A New Substitution-Permutation Network Cipher using Walsh Hadamard Transform 1
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R.Girija, Department of Computer Science, The NorthCap University, Sector 23-A, Gurgaon-122 017, India 1 email:
[email protected]
Hukum Singh, Departm ent of Applied Sciences, The NorthCap University, Sector 23-A, Gurgaon-122 017, India 2 email:
[email protected]
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Abstract²As we all know Cryptography is one of the oldest technique analogous to Mathematics. Modern cryptography progressed some systematic methods for providing confidentiality, Integrity, Availability and Authenticity. The contrast in between symmetric key cryptosystem is Block cipher and Stream cipher. Block Cipher is important primordial in modern cryptography and network security. In this paper, we investigate the structure of Substitution and Permutation Network (SPN) Cipher and constructing it using Walsh ± Hadamard Transform (WHT). S-Boxes are the key component of SPN cipher. WHT is characteristics two case of DFT and it is mainly used for computation of Non-linearity. Most of the Cryptographic properties are connected with Walsh transformation.
The most common values of KY are 64, 80, 96, 128, 192 or 256 bits and BL values are 64, 128 or 256 bits are used. There are 2 common approaches for designing Block ciphers. 1. Feistel networks 2. Substitution-Permutation Networks(SPN)
Index Terms²Block Cipher, SPN Cipher, WalshHadamard Transform (WHT), S-Box. I. INTRODUCTION Figure 1.a) Feistel Networks
C
ryptography has desperately increased in last few years. The most important activities of cryptography are encryption and decryption. Two paramount techniques in symmetric key cryptosystem are block cipher and stream cipher. Block ciphers are the building blocks of Symmetric key cryptography and it establishes the confidentiality of data. Block ciphers encrypt group of plaintext as one block. Stream ciphers encrypt or decrypts as a one symbol. Mostly all symmetric key algorithms are block ciphers. Blocks in the block cipher varies (64 bits for DES, 128 bits for AES, etc.) But in stream cipher, plaintext is considered as Pi , ciphertext Ci is produced by performing mod 2 addition of Pi and Ki; where Ki is keystream sequence. Ci=Pi + Ki (mod 2)
1.
The two approaches are used for designing Block cipher. 1.1 FEISTEL NETWORK: By referring the Figure 1 :( a), Feistel networks are splitted into 2 halves. (Xi and Yi); left half is called as Xi and right half is called as Yi; ¦LVQRQOLQHDUIXQFWLRQDQGLW depends on Ki and it is applied adjacent one of the halves and the result is XORed to the other. Ultimately left half and right half are swapped to produce the result. Feistel encryption for single round is given below, Xi+1 = Yi (3) Yi+1 = Xi ْ ¦.i (Yi) (4) This pURFHGXUHLVUHSHDWHGIRUµQ¶QXPEHURI rounds.
(1)
BLOCK CIPHERS The basic definition and thereafter discussion of Block cipher is given below. /HW.
--------------------------------------------------INVW1=0010
1110
0000
0111
1101
0001
After Permutation: INVV1= 0100
0101
After substitution: INVU1= 0001
1100
0010
0011
Key1= 0011
1010
1001
0100
------------------------------------------------------INVW0=0010
0110
1011
0111
Plaintext=0010
0110
1011
0111
The inverse walsh hadamard coefficients are, (1 , 0 , 1 , 1 , 1 , 1 , 0 , 0 , 1 , 1 , 0 , 1 , 0 , 1 , 1 , 0) 2017 International Conference on Computing and Communication Technologies for Smart Nation (IC3TSN)
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V.
CONCLUSION AND FUTURE WORK
Finally, this paper is concluded with the construction of substitution-permutation ciphers using walsh hadamard transform. Moreover WHT gives a clear view for nonlinearity function. The future work is to cryptanalysis of substitution-permutation cipher using walsh hadamard transform. REFERENCES [1] Cryptographic Boolean functions and applications, by Thomas w. cusick and Pantelimon Stanica. © 2009 Elsevier Inc. [2] Oprina, A., et al. "Walsh-Hadamard randomness test and new methods of test results integration." Bulletin of Transilvania University of Braov 2 (2009): 51. [3] Girija, R., and Pramod Kumar. "Walsh Hadamard transform and cryptographic properties in stream cipher." Contemporary Computing and Informatics (IC3I), 2016 2nd International Conference on IEEE, 2016. [4] Walsh-Hadamard Transform and Cryptographic Applications in Bias Computing כ [5] Mehdi-Laurent Akkar and C. Giraud. An Implementation of DES and AES, Secure against Some Attacks. In C¸ .K. Ko¸c, D. Naccache, and C. Paar, editors, Cryptographic Hardware and Embedded Systems ± CHES 2001, volume 2162 of Lecture Notes in Computer Science, pages 309± 318. Springer, 2001. [6] Cryptography and Network security, by Behrouz A Forouzan, Debdeep mukhopadhyay, 3e. . © 2015, 2010, 2008 by The McGraw-Hill companies. [7] Cryptography and Network security, Principles and Practice, sixth edition, by William Stallings. © 2006 by prentice- hall inc( now known as Pearson education) [8] Carlet, Claude, and Sihem Mesnager. "On the supports of the Walsh transforms of Boolean functions." IACR Cryptology ePrint Archive 2004 (2004): 256. [9] Linear Cryptanalysis of Substitution-Permutation 1HWZRUNVE\/LDP.HOLKHU4XHHQ¶V8QLYHUVLW\ Kingston, Ontario, Canada October 2003 Copyright Liam Keliher, 2003. [10] Biryukov, Alex. "Substitution±Permutation (SP) Network." Encyclopedia of Cryptography and Security. Springer US, 2011. 1268-1268. [11] Keliher, Liam, and Henk Meijer. "A New Substitution-Permutation Network Cipher Using Key-Dependent S-Boxes." (1997).
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