Attacking Transposition Cipher Using Improved Cuckoo Search Ahmed Tariq Sadiq 1,a,Laith Ali 2,b Hashim Kareem 3,c

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1 Attacking Transposition Cipher Using Improved Cuckoo Search Ahmed Tariq Sadiq 1,a,Laith Ali 2,b Hashim Kareem 3,c 1 Computer Science Department, University of Technology, Baghdad, Iraq 2 Electrical Eng. Department, University of Babylon, Babylon, Iraq 3 Computer Network Department, University of Babylon, Babylon,Iraq , a drahmaed_tark@yahoo.com b drlaithanzy@yahoo.com c aljobori1965@yahoo.com Article Info Received: 25 th December 2013 Accepted: 29 th January 2014 Published online:1 st March 2014 e-issn: ABSTRACT This paper presents an improved cuckoo search algorithm for automatic cryptanalysis of transposition ciphers. Transposition ciphers are a class of ciphers In which, a plaintext block is encrypted into a ciphertext block using a fixed permutation. The Improved cuckoo search(ics) algorithm is done by adding a procedure to cuckoo search(cs) steps utilizing the similarities between population strings to find the global maxima of a cost function to find the secret key. The experiments show that for lower length of ciphertext there are cases that the secret key cannot be correctly found. This is the expected behavior of all cryptanalysis methods. Experimental results showed the ability of the proposed algorithm to attack 95% of encrypted messages with different key length using transposition cipher and gave better results compare with the traditional cuckoo algorithm on the amount of key recovery and time complexity. Keywords: Transposition cipher, Cryptanalysis, Improved Cuckoo Search 1. Introduction Cryptography is the art and science of making secure communication systems. The term is derived from the Greek words: kryptos means hidden and graphos. Cryptanalysis is derived from the Greek words: kryptos, and analyein, means "to loosen" or "to untie" (Stallings 1999). It is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so. Cryptanalysis is the flip-side of cryptography. It is the science of cracking codes, decoding secrets (Menzes et. al. 1996). Cryptography and Cryptanalysis comprise Cryptology. In past years.many researchers in the field of cryptology and intelligent computing are interested in developing automated attacks on transposition cipher. In the literature, lot of studies can be found in this regard. However, all those works made cryptanalysis either by using classical heuristic search algorithms or by using a slightly modified/ improved version

2 of those algorithms. The property which make this cipher vulnerable, is that it is not sophisticated enough to hide the inherent properties or statistics of the language (Dimovski & Gligoroski 2003). Stochastic Optimization Algorithms (often referred to as metaheuristics") employ randomization to find near-optimal solutions to computationally intractable problems (Yang 2008). It's reasonable to assume that any problem solvable by an evolutionary algorithm can also be solved by another metaheuristic. Recently, a novel metaheuristic technique, called Cuckoo Search (CS), based on cuckoo bird s behavior has been developed by Yang and Deb 2009 (Yang & Deb 2009). CS algorithm was developed to solve unconstrained optimization problems, where its performance was compared with the performance of the genetic algorithm (GA) and particle swarm optimization (PSO). Simulations and comparison have shown that CS is superior to these algorithms for multimodal objective functions (Brajevic, et. al. 2012). This article presents the automatic cryptanalysis of typical transposition Cipher based on improved cuckoo search algorithm by adding a new sub procedure to cuckoo steps by exploiting the similarities between population vectors (nests). The paper is organized as follows. A brief introduction is given in section 1. A brief discussion of transposition cipher is given in section 2. Section 3 discusses the cryptanalysis, A discussion on related work presented in section 4. The details and a discussion of cuckoo search algorithm given in section 5. The proposed improved algorithm and results section 6 and 7 respectively, lastly the conclusion in the section Transposition Ciphers The concept of transposition is an important one and is widely used in the design of modern ciphers, as will be seen in subsequent sections. Note that the key must provide sufficient information to unscramble the ciphertext (Menzes et. al. 1996). A transposition or permutation cipher works by breaking a message into fixed size blocks, and then permuting the characters within each block according to a fixed permutation, say P. The key to the transposition cipher is simply the permutation P. So, the transposition cipher has the property that the encrypted message i.e. the ciphertext contains all the characters that were in the plaintext message. In other words, the unigram statistics for the message are unchanged by the encryption process (Giddy & Safavi-Naini 1994). The size of the permutation is known as the period. Let's consider an example of a transposition cipher with a period of six 6, and a key P={4,2,1,5,6,3}. In this case, the message is broken into blocks of six characters, and after encryption the fourth character in the block will be moved to position 1, the second remains in position 2, the first is moved to position 3, the fifth to position 4, the sixth to position 5 and the third to position 6. In fig.1 is shown the key and the encryption process of the previously described transposition cipher. It can be noticed that the random string "X" was appended to the end of the message to enforce a message length, which is a multiple of the block size. It is also clear that the decryption can be achieved by following the same process as encryption using the "inverse" of the encryption permutation. In this case the decryption key, P -1 is equal to {3,2,6,1,4,5}. 23

