An Agent-Based Auction Protocol on Mobile Devices

Table 3

Analysis of computation complexity

Phase	[4]	The proposed system
Registration	5𝑛𝑇EXP+1𝑛𝑇MUL+2𝑛𝑇𝐻	5𝑛𝑇EXP+2𝑛𝑇MUL+3𝑛𝑇𝐻
Generation of transaction public key	7𝑛𝑇EXP+5𝑛𝑇MUL+1𝑛𝑇𝐻	(2𝑛+1)𝑇EXP+1𝑛𝑇MUL
Signature	3𝑇EXP+5𝑇MUL+1𝑇𝐻	4𝑇EXP+8𝑇MUL+2𝑇𝐻
Auction bidding	3𝑇EXP+3𝑇MUL+2𝑇𝐻	3𝑇EXP+2𝑇MUL+1𝑇𝐻
Winner announcement	2𝑇EXP+1𝑇MUL+1𝑇𝐻	2𝑇EXP+1𝑇MUL+1𝑇𝐻

As seen in the comparison table, the computation amount of this system is much lower than [4], especially in the generation phase of transaction public key.