Abstract by anuja a sonalker on Asymmetric Key Distribution

k
is chosen from a large enough set ( ideally, d
k
 > 
max (p,q)) so that a cryptanalyst cannot find it by a direct search. 
e:
public key exponent. This exponent is smaller compared to d
k 
so that the 
verification process is faster. Typically, e=3. 
d
s1
, d
s2
,d
s3
, d
s4
,……d
sk
 : private share server key shares. 
d
ss
 :
Special Server’s private-key share. 
M:
A message, which the client wants, signed.
Mx: An initial message sent by the trusted dealer if present in a scheme, containing the 
x
th
share servers private keys d
sx
. 
Ex, Dx : The encryption and decryption keys of the x
th
share server used in order to send 
the x
th 
server its set of private keys initially. 
Assumption #1: The number of shares for generating a valid key is dependent upon the 
threshold t. The value of t needs to be negotiated beforehand. In this setup, one of the 

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Share Servers (Server 1) decides the value of threshold t. It is also assumed that all other 
factors that need to be decided prior to setup are done either by Server1 or the Special 
Server. 
The Trusted Dealer computes the secret components (N, e, d ) and then starts dividing the 
private-key into smaller shares. The Trusted Dealer creates a set of t+1 private-key shares 
for every possible combination of t share servers. Each combination is marked by a 
lookup that serves as an identifier for the share servers participating in that combination. 
The TD then sends each share server its private-key shares. Key share generation and 
distribution by the Trusted Dealer is discussed in detail in the next section. 
We consider a generic scenario where the Special Server (SS) sends a message M, to be 
signed, to Server 1 (SA) who generates a random sequence of t numbers from 1 to k, to 
decide which of the k share servers participate in this Certificate Signing Request (CSR). 
Once the server combination is decided upon and the SS is made aware of this 
combination, the share servers are individually contacted by the Special Server 
(implementation preference
*
). Each share server looks up its private-key share 
corresponding to this combination and computes its signature share as S