3 KEY: Plaintext: Ciphertext: ENCRYPTION: Position: Plaintext: HOW_ARE_YOUX Ciphertext _OHARWO_RUXY Fig. 1: Example Of Transposition Cipher Encryption And Decryption Process 3. Cryptanalysis for Classical Cipher The study of principles and methods of transforming an unintelligible message back into an intelligible message without knowledge of the key, also called code breaking. The previous studies show that Each language has characteristics that aid successful cryptanalysis methods, for example each character in English language has specific probability on the text. in most languages letters are not equally common e is by far the most common letter requencies On the basis of the probabilities, Baker and Piper partition the 26 letters into five groups as follows (Dimovski & Gligoroski 2003) (Giddy & Safavi-Naini 1994): 1. E, having probability about T, A, O, I, N, S, H, R, each having probabilities between 0.06 and D, L, each having probabilities around C, U, M, W, F, G, Y, P, B, each having probabilities between and V, K, J, X, Q, Z, each having probabilities less than It also be useful to consider sequences of two or three consecutive letters called digrams and trigrams, respectively. The 30 most common digrams are (in decreasing order) TH, HE, IN, ER, AN, RE, ED, ON, ES, ST, EN, AT, TO, NT, HA, ND, OU, EA, NG, AS, OR, TI, IS, ET, IT, AR, TE, SE, HI, and OF Fig. 2 show digrams frequency in English language. The twelve most common trigrams are (in decreasing order) THE ING, AND, HER, ERE, ENT, THA, NTH, WAS, ETH, FOR, and DTH. BT: CG: TX: XW: ZE: CP: PB: PZ: GB: GS: RG: WZ: XA: XC: ZG: ZU: BX: ER: GX: JX: Fig. 2: Frequently Occurring Digrams In The Ciphertext One potential problem when using frequency analysis to score the fitness of candidate keys is the chance to encounter a local maximum. This can happen when a particular key's 24

4 decryption of a particular ciphertext resembles English to a certain extent, and every small mutation that would bring the key closer to the correct key would result in analysis-based fitness scores that are actually worse. The problem of local maxima Fig. 3, plagues much research with Stochastic Optimization Algorithms, and using them for cryptanalysis on transposition ciphers is no exceptions (Hilton 2012). Fig. 3: Local Maxima Illustration From A great deal of the work in the field of metaheursitics is an attempt to reduce or remove the problem of local maxima from the search process. Here in this work is good step toward reduce the local maxima. 4. Related Work Much research has already been done to investigate the efficiency of performing automated cryptanalysis against transposition ciphers or substitution cipher using Stochastic Optimization Algorithms. Though by no means exhaustive, below is a sampling of some of this work. In the literature, lot of studies can be found in this regard. However, all those works made cryptanalysis either by using classical heuristic search algorithms or by using a slightly modified/ improved version of those algorithms 1993 robert Mathews andrew clark &ts and sa 2003 dimovski 2003 ant colony russel 2005 scatter search garici 2007 toemeh. genetic algorithm.breaking transposition has been carried out by many researchers. Methew (Mathew 1993) presented an attack on transposition cipher using genetic algorithm. Giddy and Safavi-Naini (Giddy & Safavi-Naini 1994) have published an attack on the transposition cipher using simulated annealing. Russell (Russell et. al. 2003) presented an attack on transposition cipher using ant colony. Garg P. (Garg 2005) proposed a cryptanalysis method based on genetic algorithm, tabu search & simulated annealing to break a transposition cipher. Toemeh (Toemeh & Arumugam 2007) presented an attack on transposition cipher using genetic algorithm. Werner R. Grundlingh (2007) presented an 25

