Triple Sv: a Bit Level Symmetric Block Cipher Having High Avalanche Effect

— The prolific growth of network communication system entails high risk of breach in information security. This substantiates the need for higher security for electronic information. Cryptography is one of the ways to secure electronic documents. In this paper, we propose a new block cipher, TRIPLE SV (3SV), with 256-bit block size and 112-bit key length. Generally, stream ciphers produce higher avalanche effect but Triple SV shows a substantial rise in avalanche effect with a block cipher implementation. The CBC mode has been used to attain higher avalanche effect. The technique is implemented in C language and has been tested for feasibility. I. INTRODUCTION With the transformation of classical [1] methodology in business to conventional methodology, security of electronic documents is in need. A Cipher is something that converts the actual document into a format that cannot be recognized by anyone except the sender and intended receiver. One of the vital considerations for a good cipher is its avalanche effect. This effect obviates the brute force attack to a greater extent. Modern techniques of encryption either use a single symmetric key or two asymmetric keys. The algorithm is called as Symmetric Key Cryptography if only one key is used on both ends of the communication and it is called as a Public Key Cryptography if two distinct keys are used. The proposed technique is based on Private Key Cryptography in Cipher Block Chaining mode [1,2] with high avalanche effect i.e. a one-bit change in a plaintext affects all following cipher-text blocks [2,3].


I. INTRODUCTION
With the transformation of classical [1] methodology in business to conventional methodology, security of electronic documents is in need.A Cipher is something that converts the actual document into a format that cannot be recognized by anyone except the sender and intended receiver.One of the vital considerations for a good cipher is its avalanche effect.This effect obviates the brute force attack to a greater extent.Modern techniques of encryption either use a single symmetric key or two asymmetric keys.The algorithm is called as Symmetric Key Cryptography if only one key is used on both ends of the communication and it is called as a Public Key Cryptography if two distinct keys are used.The proposed technique is based on Private Key Cryptography in Cipher Block Chaining mode [1,2] with high avalanche effect i.e. a one-bit change in a plaintext affects all following cipher-text blocks [2,3].
The Section II of this paper deals with the proposed technique.A concept of key-generation [1] is given in Section III.Results and comparisons are illustrated in Section IV. Conclusions are drawn in Section V.

II. TRIPLE SV (3SV)
The Triple SV is a block cipher that uses secret key encryption.This algorithm takes a fixed-length string of plaintext bits and transforms it through a series of complicated operations into another cipher-text bit string of the same length.The proposed block size is 256 bits.
The Key comprises 112 bits.Fig. 1 summarizes the overall structure of Triple SV.

A. Modes of Operation
Like other block ciphers, Triple SV by itself is not a secure means of encryption but must instead be used in one of the several modes of mode of operation, like Electronic codebook (ECB), Cipher-block chaining (CBC), Propagating cipher-block chaining (PCBC), Cipher feedback (CFB), and Output feedback (OFB).We have designed and implemented Triple SV in CBC mode In the CBC mode, each block of plaintext is XORed with the previous cipher-text block before being encrypted.This way, each cipher-text block is dependent on all plaintext blocks processed up to that point.Also, to make each message unique, an initialisation vector must be used in the first block.
A one-bit change in a plaintext affects all following ciphertext blocks.A plaintext can be recovered from just two adjacent blocks of cipher-text.As a consequence, decryption can be parallel zed, and a one-bit change to the cipher-text

B. Encryption
The algorithm's overall structure (for encryption) is shown in Fig. 4.There are basically seven similar levels of processing.In addition there is also an initial and final inversion operation.The seven similar levels of processing have identical structure but differ in the number of consecutive n bits out of the input 256 bits to each level, which are coupled together and treated as a single entity while being processed inside each level.The values that n take in the 7 distinct levels are 2, 4, 8, 16, 32, 64,  128, (i.e. 2 (level number) ), respectively.Hence the seven levels of processing are named as 2-bit level, 4-bit level, 8-bit level, 16bit level, 32-bit level, 64-bit level, and 128-bit level, respectively.4, 8, 16, 32, 64, or 128, depending on the level at which we are operating.The groups are formed by starting from the first bit and grouping together the first n consecutive bits, then the next n consecutive bit, and so on.These distinct n-bit groups behave as individual entities at that particular level.

1) n-Bit Level Structure
For n-bit far swapping, the first n-bit group gets swapped (interchanged) the last (farthest) n-bit group.The second n-bit group gets swapped with the penultimate n-bit group, and so on.The function takes the 16-bit K n string as input.Next, it determines the number of iteration of the particular level (a).Then the K n is given a left-rotations and the modifies string makes the first 16 bits of the expanded string.Next, another left-rotation is given to the first 16-bits to produce the next 16bits, and so on.Sixteen such modifications of the 16-bit string finally produce the 256-bit string for that particular level and that particular iteration.Thus, a 256-bit output is generated by the expansion function, which then gets XORed with the 256-bit output of the n-bit near swapping of that particular iteration of the level.

C. Decryption
The decryption algorithm is just the reverse of the encryption algorithm.In case of decryption, the 256-bit cipher text fed to the cipher first undergoes 128-bit level, then 64-bit level and so on till 2-bit level.Fig. 9 shows the decryption algorithm.

