DOI: 10.7763/IJMO.2017.V7.569 Abstract—Based on Elliptic Curve Discrete Logarithm Problem (DLP), Elliptic Curve Cryptography (ECC) shows promise in the public key cryptography methods. In this article, a new algorithm based on ECC is introduced, which has lower complexity than Menezes-Vanstone algorithm. Meanwhile our method introduces “one-time pad” to increase the security, and solve data redundancy encryption problem while at the same time maintains the authenticity of the transmitted message, which cannot be fabricated by the eavesdropper and cannot be denied by the legal transmitter. The simulations result shows that the redundancy problem is totally solved, and the correctness of the algorithm is verified through an example. A comparisons and resistance to different attacks are included also in the essay. Index Terms—ECC, mvecc, ElGamal, one-time pad, Menezes-vanstone cryptosystem. I. INTRODUCTION Information security is crucial in various communication systems. However, with the existence of the eavesdropper/attacker, the message transmitted in the channel is not always safe and it needs to be secured. Cryptography is invented to keep the secret message away from illegal receivers, making the message of the authenticated transmitter non-forgery and undeniable. There are two categories of cryptography: the public-key cryptography and the symmetric-key cryptography. In the symmetric-key cryptography systems, such as AES, the transmitter and the receiver share the same private key. The secret transmission of the private key is difficult to be managed. In the public-key cryptography system, the identity between private key of the transmitter and the receiver is not necessary. Instead, each side owns a pair of keys, namely, the public key and the private key. The public key is generated by the private key and shared in the channel. Alice uses the private key of her own and the public key of Bob to encrypt the message, and Bob decrypts the message with his private key and the public key of Alice. Without prior knowledge of private key, it is not practical for the eavesdropper to decrypt the message, for that reason the system is called computationally secure system. The first public key cryptography is RSA, introduced by Rivest in 1977 [1], based on the hardness of integer factorization problem. However, RSA is usually combined with secure socket layer protocol (SSL), which may slows Manuscript received March 3, 2017; revised April 13, 2017. Mostafa Ahmed Mohamed Sayed and Liu Rongke are with School of Electronic and Information Engineering, Beihang University (BUAA), Beijing, China,(e-mail: mostafa_adawy@ymail.com, rongke_liu@buaa.edu.cn). down the web servers for 3-9 times [2]. Elliptic Curve Cryptography is first introduced by Miller [3] and Koblitz [4], based on the Discrete Logarithm Problem [5]. With short-length key, ECC can achieve the same security as RSA [1], [6] In hardware implementation, ECC algorithm has smaller capacity, faster computation and less power consumption [7], which will bring benefit in wireless communications and portable devices [8]. Boruah proposed ElGamal ECC implementation [9] and refined algorithm based on Menezes Vanstone ECC is proposed by Kurt [10], [11] The FPGA implementation of ECC is introduced in [12]-[14]. In order to increase the security level and achieve perfect secrecy, a different key has to be used with each message as told by Shannon, so that using of one time pad algorithms raises the security level from computationally secure to unconditionally secured systems. In this paper, the mathematical model of several previous works are examined and evaluated. Based on the previous work, a new ECC algorithm is proposed. The proposed Modified Menezes-Vanstone ECC (MMVECC) algorithm is one time pad algorithm that is used to heal many problems such as allowing rapid key change without need of key management complexity, and it solves the redundancy problem based on using one time pad technique. The complexity for calculating the modular inverse of the curve parameter is reduced by XOR operation substitution. Meanwhile the “one-time pad” is kept along with the constant part of the public key at Alice’s side to ensure the authenticity, making Eve’s fabricated massage distinguishable and Alice message undeniable. The paper is organized as follows, section II drive the problem formulation through describing previous methods that are used and it also describe development and contributions that are introduced and shows how far it fulfills and solve some related security issues, while section III shows the proposed solution to the problems in section II. In section III, the proposed model based on Menezes-Vanstone algorithm will be clarified by mathematical model and flowchart diagram, and it will be verified through an example. In Section IV, results of our proposed method will be presented and Section V will draw a conclusion to the paper. II. PROBLEM FORMULATION AND RELATED WORK In order to highlight the proposed contribution the theoretical background, previous contributions, and problems have to be presented in this section. The main challenge in public key filed of research embodies in complexity reduction represented in the number of multiplications in MMVECC Encryption Algorithm for Redundancy Problem Solving and Authentication Verification Mostafa Ahmed Mohamed Sayed and Liu Rongke 116 International Journal of Modeling and Optimization, Vol. 7, No. 2, April 2017