2009 International Conference on Electronic Computer Technology
A New Symmetric Key Encryption Algorithm based on 2-d Geometry Mohammad Jabed Morshed Chowdhury
Tapas Pal
Programmer, Prime Ministers’ Office, Dhaka, Bangladesh e-mail:
[email protected]
Programmer, Tripad Labs Dhaka, Bangladesh, e-mail:
[email protected]
Abstract -- Symmetric Key Cryptography is one of the prominent means of secure data transfer through unreliable channel. It requires less overhead than Public Key Cryptosystem. We present here, a new algorithm based on 2-d geometry using property of circle, and circle-centered angle. It is a block cipher technique but has the advantage of producing fixed size encrypted messages in all cases. It incorporates low computational complexity with fairly high confidentiality.
given only knowledge of the cryptographic algorithm and the encryption key. [3] Symmetric Key Cryptography: The same key is used for both encryption and decryption and it is shared between the two communicating parties. In symmetric key cryptography, a single key is used for both encryption and decryption. As shown in Figure 1, the sender uses the key (or some set of rules) to encrypt the plaintext and sends the cipher-text to the receiver. The receiver applies the same key (or rule-set) to decrypt the message and recover the plaintext. Because a single key is used for both functions, secret key cryptography is also called symmetric encryption. With this form of cryptography, it is obvious that the key must be known to both the sender and the receiver. [4]
Keywords: Cryptography, Symmetric Key Algorithms.
Encryption,
Decryption,
I. INTRODUCTION
III. OVERVIEW OF THE BASIC ALGORITHM
The Internet today is a truly global marketplace, with a wide variety of goods and services available online. Secure communication is an intrinsic requirement for many popular online transactions such as e-commerce, stock trading and banking. Two main security mechanisms are used to provide the digital equivalents of the Paper World security services: Cryptography and Digital Signature. Our focus in this paper is on deriving a new, efficient symmetric key encryption algorithm. "Cryptography" derives from the Greek word kruptos, meaning "hidden". The key to hiding data is to devise a hiding (encryption) mechanism that is very difficult to reverse (i.e., to find the original data) without using the decryption key. Usually, the harder it is to discover the key, the more secure the mechanism. In symmetric key (also called "secret-key") encryption, the same key is used for both encryption and decryption. In asymmetric (also called "public-key") encryption, one key is used for encryption and another for decryption [1].
Our cryptographic scheme is inspired by Elliptic Curve Cryptography (ECC) [8]. This has been made computationally efficient by reducing the order of equation from cubic to quadratic. The idea of ECC evolves around a cubic curve. Here, a circle is the basis of all computation. Also, ECC is based on congruency relation for large prime numbers. Here, planar geometric computation in 2D [11] coordinates is performed and all points on a circle are considered. So, computations are in real value domains rather than integer domains. This algorithm is a Shared Symmetric Key algorithm. The communicating parties may initiate the communication with ECC having their own public and private key. Then they would compute their shared key which will be used as the symmetric key for this algorithm. Thus, finding out the shared symmetric key is a discrete logarithmic problem [12] which means it is as hard as breaking the security of ECC. This algorithm requires a pair of geometric points as the shared symmetric key. The first point is the center O of the circle. The second point is a shared secret point S lying on the perimeter of the circle. It is proposed that both these keys should be exchanged by ECC. It should also be mentioned that, the radius r of the circle is, r2= (sx− cx)2+ (sy− cy)2
II. DIFFERENT TYPES OF CRYPTOGRAPHIC ALGORITHMS There are several ways of classifying cryptographic algorithms. Based on the number of keys employed for encryption and decryption, there are mainly two types of algorithms: [2] Public Key Cryptography: Each communicating entity has its own private key and public key. One is used for encryption and the other for decryption. It is computationally infeasible to determine the decryption key 978-0-7695-3559-3/09 $25.00 © 2009 IEEE DOI 10.1109/ICECT.2009.130
Else, C, SX and r can be transmitted as shared symmetric key. Then, SY will be the unknown quantity of the above equation and can be easily computed. 541
Find point M′≡(MX′,MY′) such that = 232 Let, Circle Center, C = (CX, CY) Encryption: Input: M, a 64 bit value Output: E, a 32 bit value Interpretation: [byte0-1] Circle-centered angle between Input and Secret Point [byte2-3] A random value (k); [0