IV. RESULTS AND COMPARISONS A. The Avalanche Effect:
Calculation of Avalanche Effect, Avalanche Effect refers to a desirable property of any cryptographic algorithm where, if an input is changed slightly (for example, flipping a single bit) the output changes significantly (e.g., more than half the output bits flip).
Table I compares the avalanche effect ratio for 3SV, TDES and RSA algorithm and Fig. 12 gives the graph of the same which are obtained after calculating the respective Avalanche Effect by making a change of a few (approx 3) characters in each file.It is observed that the proposed technique is showing an average avalanche ratio percentage of 95.77%, which is way higher than that obtained using Triple DES or RSA.High avalanche ratio ensures higher security from brute force attack.

B. Frequency Distribution
The results [4] shown in Fig. 13, Fig. 14, Fig. 15 are obtained after calculating the respective Frequency Distributions of the source file ‗ANSI.DOC' and the corresponding encrypted files using Triple SV, RSA and Triple DES.From Fig. 13, it is substantiated that the frequency distribution of the proposed technique is well distributed over a range that is exclusive to the range of the source file.This makes statistical cryptanalysis [1,5,6,7] immensely improbable.

C. Non-Homogeneity Test
Another way to analyse the technique is to test the nonhomogeneity of the source and the encrypted file.The Chi-Square test has been performed for this purpose.Table II and Fig. 16 show the file size and the corresponding Chi-Square values for ten different files.The Chi-Square values for the proposed technique are comparatively lower than those obtained by RSA or TDES.The value of degree of freedom is on an average 127.Hence the source and the corresponding encrypted files are considered to be heterogeneous.

D. Time Complexity Analysis
This section compares the time complexity of the Triple SV with that of RSA and TDES by taking the encryption and decryption times into consideration.
The graphical analysis of the encryption and decryption time of Triple SV, RSA and TDES has been depicted in Fig. 17 and Fig. 18 respectively where x-axis represents the 25 test files (of increasing sizes varying from 1 KB to 758 KB) and yaxis represents the time taken for encryption/decryption (in seconds).The time complexity of the proposed technique is well comparable to RSA and TDES.www.ijacsa.thesai.orgV. CONCLUSIONS The cryptographic algorithm, Triple SV is a symmetric block cipher using a 256-bit block and 112-bit key.From the above discussions it can be inferred that Triple SV is potentially a promising algorithm, which can find its efficient implementation in different fields.Triple SV has a way better Avalanche Effect than any of the other existing algorithms and hence can be incorporated in the process of encryption of any plain text.The high avalanche ratio and a key size of 112 bits ensure sound security from brute force attacks.The implementation in CBC mode ensures low predictability and tougher cryptanalysis.Even the time complexity of the proposed algorithm is considerably viable and even better than RSA and TDES at many instances.

Figure 1 .
Figure 1.Overview of the Triple SV Algorithm.

Fig. 5
Fig. 5 explains the entire construct of the n-bit level.Each level basically comprises three major functions, namely, Far Swapping, Near Swapping and Expansion Function, and a XOR Function.The 256-bit input to the level first undergoes an n-bit far swap.The 256-bit output of the n-bit far swap is then introduced to an n-bit near swap, which again generates a 256bit output.

Figure 3 .
Figure 3.The Cipher Block Chaining (CBC) mode (decryption) b) n-Bit Near Swap Function: The n-bit near swap function is quite similar to n-bit far swapping function, with a subtle change in swapping pattern, as demonstrated in Fig. 7.For n-bit near swapping, the first n-bit group gets swapped (interchanged) the second (nearest) n-bit group.The third n-bit group gets swapped with the fourth n-bit group, and likewise the penultimate n-bit group is swapped with the ultimate n-bit group.c) Expansion Function (for encryption): The ExpansionFunction, in comparison to the earlier functions is a little more complex.For a certain n-bit level, the Expansion Function transforms the 16-bits string, K n into a 256-bit string, which is used as an input to the XOR Function.Fig.8summarizes the expansion function for encryption.

Figure 6
Figure 6.n-Bit Far Swap Function

Figure 11 .
Figure 11.Expansion Function (for Decryption) III.KEY STRUCTURE Key length is one of the two most important security factors of any encryption algorithm-the other one being the design of the algorithm itself.The effective key length of Triple SV is 112 bits, giving 2 112 possible combinations.The 112-bit key is completely user defined and is provided by the user in the form of numbers of iteration that each of the n-bit levels would have while the encryption or decryption process progresses.The 112 bits of the key have been logically divided into seven 16-bit binary sequences, each of which relates to a particular n-bit level.The association is elucidated below. Bit number 1 to 16 form string K2, and is associated with 2-bit level. Bit number 17 to 32 form string K4, and is associated with 4-bit level. Bit number 33 to 48 form string K8, and is associated with 8-bit level. Bit number 49 to 64 form string K16, and is associated with 16-bit level. Bit number 65 to 80 form string K32, and is associated with 32-bit level. Bit number 81 to 96 form string K64, and is associated with 64-bit level. Bit number 97 to 112 form string K128, and is associated with 128-bit level.

Figure 15 .
Figure 15.Graph for Distribution of Characters for TDES

Figure 16 .
Figure 16.Graph for Comparison of Chi Square Values for Triple SV, Triple DES and RSA

TABLE I .
COMPARISION OF AVALANCHE RATIO FOR 3SV, TDES AND RSA ALGORITHM

TABLE II .
THE CHI SQUARE VALUES AND DEGREE OF FREEDOM FOR TRIPLE SV, TRIPLE DES AND RSA ALGORITHMS