Abstract by anuja a sonalker on Asymmetric Key Distribution

1
, S
2
, S
3
…S
t
, 
where S
i
= M
d
i
mod N.
After computing their signature shares, the share servers send their signature shares either 
to the SS directly or to the SA. In the above-mentioned setup it would be to the SS 
himself as our objective here is to minimize communication overheads. In case of SA 
intervention, the SA passes on the uncombined shares to the Special Server only after 
verifying that the servers are not compromised and that the shares are otherwise 
authentic. In the absence of an SA, the Special Server would perform the server 
verification. The SS on reception of t shares examines them & selects the appropriate 
private-key share out of its 
C
k
t
§ 
shares to successfully complete the signature request. 
* Certain decisions, unrelated to the algorithm, were made at the time of implementation based on ease and minimum 
overheads. 
§ 
C
k
t
= 
)!
(
!
!
t
k
t
k
−
is the number of combinations of k items taken t at a time. 

---

24 
Mathematically,
The Client signature share is represented by:
S
c 
= M
d
c
mod N 
And each of the t Share Server’s would create a share represented by: 
S
i 
= M
s
i
mod N where i 
∈
{1,….k}. 
And finally the completely signed signature would be : 
S = S
c x
∏
=
t
i
i
S
1
mod N. 
To check if the shares have been applied correctly, the client computes S
e
with the help 
of the public exponent e and checks whether S
e 
mod N = M. If that is the case, the
private keys were applied correctly and the Signed Message S is a valid signature.