On Quantum 3-Pass Protocol
Ahmed E*
Department of Mathematics, Faculty of Science, Egypt
Submission: November 22, 2017; Published: February 01, 2018
*Corresponding author: Ahmed E, Department of Mathematics, Faculty of Science, Mansoura 35516, Egypt, Email: magd45@yahoo.com
How to cite this article: Ahmed E. On Quantum 3-Pass Protocol. Biostat Biometrics Open Acc J. 2018; 4(5): 555648. DOI:10.19080/BBOAJ.2018.04.555648
Abstract
Some proposed 3-pass protocols in quantum cryptography assumes that the qbits are 2-component. Here we propose a protocol without this assumption
Keywords: cryptography; Three-pass protocol; Private decryption key; Three encrypted messages
Opinion
Three pass protocol [1,2]
In cryptography, the three-pass protocol for sending messages is a framework which allows one party to securely send a message to a second party without the need to exchange or distribute encryption keys. It is called the three-pass protocol because the sender and the receiver exchange three encrypted messages. The first three-pass protocol was developed by Adi Shamir circa 1980. The basic concept of the three-pass. Protocol is that each party has a private encryption key and a private decryption key. The two parties use their keys independently, first to encrypt the message, and then to decrypt the message.
The Three-Pass Protocol works as follows
o The sender chooses a private encryption key es and a corresponding decryption key The sender encrypts the message m with the key es and sends the encrypted message to the receiver
o The receiver chooses a private encryption key and a corresponding decryption key er and encrypts the first message E(es,m) with the key dr and sends the doubly encrypted message E(er,(E(es,m))( back to the sender
o The sender decrypts the second message with the key ds. Because of the commutativity property described above D (ds, E (er,E(es,m)) E (es, m))) = E (er, m) which is the message encrypted with only the receiver's private key. The sender sends this to the receiver
The receiver can now decrypt the message using the key dr, namelyD(dr,E(er, m)) = m the original message. Notice that all of the operations involving the sender's private keys es and ds are performed by the sender, and all of the operations involving the receiver’s private keys er and dr are performed by the receiver, so that neither party needs to know the other party's keys.
Quantum 3-pass protocol
Recently quantum 3-pass protocol has been proposed [3]. It was assumed that the qbits are 2-component hence they use the fact that the group SO(2) is commutative. This is Not true for SO(n), n>2. Here we propose the following protocol which does not make this assumption. Assume that sender A sends a string of qbits {qb (l), qb ( 2 ~)...qb (s )} to a receiver B. He receives them which causes some errors according to Uncertainty principle [4]. The receiver B sends back the Extended string {qb' (l), qb' (2). qb'(s ), qb (s +1) ,...qb (s + r)}. When the sender A receive it the correct subset of {qb'(l),qb' (2).qb' (s)} will form her key. The extended string is sent back to the receiver B and he gets {qb' (l), qb' (2). qb' (s), qb' (s +1) ,...qb' (s + r)}. The correct subset of the string {qb' (s +1) ,...qb' (s + r)} will be his key. No assumptions are made on the number of components used for each qbit.
References
- Feige U, Fiat A, Shamir A (1987) Zero knowledge proofs of identity. Proceedings of the nineteenth annual acm symposium on theory of computing, New York, USA pp. 210-217.
- 3-pass protocol, Wikipedia.
- Yoshito K, Seong MY (2009) Quantum Three-Pass Protocol: Key Distribution Using Quantum Superposition States. IJNSA Volume 1.
- Schiff LI (1980) Quantum mechanics. McGraw-Hill, New York, USA.