5 attack on the simple cryptographic cipher using genetic algorithm compare with (Toemeh, R. & Arumugam, S. 2007) (Uddin & Youssef 2006) (Dimovski & Gligoroski 2003), an improved particle swarms used in (Salih et. al. 2009) to cryptanalyse transposition ciphers. 5. Cuckoo Search Cuckoo search (CS) was inspired by the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds (of other species). Some host birds can engage direct contest with the infringing cuckoos. For example, if a host bird discovers the eggs are not their own, it will either throw these alien eggs away or simply abandon its nest and build a new nest elsewhere. In addition, the timing of egg-laying of some species is also amazing. Parasitic cuckoos often choose a nest where the host bird just laid its own eggs. In general, the cuckoo eggs hatch slightly earlier than their host eggs. Once the first cuckoo chick is hatched, the first instinct action it will take is to evict the host eggs by blindly propelling the eggs out of the nest, which increases the cuckoo chick s share of food provided by its host bird. Studies also show that a cuckoo chick can also mimic the call of host chicks to gain access to more feeding opportunity (Yang & Deb 2009). In nature, animals search for food in a random manner. In general, the foraging path of an animal is effectively a random walk because the next move is based on the current location/state and the transition probability to the next location. Which direction it chooses depends implicitly on a probability which can be modeled mathematically. Various studies have shown that the flight behavior of many animals and insects has demonstrated the typical characteristics of Levy flights (Bacanin 2012). CS is based on three idealized rules (Bacanin 2012): -Each cuckoo lays one egg at a time, and dumps its egg in a randomly chosen nest. -The best nests with high quality of eggs will carry over to the next generation. -The number of available host nests is fixed, and the egg laid by a cuckoo is discovered by the host bird with a probability P a ϵ (0, 1) discovering operate on some set of worst nests, and discovered solutions dumped from further calculations. An important issue is the applications of Levy flights and random walks in the generic equation for generating new solutions. When generating new solutions : where α > 0 is the step size which should be related to the scales of the problem of interests. In most cases, we can use α = 1. The Levy flight essentially provides a random walk while the random step length is drawn from a Levy distribution. which has an infinite variance with an infinite mean. Here the steps essentially form a (1) (2) 26

6 random walk process with a power-law step-length distribution with a heavy tail. Some of the new solutions should be generated by Levy walk around the best solution obtained so far, this will speed up the local search. However, a substantial fraction of the new solutions should be generated by far field randomization and whose locations should be far enough from the current best solution, this will make sure the system will not be trapped in a local optimum (Hilton 2012). The basic steps of the Cuckoo Search (CS) can be summarized as the pseudo code shown as below (Yang & Deb 2009). Input: problem initial parameters Output: The best of solutions Start Objective function f(x), x= (x 1,x 2 x u ) T Generating initial population (pop) of n host nests x i (i=1,2, n) While (t<maxgenerations) and (!stop criterion) Get a cuckoo randomly via Lévy flights Evaluate its fitness F i If( f j > F i ) Replace j by the new solution; Fraction p ɑ of worse nests are abandoned and new nests are being built; Keep the best solutions or nests with quality solutions; Rank the solutions and find the current best End while Post process and visualize results End Here the consecutive jumps/steps of a cuckoo essentially form a random walk process which obeys a power-law step-length distribution with a heavy tail. In addition, a fraction p a of the worst nests can be abandoned so that new nests can be built at new locations by random walks and mixing. The mixing of the eggs/solutions can be performed by random permutation according to the similarity/difference to the host eggs (Yang & Deb 2009). 6. The Improved Cuckoo Search Algorithm (ICS) This section describes the improved optimization heuristics for attacks the transposition cipher using improved cuckoo search. Also, a method of evaluate intermediate solutions, in the search for the optimum, is discussed. Fig.5 show the steps of the improved cuckoo search 6.1 Representation of a Candidate Solution In this proposed attack of the transposition cipher, the solution key is permutation form, the position of a digit in the permutation means the order or sequence of the key is scheduled. The main emphasis is placed on how to develop an alternative method for the permutation key by utilizing the features of cuckoo search. The presented attack technique define the position vector of a egg represents a feasible solution, that is to say, the position vector means the permutation of the solution key and specifies the order of key to be executed. 27

