Abstract by anuja a sonalker on Asymmetric Key Distribution

Fig 3.3: The Asymmetric Key Distribution algorithm
3.4 Mathematical Analysis of the Asymmetric Key Distribution Algorithm 
Before the mathematical analysis, it is necessary to define all the key variables and the 
manner in which they are used. 
N :
is a strong prime, which comprises of two strong, large prime factors p & q.
Strong primes have certain properties that make the product N hard to factor by 
specific factoring methods; such properties have included, for example, the 
existence of a large prime factor of p-1 and a large prime factor of p+1. This is 
because certain factoring algorithms look for certain properties and strong primes 
can survive such factoring methods. Large primes survive most factoring methods 
by virtue of their size. The amount of time taken to factorize, for example a 140 
digit number using the fastest factoring method today- the Number Field Sieve is 
approximately 1.7 x 10
19 
operations.

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22 
k :
Total number of Share Servers present in the setup. 
t :
Threshold, total number of Share Servers needed to apply shares for a transaction. 
The value of t should lie between (
2
k
+1) and k. A threshold value of k would 
imply an absence of a threshold. Mathematically, the threshold selection for this 
system is made based on the following rule: 
(
2
k
+1) 
≤
t 
<
k. 
t+1 : Number of valid signature shares required to sign a message successfully. Of 
these, t are provided by the share servers and one by the Special Server. 
d :
private key exponent. This private key is never assembled during the course of the 
operation. It is assumed that d