6th European Conference - Academic Conferences

Natarajan Vijayarangan
Client and Server negotiate an m-bit shared secret key using ECDH algorithm.
Client and Server have Session key of m bits for Encryption. Client and Server have a cipher
suite.
A secure communication is established between Client and Server.
6. Description of NSP 3
It is similar to Network security protocol 1 and the difference can be seen in Signature generation.
Client uses Jacobi identity, a special product on Lie algebras [8], to authenticate server. The Jacobi
identity (Jacobson 1979) performs on a random challenge RC = x || y ||z (divide into 3 parts -
trifurcation) and satisfies the relationship [[x,y],z] + [[y,z],x] + [[z,x],y] = 0. It is important to know that
Lie product (Lie bracket) has a special property: [x, y] = -[y, x].
Following is the workflow of NSP 3:
(Pre-Shared Key Mechanism) Every client has a pair of Public and Private keys generated by the
server which acts as a Key Generation Center (KGC).
Client initiates the communication to server by sending a message ‘Client Hello!’.
Server generates Random challenge (RC) of n-bits using Pseudo Random Number Generator
(PRNG). Further, Server encrypts RC with client's public key using Elliptic Curve Encryption
(ECE) method.
Client decrypts the encrypted RC with its private key using ECE.
Client computes Jaboci identity on RC = x||y||z and sends the Lie product [[x,y],z] to server.
Server verifies the relationship [[x,y],z] + [[y,z],x] + [[z,x],y] = 0. Server sends its public key using
ECC to Client.
Client and server negotiate an m-bit shared secret key using ECDH algorithm.
Client and server have Session key of m bits for Encryption. Client and server have a cipher suite.
A secure communication is established between Client and Server.
7. Analysis
The proposed network security protocols do not allow replay and rushing attacks. An attacker cannot
guess a random challenge (RC) in NSP 1, since it traverses in an encrypted form. It is safe to use
NSP 1 in different nodes/channels.
Considering NSP 2 that is different from NSP 1 and sends RC in plain with MP(RC). It is interesting to
see the notion of bijective property in MP where an attacker can change RC, but not MP(RC). Given
two distinct random challenges RC1 and RC2, MP(RC1) is not the same as MP(RC2). If the attacker
tries to insert another random challenge, then server could detect this fraud by verifying a client's
signature. Since MP function has Shuffling, T-function and LFSR operations that are invertible
(Vijayarangan and Vijayasarathy 2005, Vijayarangan 2009), the inverse operations of MP -1 { MP(RC1)}
and MP -1 { MP(RC2)} are performed through a primitive polynomial of LFSR, T -1 -function and deshuffling
and their values RC1 and RC2 must be distinct.
In NSP 3, the server will not satisfy Jacobi identity if an attacker changes RC. The rationale behind on
using Jacobi identity is that a Lie product computed on RC from client end must match with the server.
Then the server checks Jacobi identity and ensures that the same client has sent the Lie product. If
the attacker alters a Lie product, then the server could detect this fraud by verifying Jaboci identity. It
is important to know that Abelian Lie algebras (for every x and y , [x,y] = 0 ) should not be considered.
From the above protocols, we can make out a proposition that dishonest clients can be eliminated in a
Mesh Topology Network (MTN) based on NSP 1,2 and 3. Thus, a system of protocols 1,2,3 can be
plugged into an MTN which brings out a strong and secure network.
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