7 For the purpose of this study, a key for decoding a cipher is given by an ordered list of the d digits to represent the key (permutation). 6.2 Fitness Function Assessment All metaheuristic search algorithm specially population based need fitness to help guide their search toward best new generations.here the fitness function derived from language statistics (Dimovski & Gligoroski 2003), where The candidate keys is to compare n-gram statistics of the decrypted message with those of the language (which are assumed known). Eq.3 is a general formula used to determine the suitability of a proposed key. (3) K is known as language statistics. In this paper English language is used. b and t are the bigram (2-gram)and trigram (3-gram) statistics. A denotes language alphabet (i.e. for English language A Z). D is the decrypted message statistics b and t are the bigram (2-gram) and trigram (3-gram) statistics. The values of and allow assigning of different weights to each of the two n-gram types (i.e. bigram and trigram). The range of and are [0, 100]. In the process of determining the cost associated with a transposition cipher key the proposed key (i.e. evaluate particle i) is used to decrypt the ciphertext and then the statistics of the decrypted message are then compared with statistics of the language. Where the unigram frequency are ignored when evaluating a key in Eq Improved Cuckoo Search pseudo code : The following steps represent the main steps of the improved Cuckoo Search algorithm: Input: problem initial parameters Output: The best of solutions Start Objective function f(x), x= (x 1,x 2 x u ) T Generating initial population (pop) of n host nests x i (i=1,2, n) While (t<maxgenerations) and (!stop criterion) Move a cuckoo randomly via Lévy flights Evaluate its fitness F i Randomly choose nest among n available nests (for example j) If( f j > F i ) Replace j by the new solution; Fraction p ɑ of worse nests are abandoned and new nests are being built; Keep the best solutions or nests with quality solutions; /* build the similarity matrix between nests */ MAT []=null; For each nest in pop 28

8 For each digit in nest Increase MAT[nest(k),sol(k+1)] by 1 End for Round last digit with first digit in current nest End for Best=[] For each row in MAT find the higher value and take its Indices i,j Best =Best best of MAT(i, j) End for Evaluate this best solution But the best in pop Rank the solutions and find the current best End while Post process and visualize results End For more illustration about similarity between nests and how it measure for example take the nests (keys) [6,3,5,2,4,1];[5,2,1,6,4,3];[3,1,5,2,6,4] note that the digit 5 follow by digit 2 on all nests here this mean the MAT[5,2]=3 it mean that digit 2 have high priority to come after digit 5 and so on. 7. Experimental Results Results of applying improved cuckoo search algorithm on cryptanalysis transposition cipher system are offered in this part. Mentioned algorithm is executed in a system, with CPU Core i3, 2.30GHz with 4GB RAM capacity, using Visual Basic.Net 2010 programming language, utilized results that come from ICS are compared with the same results in traditional CS. Different permutations (keys), ciphertexts with different lengths are experimented. The results show that the behavior of the improved algorithm increasing the convergence rate more than traditional cuckoo algorithm.. All Case studies s are executed in MCS and CS at the same conditions in 200 generations, and the best created amounts by them are compared. Superiority of improved cuckoo search and its stability comparing with CS can be seen Fig. 4. The parameters are set as follows: itermax=1000, p ɑ =0.25, σ=0.2,. To avoid the influence of random algorithm every experiment is run respectively 200 trials. Statistical results such as in table 1. Table 1 show Experimental results under different ciphertext sizes and corresponding key length. 29

9 Fig. 4: Average Fitness Function For CS & ICS Using Different Key Lengths For each key (nest) the Statistical Analys of letter frequencies of a decrypted ciphertext is done. Afterwards compare the letter frequencies with those of the English language ( target). Table.1: Solved Key Versus Amount of Ciphertext for Deferent Transposition Size Ciphertext Length Decryption key recovered Key length Characters The experiment showed also showed that the population must be increase with the key length. Table 2 show experiment when the cipher text size is stable and the population size variable. Table.2: Solved Keys Versus Population Size (Nests) for Stable Ciphertext Size Ciphertext Decryption key size recovered Length=2000 Key length Popsize

