Evaluation of Authentication Algorithms for Small Devices

A
B
1 s : 1 ≤ s ≤ (n − 1)
coprime(n, s)
1 Public Key 3 : v = s 2 mod n
1 r ∈ [1, (n − 1)]
1
2 (n2 + n) x = r 2 mod n −→
+(2n − n)(n + 3)
←− e ∈ [0, 1] 1
0 e = 0 : y = r −→
(n-1)(n-1) e = 1 : y = r · s mod n −→ y = 0: reject
+(2n-n)(n+3) y 2 ≡ x· v e 1
: accept
2 (n2 + n)
+(2n − n)(n + 3)
Now again the number of simple multiplications can be summed up. Because of the
probability getting a one or zero as repsonse causes the need of a probality b which
is, because of the random out of two elements b= 1 2 .
A: 3 + ( 1 2 (n2 + n) + (2n − n)(n + 3) + 1 [(n − 1)(n − 1) + (2n − n)(n + 3)]
2
= 3 + 1 2 (5n2 + 2n + 1)
B:1 + 1 2 [(n − 1)(n − 1)] + 1 2 [(2n − n)(n + 3)] + ( 1 2 (n2 + n) = 1 + 1 2 (3n2 + 6n + 1)
In every round the chance of being lucky with guessing the corresponding response
r without the knowledge of s is 1 . This means that the probability to successful
2
guess in every round and to cheat the authentication is ( 1 2 )n . In order to satisfy the
verifiers demands for a successful authentication, the algorithm works with multiple
rounds. To achieve a equivalent confidence as for example we would get with SSH
we assume that about 20 to 40 rounds are required. The hope in using this protocol
is to be able to adapt the complexity to the actual needs.
Running the protocol over x rounds does not mean that the number of messages is
increased to: number of messages · x, as we will show later on.
3 It’s only one calculation because it’s only done once