Design and Implementation of Enhanced Affine and Inverse Affine Transformation Based Composite S-box for AES Encryption and Decryption

The Substitution Box (S-Box) and Inverse MixColumn (Inv MixColumn) forms core building blocks in Advanced Encryption Standard (AES) based Security Algorithm. This study presents full custom design of Composite S-Box by reducing the composite field arithmetic of Multiplication Inverse (MI) and Affine/Inverse Affine Transformation. Design of proposed new MI and Affine/Inverse Affine Transformation techniques are integrated in Composite S-Box of both AES Encryption and Decryption. Very Large Scale Integration (VLSI) System design environment is considered in this research work to measure the performance improvement. High Speed, less area utilization and Lower power consumptions are the important parameter in VLSI System design environment. Hence, the main goal of this research work is to reduce the hardware complexity, Power and Delay consumption of AES Encryption and Decryption process. The principle of reducing the redundant functions is used in both MI and Affine/Inverse Affine Transformation of Proposed Composite S-Box design for reducing the hardware complexity and power consumption. Proposed new Composite S-Box design offers 6.52% reduction of Slices, 5.68% reduction of Look up Tables (LUTs), 2.24% reduction of delay and 6.15% reduction of Power consumption than traditional Composite S-Box design. Further Proposed new composite S-Box design is integrated into both AES encryption and AES decryption process to improve the performance evaluation of AES algorithm.


INTRODUCTION
Advanced Encryption Standard (AES) algorithm provides best security in the field of wireless transmission mechanism.With ever increasing the 3G and 4G mobile products, low on-chip and high speed cryptography algorithms are necessary.For instance, in a banking system (net banking, mobile banking, ATM) and mail delivery system, secure crypto mechanism is essential with high speed and low-on chip processors.AES meets advantages in both Security and Hardware Performance Improvement.Hence, a lot of researches have been suggested the AES processes for transferring different kinds of things in Wireless.In general AES Encryption and Decryption has four steps for producing Chiper data and reconstructing the plain data.Each and every transformation has critical logics developed by hardware for making secure transformation.AES is a Rijndael algorithm selected for encrypting and decrypting the digital information by National Institute of Standards and Technology (NIST) in 1997 (Jamil, 2004).A single Multi-Core architecture is developed in Wang et al. (2010) for performing AES Encryption and Decryption process.Similarly, Dual Single-Core architecture has been developed in Li and Li (2008).In those research works, single VLSI based core architecture controls the operation of S-Box/Inv S-Box, MixColumn/Inv MixColumn, Shift Rows/Inv Shift Rows and Add Round Key transformation.Among all those transformation, S-Box/Inv S-Box and MixColumn/Inv MixColumn transformation has more hardware complexity than other transformations like Shift Rows/Inv Shift Rows and Add Round Key Transformation.In general, Add Round Key transformation performs N rounds of redundant operation of S-Box/Inv S-Box, Shift Rows/Inv Shift Rows and MixColumn/Inv MixColumn transformation.Hence, any architectural improvements in S-Box/Inv S-Box or MixColumn/Inv MixColumn would also helps to improve the performances of Add Round Key transformation.
In this study, a new Affine Transformation (AT)/Inv Affine Transformation (IAT) techniques is proposed by realizing the architecture of traditional AT/IAT and eliminating the redundant logics by solving the arithmetic logics.Also Multiplication Inversion (MI) unit has been realized and improved.Proposed new AT/Inv AT and MI unit has been incorporated into Composite S-Box for improving the performance of AES Encryption and AES Decryption.

LITERATURE REVIEW
The Rijndael algorithm is used for encrypting and decrypting the data.AES standards are selected for encrypting the data by National Institute of Standards and Technology (NIST) in 1997 (Jamil, 2004).AES Rijndael proposal has been implemented in Sklavos and Koufopavlou (2002) with the help of VLSI System design environment.It consists of flexible architecture for both encrypting and decrypting the data (Li, 2006).In order to perform four types of functions (S-Box/Inv S-Box, Shift Rows/Inv Shift Rows, MixColumn/Inv MixColumn, Add Round Key) Dual Core architecture has been proposed in 2008 (Li and Li, 2008).Further in 2010, (Wang et al., 2010) Single-Multi Core has been proposed for integrating four types of functions in single architecture.Also it is possible to design the fault detection scheme for transformation of data in AES Encryption and AES Decryption process.Mozaffari-Kermani and Reyhani-Masoleh (2010), a Fault detection technique has been proposed with the help of hamming codes for AES Encryption and AES Decryption.Further to improve the fault detection technique of AES Encryption and AES Decryption, Pipelining technique has been introduced in Liu et al. (2015).Ahmad and Rezaul Hasan (2013) Thillaikkarasi and Vaishnavi (2014), Optimum Composite AES S-Box has been proposed for reducing the critical path of data flow architecture in S-Box architecture.Further Wave Pipelining Techniques (WPT) is used in AES S-Box to increase the speed and throughput of the system.Sandhya and Deepa (2013) and Sandhyarani andNirmal Kumar (2014a, 2014b), Composite S-Box based AES Encryption and Decryption techniques are integrated into Cipher Block Chaining (CBC) and Counter Mode (CM) mode of AES Encryption and Decryption.In addition to Composite S-Box, Inverse MixColumn transformation also plays a vital role in Performance Improvement.In order to improve the architectural performances of Inverse MixColumn transformation, Optimized MixColumn has been designed in Balamurugan and Logashanmugam (2015) and Khose and Raut (2014).