10 Thus the time cost increase with the largest secret keys Table 3 illustrate required time to break transposition cipher with 2000 letters for different sizes Table 3. Required Time to Break Transposition Cipher with 2000 Letters for Different Sizes Key length (Digits) Time (Seconds) Conclusions The paper introduce improved CS attack on the transposition cipher,similarity between keys are exploited to reduce local maxima and used to generate candidate secret keys and choice the correct one (secret key) to break the ciphertext and to recover the plaintext. Experimental results show that the improved cuckoo search is efficient in determining the optimal choice of key to find the plaintext. The number of possible visited keys required for breaking the key (i.e. recover plaintext) is less than the number of possible visited keys required in the Brute Force attack, because the number of possible visited keys possible keys for a transposition cipher with N key size is N factorial. Quick convergence toward the global optimum response, low possibility of difficulty in local optimum points, and general movement of population toward the better points via destroying the improper responses are some advantages of mentioned algorithm. improved cuckoo search can be utilized in future to attack another cipher systems and can be used to solve more general problems tsp problem variants. In summary, modified cuckoo search greatly facilities cryptanalysis of transposition ciphers and provides a potentially powerful method for analyzing more sophisticated ciphers. References Bacanin, N. (2012). Implementation and Performance of an Object-Oriented Software system for Cuckoo Search Algorithm, International journal of mathematics and computers in simulation Issue 1, Volume 6. Brajevic, I., Tuba, M. & Bacanin, N (2012). Multilevel Image Thresholding Selection Based on the Cuckoo Search Algorithm Advances in Sensors, Signals, Imaging and Simulation. Dimovski, A. & Gligoroski, D. (2003). Attacks on the Transposition Ciphers Using Optimization Heuristics, Proceedings of ICEST 2003, October 2003, Sofia, Bulgaria. Garg P, (2005) Genetic Algorithms, Tabu Search and Simulated Annealing: A Comparison between Three Approaches for the Cryptanalysis of Transposition Cipher,Journal of Theoretical and Applied Information Technology Giddy, J. P. & Safavi-Naini, R. (1994). Automated Cryptanalysis of Transposition Ciphers, the Computer Journal, Vol. 37, No. 5. Hilton, Rod (2012). Automated Cryptanalysis of Monoalphabetic Substitution Ciphers Using Stochastic Optimization Algorithms Menezes, A., Oorschot, P. Van & Vanstone, S. (1996). Handbook of Applied 31

11 Cryptography, CRC Press. Methew, R. (1993). The Use of Genetic Algorithms in Cryptanalysis, Cryptologia, Vol. 7, No. 4 April 1993, pp Russell, M. D., Clark, J. A. & Stepney, S. (2003). Making the Most of Two Heuristics: Breaking Transposition Ciphers with Ants Evolutionary Computation, CEC 03, Vol.4, Dec. 2003, pp Salih, Hilal Hadi. Sadiq, Ahmed Tariq. & Ali, Ismail Khalil. (2009). Attack on the Transposition Ciphers Using Particle Swarm Optimization, 1st Conference of Software Eng., University of Technology, Baghdad, Iraq. Solso, R., Barbuto, P. & Juel, C., (1979). Bigram and Trigram Frequencies and Versatilities in the English Language, Behavior Research Methods 11. Stallings, W. (1999). Cryptography and Network Security, 2 nd Edition, Prentice Hall. Toemeh, R. & Arumugam, S. (2007). Breaking Transposition Cipher with Genetic Algorithm, Electronics and Electrical Engineering, No. 7(79), pp Werner R. Grundlingh and Vuuren Jan H. Van(2007), Using genetic algorithms to break a simple cryptographic cipher, accessed in Uddin, M. F. & Youssef, A. M. (2006). Cryptanalysis of Simple Substitution Ciphers Using Particle Swarm Optimization, IEEE Congress on Evolutionary Computation, Vancouver, BC, Canada, July Yang, X. (2008). Nature-Inspired Metaheuristic Algorithms, Luniver Press, UK. Yang, X. S. & Deb, S. (2009), Cuckoo Search via Lévy Flights, in Proc. of World Congress on Nature & Biologically Inspired Computing, pp

PARTICLES SWARM OPTIMIZATION FOR THE CRYPTANALYSIS OF TRANSPOSITION CIPHER

Journal of Al-Nahrain University Vol13 (4), December, 2010, pp211-215 Science PARTICLES SWARM OPTIMIZATION FOR THE CRYPTANALYSIS OF TRANSPOSITION CIPHER Sarab M Hameed * and Dalal N Hmood ** * Computer