1170/24, Shivaji Nagar, Vinayak Apts, Pune-411005, Maharashtra, India ..... 1978, A method for obtaining digital signature and public-key cryptosystems, Comm.
ISBN: 978-972-8924-40-9 © 2007 IADIS
A PROVABLY SECURE MESSAGE TRANSFER SYSTEM USING EULER’S TOTIENT FUNCTION Rohit Pandharkar Dept of E&TC, College of Engineering Pune F-55 Ganga Vishnu heights, Off Samarth Path, Karve Nagar, Pune-411052, Maharashtra, India
Madhuri Joshi Dept of E&TC, College of Engineering Pune 1170/24, Shivaji Nagar, Vinayak Apts, Pune-411005, Maharashtra, India
Nitin Narappanawar AESD, IsquareIT,Pune ‘Snehal’,24, Alankar Hsg.Soc.,Karve Nagar, Pune-411052, Maharashtra, India
ABSTRACT A provably secure message transfer system is proposed using the concept of applying Euler’s Totient function. The scheme enables two users to transfer a message x without having to share their individual private keys. Selection of private keys for the scheme is easier than the other schemes in use. It also reduces the required computations before each pass. Every user decides two sets of two private keys of his own and keeps operating the key generating function alternatively with the other user, ultimately letting the other user know first user’s secret message. The same method can be used with role of users interchanged, for changing direction of message transfer. For security analysis, we also examine possible attacks on the scheme. KEYWORDS Public Key Cryptography, Euler’s Totient Function, Linear Diophantine Equations.
1. INTRODUCTION For security considerations, day by day, message transfer protocols are becoming complicated. Primary reason for this is the increase in mathematical constraints imposed for the selection of private keys. This in turn leads to higher real-time computations. Apart from that, the exhaustive use of exponentiation generally seen in such algorithms also increases the computations. This paper presents a solution for above problems, with use of simple Diophantine equations for private key selection and use of multiplication rather than exponentiation. One of the widely known protocols for message transfer is Shamir’s three pass protocol [2]. Dr. Adi Shamir put forth this innovative multiple pass algorithm. It works with ciphers that can be applied to a message in either order to produce the same final enciphered result; meaning that ciphers commute with each other. For such cases, Shamir proposed following steps: 1.Alice wants to send a message to Bob. So, Alice takes the message, and enciphers it in cipher A, sending the result to Bob. 2.Bob enciphers it in cipher B, sending it back. 3.Alice can still decipher in cipher A, and does so, leaving behind the message only enciphered in cipher B. This is sent back to Bob.
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IADIS International Telecommunications, Networks and Systems 2007
4.Bob reads the message, since it's only enciphered in his cipher. Noting that, it is quite possible to design ciphers that commute, this idea is important for public key cryptography because, like in public-key cryptography, it allows secure communications without exchange of private keys. Diffie Hellman [4], [7] in their seminal paper on Public Key Cryptography in 1976 had used a similar notion with lesser number of passes, for generating a common key. However, their scheme too had computational drawbacks and stringent constraints for selection of private keys [5], creating a need for simpler systems. As there is no public "key" in Shamir’s protocol, it is considered to be distinct from PublicKey Cryptography. Only the Massey-Omura cryptosystem [8] (and essentially similar ones derived) is a secure method based on this protocol. Massey Omura cryptosystem utilizes “exponentiation” to implement idea proposed by Shamir. The authors intend to propose a new protocol based on Shamir’s generalization. The proposed protocol reduces computations leading to much saving of real-time computations.
2. THE SCHEME 2.1 Set Private Keys Both Alice and Bob agree over a big prime ‘p’ first.
2.1.1 Decide over Primes Both Alice and Bob privately pick some large primes m and M respectively. Each also checks that their primes have no common factor with p-1. (Here p is the publicly known prime).
2.1.2 Solving Diophantine Equations Alice privately finds an integer n so that m+n=(p-1)z+1, where z is any integer. And Bob finds an integer N so that that M+N=(p-1) k, where k is any integer. Then, m and n are the private keys of Alice, and M and N are private keys of Bob.
2.1.3 Message and Secret Number Selection Alice selects her message x and Bob decides his secret number y such that x
