An Authenticated and Secure Group Key Transfer Protocol with Circulant Matrices

User Multi Group Key Distribution Using Secret Sharing with Circulate Matrices Based on Diophantine Equation and Ecdh Key Exchange Protocol

“…In [21] explain difference the Cost of computation of [19] and [21] as mentioned table 3 in [22] and our protocol it is clear computation cost is less than [22] because diversity between modular addition and subtraction not just modular multiplication as [22] use. The time for performing modular addition or subtraction required in the proposed scheme can be ignored [21]. So the computational cost of our protocol less.…”

“…As for the length of the key the least is 4 byte. In this paper we camper our protocol with [21] in term of performance where we use a long-term secret key and random number as the author mentioned in his example as simple numbers but the result was simple keys within close groups compared to our results as explain 1 figure. While we use privet key as a long-term secret key and public key as a random number the Nathani's scheme spent 12.9 minute when it is ran with 10 group and each of group have 10 all groups are generated 1000 key, while minimum when it is ran with 3 groups and each group have 3 to generate 27 Kseckey , spent 0.04 second as explain in figure 2.…”

“…𝑛 𝑖. In[21] produce multi group key protocol in multi time that means it has been expanded group's key establishment and communication cost is ∑ ∑ 𝑚 𝑖𝑗 𝑛 𝑗 │𝑝│ + │ℎ│ 𝑘 𝑖 . So, in our protocol we rely on[21] as communication cost which is…”

“…𝒎 𝒊 * (𝑻𝑴 + 𝑻𝑰)+𝒎 𝒊 TH storage requirement in[19] using two keys (x, y) while in[21][22] using a long secret key x as in our protocol in spite of is generated user key by ECDH protocol except if use and save just one key.…”