(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 1, No.6, December 2010 30 | Page http://ijacsa.thesai.org/ Modified ID-Based Public key Cryptosystem using Double Discrete Logarithm Problem Chandrashekhar Meshram Department of Applied Mathematics, Shri Shankaracharya Engineering College Junwani, Bhilai (C.G) India Email: cs_meshram@rediffmail.com Abstract — In 1984, Shamir [1] introduced the concept of an identity-based cryptosystem. In this system, each user needs to visit a key authentication center (KAC) and identify him self before joining a communication network. Once a user is accepted, the KAC will provide him with a secret key. In this way, if a user wants to communicate with others, he only needs to know the “identity” of his communication partner and the public key of the KAC. There is no public file required in this system. However, Shamir did not succeed in constructing an identity based cryptosystem, but only in constructing an identity-based signature scheme. Meshram and Agrawal [4] have proposed an id - based cryptosystem based on double discrete logarithm problem which uses the public key cryptosystem based on double discrete logarithm problem. In this paper, we propose the modification in an id based cryptosystem based on the double discrete logarithm problem and we consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system. Keywords- Public key Cryptosystem, Identity based Cryptosystem, Discrete Logarithm Problem, Double Discrete Logarithm Problem. I. INTRODUCTION In a network environment, secret session key needs to be shared between two users to establish a secret communication. While the number of users in the network is increasing, key distribution will become a serious problem. In 1976, Diffie and Hellman [6] introduced the concept of the public key distribution system (PKDS). In the PKDS, each user needs to select a secret key and compute a corresponding public key stored in the public directory. The common secrete session key, which will be shared between two users can then be determined by either user, based on his own secret key and the partner‟s public key. Although the PKDS provides an elegant way to solve the key distribution problem, the major concern is the authentication of the public keys used in the cryptographic algorithm. Many attempts have been made to deal with the public key authentication issue. Kohnfelder [7] used the RSA digital signature scheme to provide public key certification. His system involves two kinds of public key cryptography: one is in modular p, where p is a large prime number; the other is in modular n, where n = p q, and p and q are large primes. Blom [11] proposed a symmetric key generation system (SKGS based on secret sharing schemes. The problems of SKGS however, are the difficulty of choosing a suitable threshold value and the requirement of large memory space for storing the secret shadow of each user. In 1984, Shamir [1] introduced the concept of an identity- In this system; each user needs to visit a based cryptosystem. Key authentication center (KAC) and identify him self before joining the network. Once a user is accepted, the KAC will provide him with a secret key. In this way, a user needs only to know the “identity” of his communication partner and the public key of the KAC, together with his secret key, to communicate with others. There is no public file required in this system. However, Shamir did not succeed in constructing an identity-based cryptosystem, but only in constructing an identity-based signature scheme. Since then, much research has been devoted, especially in Japan, to various kinds of ID- based cryptographic schemes. Okamoto et al. [10] proposed an identity-based key distribution system in 1988, and later, Ohta [12] extended their scheme for user identification. These schemes use the RSA public key cryptosystem [18] for operations in modular n, where n is a product of two large primes, and the security of these schemes is based on the computational difficulty of factoring this large composite number n. Tsujii and Itoh [2] have proposed an ID- based cryptosystem based on the discrete logarithm problem with single discrete exponent which uses the ElGamal public key cryptosystem. Meshram and Agrawal [5] have proposed an ID- based cryptosystem based on the integer factoring and double discrete logarithm problem which uses the public key cryptosystem based on integer factoring and double discrete logarithm problem. Meshram and Agrawal [4] have also proposed an ID- based cryptosystem based on double discrete logarithm problem which uses the public key cryptosystem based on double discrete logarithm problem. Now we Modified this cryptosystem for discrete logarithm problem with distinct double discrete exponent because we face the problem of solving double and triple distinct discrete logarithm problem at the same time in the multiplicative group of finite fields as compared to the other public key cryptosystem where we face the difficulty of solving the traditional discrete logarithm problem in the common group. In this paper , we present modification in an ID based cryptosystem based on the double discrete logarithm problem with distinct discrete exponent (the basic idea of the proposed