />
⋅⋅<br />
⎜1−<br />
⎟ =<br />
⎝ 365 ⎠ ⎝ 365 ⎠ ⎝ 365 ⎠<br />
365⋅<br />
( 365 −1)<br />
⋅⋅⋅<br />
( 365 − 22)<br />
=<br />
=<br />
23<br />
365<br />
365!<br />
/ ( 365 − 23)!<br />
=<br />
= 49.<br />
3%<br />
23<br />
365<br />
!!<br />
11
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