RIJINDAEL AES ALGORITHM
Rijndael AES Algorithm processes data blocks of fixed size using cipher keys of length 128, 192 and 256 bits.128-bit AES Encryption has been widely used for encryption and decryption of AES.Both Encryption and Decryption has four transformations for encrypting and decrypting the data.General data flow structure for 128 bit AES Encryption and Decryption is illustrated in

Sub-Bytes transformation ():
In Sub-Bytes transformation, substitution techniques are involved with the help of Substitution tables (LUTs/ Memories/ROM).In general, substitution box has been generated by two important transformation techniques: • Multiplicative Inverse (MI) transformation: Taking MI given input state bytes in Galois Field GF (2 8 ).• Affine Transformation (AT): Taking affine transformation of MI outputs.In this operation, XOR functions can be performed with in combined input bits itself.
Similarly, Inverse Sub-Bytes transformation performs inverse operation.

Shift rows transformation ():
In Shift Rows transformation, single bytes of every row have been shifted for increasing the security.Similarly, reverse process has been followed in Inv Shift Rows transformation.

MixColumn transformation ():
In MixColumn multiplication, state bytes are treated as a four-term polynomial.The columns are considered as polynomials over GF (2 8 ) and multiplied modulo x with a fixed polynomial.Similarly, in Inv MixColumn transformation, reverse process has been followed (i.e.,) state bytes are multiplied with another fixed polynomials.

Add round key transformation ():
In the Add Round Key () transformation, a Round Key is added to the State by a simple bitwise XOR operation.Each Round Key consists of Nb words.Those Nb words ar into the columns of the State.

DESIGN OF AES COMPOSITE S
In Rijndael AES Algorithm, Substitute Box (S Box) is the first step of encryption operation.In S transformation, Substitution bytes are used to replace the state bytes.Symbolic block diagram of Sub Bytes In MI unit, inverse multiplication has been performed with the help of digital logics and affine transformation has been performed by taking exclusive operation MI outputs with 63.Block diagram of Composite S-Box is illustrated in Fig. 3, which performs both Sib-Bytes and Inv Sub transformation by switching combinational logics using multiplexers.To make a compact AES implementations composite field inversions are extended to GF (((2 from GF (2 8 ).This approach is used to reduce the chip size to design.The column vector of the input State matrix first goes into isomorphic transformation from GF (2 8 ) into the composite field GF (((2 by inversion in composite field and inverse isomorphic transformation.Finally, an affine transformation is carried out to create the cipher data. In S-Box Transformation, Isomorphic Mapping function (q) has performed initially on the input State Bytes (b).Secondly, Inverse Multiplication (q') has been performed on isomorphic output data.Then inverse isomorphic mapping function (b') has been performed on q'.Finally, affine function (b'') has been carried out by inverse transformation is illustrated in Fig. 2

