Privacy-Preserving Two-Factor Key Agreement Protocol Based on Chebyshev Polynomials

Table 5

Notations of BAN logic.

Symbol	Descript
	The principal P believes a statement X, or P would be entitled to believe X.
	P sees X. P has received a message containing X and can read and repeat X (possibly after doing some decryption).
	P once said X. P at some time sent a message containing X. It is not known whether this is a replay, though it is known that P believed X when he or she sent it.
	P has jurisdiction over X. P is an authority on X and is trusted on this matter.
#(X)	The formula X is fresh. That is, X has never been sent in a message at any time before the current run of the protocol
	K is a key shared between P and Q. P and Q may use K to communicate. And K is good since it can never be discovered by any principal except P or Q, or a principal trusted by either P or Q.
	The formula X is a shared key known only to P and Q, possibly to principals trusted by them.
{X}K	The formula X is encrypted by K.
<X>Y	This represents X combined with the formula Y. It is intended that Y be a secret and that its presence proves the identity of whoever utters <X>Y. X is simply concatenated with Y while Y plays a role as proof or origin for X.