OUR PROPOSED SCHEME. In this section we describe our Authenticated Key Agreement (AKA) protocol. In our protocol, there are two entities, the user’s smart card and the server. The proposed protocol consists of four phases: system setup phase, registration phase, authentication phase, and password changing phase. The procedure of the protocol is described in details as follows:
OUR PROPOSED SCHEME. TLPKA TLPKA is based on a geometric property of the tangent line: a tangent line is tangent to the curve of certain function at a unique point. And utilizing the concept of the existence of a unique point of intersection between two tangent lines, a unique pairwise key can be established between the sender and receiver. In TLPKA, there are two separated parts: the Source Node part and the Destination Node part: Firstly, we define the factors and parameters in the notation as follows: NOTATIONS Symbol Meaning N The number of members. P The prime number for the characteristic of the finite field, Zp. IDi The unique identification of member i , i = {1, 2,3,..., n} , which is public. F A polynomial generated by the central authority, of degree t , which is kept secret. T The degree of f , the critical value of the system, which is public in this system. aj The coefficient of x j in f , where j = {1, 2,3,...,t} , which is kept secret. yi The secret used to authenticate member i , f (IDi ) , which is always kept secret. G The primitive root, which is publicly known in this system. sj s ≡ ga j (mod p), which is public. j li The tangent line of f passes through (IDi, yi ) , i = {1, 2,3,..., n} , which is kept secret.
OUR PROPOSED SCHEME. In this section, our proposed scheme is described in de- tail containing four phases: initialization phase; registration phase; authentication and key agreement phase; password changing phase. The notations used in our scheme are summarized as follows: Ui: One of the legal users to communicate with the server. S: The remote server.
OUR PROPOSED SCHEME. In this section we describe our two pass key agreement protocol (KAP) between two entities A and B, and consider its security. to guess a or b from ab. We assume that n is even, and denote by LBn (resp.UBn) the subgroup of Bn generated by a1 … . an–1 , i.e., braids where the n/2 lower strands only are braided ( resp. in the subgroup generated by an+1 … . an–1). We know that every element in LBn commutes with every element in UBn . Bn is finite and non-commutative, so problem on braid group are non trivial. R : SÆ1 (V), SÆ2 (V) C LBn Se (V)R Se (V) = XÆ Æ1 Æ2 SB (W), SB (W) C UB n Se (W)R Se (W) = XB Ue (V), Ue (V) C LBn B1 B2 Ze (W), Ze (W) C UB Æ1 Æ2 : : : : : : : : sufficiently complicated braid group V= IDÆ║R W=IDB║R Aus long term private key pair Aus long term public key Bus long term private key pair Bus long term public key Ue (V)R Ue (V) = YÆ Æ1 Æ2 Se (V)Xb Se (V) B1 B2 n Ze (W)R Ze (W) = YB B1 B2 Æ1 Æ2 KÆ Se (W)Xa Se (W) Ke(YB)Ke = KeZe (W)R Ze (W)Ke B1 B2 Ue (V) 魔–e Ze (W)R Ze (W)K–eUe (V) : X X X X0 X0 X : Æ1 Æ B1 B2 Æ Æ2 Ze (W)Ue (V)R Ue (V)Ze (W) = K X0 X0 Æ2 B2 KB YB Key YÆ : Key YB : strong one — way hash function
