International Journal of Information, Control and Computer Sciences ISSN: 2517-9942 Vol:1, No:12, 2007 3783 Abstract—With the exponential growth of networked system and application such as eCommerce, the demand for effective internet security is increasing. Cryptology is the science and study of systems for secret communication. It consists of two complementary fields of study: cryptography and cryptanalysis. The application of genetic algorithms in the cryptanalysis of knapsack ciphers is suggested by Spillman [7]. In order to improve the efficiency of genetic algorithm attack on knapsack cipher, the previously published attack was enhanced and re-implemented with variation of initial assumptions and results are compared with Spillman results. The experimental result of research indicates that the efficiency of genetic algorithm attack on knapsack cipher can be improved with variation of initial assumption. Keywords—Genetic Algorithm, Knapsack cipher, Key search. I. INTRODUCTION HE demand for effective internet security is increasing exponentially day by day. Businesses have an obligation to protect sensitive data from loss or theft. Such sensitive data can be potentially damaging if it is altered, destroyed, or if it falls into the wrong hands. So they need to develop a scheme that guarantees to protect the information from the attacker. Cryptology is at the heart of providing such guarantee. Cryptology is the science of building and analyzing different encryption and decryption methods. Cryptology consists of two subfields; Cryptography & Cryptanalysis. Cryptography is the science of building new powerful and efficient encryption and decryption methods. It deals with the techniques for conveying information securely. The basic aim of cryptography is to allow the intended recipients of a message to receive the message properly while preventing eavesdroppers from understanding the message. Cryptanalysis is the science and study of method of breaking cryptographic techniques i.e. ciphers. In other words it can be described as the process of searching for flaws or oversights in the design of ciphers. The application of genetic algorithms in the cryptanalysis of knapsack ciphers is suggested by Spillman [7]. II. KNAPSACK CIPHER One of first knapsack cipher was proposed by Markle and Manuscript received March 16, 2006. Poonam Garg is with the Institute of Management Technology, Ghaziabad, India ( phone: 0120-2821474; e-mail: poonam@imt.ac.in). Aditya Shastri is with Banasthali Vidyapith, Banasthali, India (phone: 01438-228787; e-mail: adityashastri@yahoo.com). D.C.Agarwal is with S.S.V.P.G. College Hapur, India (e-mail: dc_grwl@yahoo.co.in). Hellman in 1975 which utilized a NP-complete problem for its security. The knapsack problem is formulated as follows. Let us assume the values M 1, M 2……….. M n and the sum S are given. Let it be necessary to compute values b 1, b 2 …..b n values, so that S= M 1 b 1 +M 1 b 1……… +M n b n . The values of coefficient b i can be equal 0 or 1. The 1 value shows that object will fit into the knapsack, 0 values will not in the knapsack. The Markle-Hellman knapsack cipher encrypts a message as a knapsack problem. The plaintext block transforms into binary string (the length of block is equal number of elements in knapsack sequence). One value determines that an element will be in target sum. This sum is a ciphered message. Table I shows an example of solving the knapsack problem for the entry numbers sequence: 1 3 6 13 27 and 52. TABLE I EXAMPLE OF KNAPSACK ENCRYPTION Plaintext Knapsack sequence Ciphertext 1 1 1 0 0 1 1 3 6 13 27 52 1+3+6+52= 62 0 1 0 1 1 0 1 3 6 13 27 52 3+13+27 = 43 0 0 0 0 0 1 1 3 6 13 27 52 52 = 52 The public/private key aspect of this approach lies in the fact that there are actually two different knapsack problems – referred to as the easy Knapsack and hard knapsack. The Markle-Hellman algorithm is based on this property. The private key is a sequence of number for a superincreasing knapsack problem. The public key is a sequence of number for a normal knapsack problem with the same solution. Easy knapsacks have a sequence of numbers that are superincreasing - that is, each number is greater then the sum of previous numbers : ∑ − = > 1 1 i j j i a a for i=2,……,n(where i a is i-th element of the sequence) . For example {1,3,6,13,27,52} is a superincreasing sequence but {1,3,4,9,15,25} is not. The knapsack solution with the superincreasing sequence proceeds as follows. The target sum is compared with a greatest number in the sequence. If the target sum is smaller, than this number, the knapsack will not fill, otherwise it will. Then the smaller element is subtracted from the target sum, and the result of the subtraction, is compared with next element. Such operation is done until the smallest number of sequence is reached. If the target sum is reduced to 0 value, than solution exists. In other case solution doesn’t exist. For example, consider a total knapsack target sum is 70 and the sequence of weights of {2, 3, 6, 13, 27, and 52}. The largest weight, 52, is less then 70, so 52 are in the An Enhanced Cryptanalytic Attack on Knapsack Cipher using Genetic Algorithm Poonam Garg, Aditya Shastri, and D.C. Agarwal T