Abstract by anuja a sonalker on Asymmetric Key Distribution

4.4.1.1 Effect of Key size on key generation time: 
For a threshold of 4-out-of-7, the total number of sets the Trusted Dealer needs to 
generate is 
C
7
4
= 35 without key share reuse and 
4
7
4
C
= 11 with reuse. Similarly for 5-
out-of-7 and 6-out-of-7, the required number of sets without reuse of key shares is 21 and 
7 respectively. By reusing key shares, these numbers are reduced to 7 and 4 respectively. 
From the experiment conducted, we observe that as the size of the private key increases, 
the computation time also increases. Depending on the size of the private key and the 
threshold, the onus of time hogging shifts between time spent on key generation and the 
time spent in splitting up the key into many shares. With smaller key sizes like 512, key 
generation is a fairly fast process.
As the threshold decreases, servers can be chosen out of all the servers present in many 
more ways. The number of sets required increases and hence the fraction of time spent in 
splitting up the key into the required number of key shares begins to look more 
prominent. For example, for a threshold of 4-out-of-7, a 512-bit key requires 
approximately 15 seconds out of which 6.8 seconds is the key generation time and the 
time required to split the key is almost 8 seconds. As the key size increases, key 
generation time increases sharply. For a size 1024 key, the average time required for 
generating and splitting up the key into 4 shares each for 11 sets is approximately 23 
seconds of which roughly 12 seconds is the time spent in generation of the cryptographic 
components (p, q, N, e, d) and roughly 11 seconds in splitting up the private key. 
Similarly for the same threshold, a 2048-bit key consumes 38.7 seconds out of 69.9 
seconds for key generation and 31.2 seconds for splitting up the key. Therefore, as the 
key size increases, the gap between key generation and distribution begins to lessen. Key 
generation time almost doubles from 512-bit to 1024-bit and almost triples for a 2048-bit 
key. As the threshold increases, the number of sets required reduces. This eases the time 
contribution of the key splitting process by a very big margin and widens the gap 
between key generation and key share generation since there is no apparent variation in 
key generation time for changes in threshold. For example, in the case of 1024-bit key 
the time required to generate sets of key shares reduces from a startling 11 seconds to 3.5 

---

46 
seconds for a threshold change from 4-out-of-7 to 6-out-of-7. Table 4.2 shows the time 
measurements for this experiment.