. The Substitution table has been generated by performing two functions
In MI unit, inverse multiplication has been performed with the help of digital logics and affine has been performed by taking exclusive operation MI outputs with 63.Block diagram of Box is illustrated in Fig. 3, which Bytes and Inv Sub-Bytes transformation by switching combinational logics using ompact AES implementations composite field inversions are extended to GF (((2 2 ) 2 ) 2 ) ).This approach is used to reduce the chip size to design.The column vector of the input State matrix first goes into isomorphic transformation from to the composite field GF (((2 2 ) 2 ) 2 ) followed by inversion in composite field and inverse isomorphic transformation.Finally, an affine transformation is Box Transformation, Isomorphic Mapping ion (q) has performed initially on the input State Bytes (b).Secondly, Inverse Multiplication (q') has been performed on isomorphic output data.Then inverse isomorphic mapping function (b') has been affine transformation unction (b'') has been carried out by inverse In Inv S-Box Transformation, Inv Affine Transformation (q') function has been performed initially on the given input bytes (q'').Secondly, Multiplicative Inverse function (q) has been performed on IAT outputs.
Similarly, State matrix transformation of isomorphic and inverse isomorphic transformation is demonstrated as follows: 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 [ISO -1 (b)] = The block diagram of Multiplicative Inverse (MI) unit is illustrated in Fig. 4. It performs the inverse operation of input x (i.e., 1/x).It consists of Equation ( 1) establishes the Affine Transformation techniques.In this equation, there are four redundant logic functions are identified: Hence, equations of Affine Transformations can be reduced as follows: When compared to traditional AT technique, 12 gates are reduced in proposed Enhanced AT techniques.The circuit diagram of AT technique is illustrated in Fig. 7. Similarly, Redundant Functions of Inverse Affine Transformation techniques are identified from Eq. ( 2) as follows: Redundant Function_IAT1 = q' 2 ^ q' 5 Redundant Function_IAT2 = q' 3 ^ q' 6 Redundant Function_IAT3 = q' 4 ^ q' 7 Hence, equations of Inverse Affine Transformation can be reduced as follows: Hence, equations of Isomorphic Transformation can be reduced as follows: When compared to traditional ISO technique, 5 gates are reduced in proposed Enhanced ISO technique.The circuit diagram of proposed Enhanced ISO technique is illustrated in Fig. 9. Similarly, redundant functions of Inverse Isomorphic Transformation are identified from Eq. ( 6) as follows: Redundant Function_InvISO1 = q 1 ^ q 3 Redundant Function_InvISO2 = q 5 ^ q 6 Redundant Function_InvISO3 = q 7 ^ q 5 Hence, equations of Inverse Isomorphic Transformation can be reduced as follows: When compared to traditional Inv ISO technique, 8 gates are reduced in proposed Enhanced Inverse ISO technique.The circuit diagram of proposed Enhanced Inverse ISO technique is illustrated in Fig. 10.In addition, the circuits of multiplication of x λ and x 2 are realized and re-designed by eliminating the unwanted redundant functions.Hence a new architecture has been proposed for Inverse Multiplication unit.The circuit diagram of Enhanced combined multiplication of x λ and x is illustrated in Fig. 11 by using following expressions: where, 3 2 q q h ⊕ =

RESULTS AND DISCUSSION
Design of Enhanced AT, IAT, ISO, Inverse ISO and combined multiplication of x λ and x 2 are designed

•
Substitution Box (S-Box) • Shift rows transformation • MixColumn transformation • Add round key transformation for AES Encryption • Inverse shift rows transformation • Inverse S-Box (Inv S-Box) • Inverse MixColumn transformation • Add Round Key transformation for AES Decryption, respectively

Fig. 1 .
As shown in Fig. 1, Final Round of both AES Encryption and AES Decryption doesn't have MixColumn and Inv MixColumn transformation function respectively.It has 10 Number of rounds for exhibiting cipher data from Encryption process and plain data from Decryption process.

Fig. 3 :
Fig. 3: Block diagram of composite S-box isomorphic functions.In general affine transformation (AT) function involves the multiplication with 63.In Inv S-Box Transformation, Inv Affine Transformation (q') function has been performed initially on the given input bytes (q'').Secondly, Multiplicative Inverse function (q) has been performed on IAT outputs.Finally, inverse isomorphic mapping function has been performed on MI outputs to reconstruct the original input State-Bytes.The State matrix representation of Affine and Inverse Affine transformation techniques is demonstrated as follows: Finally, inverse isomorphic mapping function has been performed on MI outputs to reconstruct the original input State-Bytes.The State matrix representation of Affine and Inverse

Fig. 4 :
Fig. 4: Block diagram of multiplicative inverse Fig. 7: Circuit diagram of proposed enhanced AT technique

Fig. 12 :
Fig. 12: Simulation result of proposed enhanced composite S-box based 128-bit AES encryption

Table 1 :
Performance evaluation of both traditional composite s-box and proposed composite s-box

Table 2 :
Performance evaluation of both traditional composite s-box based AES encryption and proposed enhanced composite s-box based AES encryption Box and Proposed Enhanced Composite S-box is analyzed and compared in Table 1.Similarly, performance evaluation of both traditional Composite S-Box based AES Encryption and Proposed Enhanced Composite S-Box based AES Encryption is analyzed and compared in Table 2.It shows that proposed enhanced techniques are used to increase the performances in terms of less area utilization, less delay and lower power consumption.Further Performance Evaluation of both traditional Composite S-Box based AES Decryption and proposed Composite S-Box based AES Decryption are analyzed and compared in Table 3. CONCLUSION In this study, Enhanced Composite S-Box is designed through Very Large Scale Integration (VLSI) System design environment.Less area utilization, high speed and lower power consumption are the main key factors in VLSI System design environment.Therefore, the main goal of this research work is to increase the speed of the AES Encryption and Decryption process.In order to meet above requirements, Enhanced Affine Transformation, Enhanced Inverse Affine Transformation, Enhanced Isomorphic Mapping, Enhanced Inverse Isomorphic Mapping and combined multiplication of x λ and x 2 are proposed in this research work.Further all the enhanced techniques are integrated in Composite S-Box.Proposed Enhanced Composite S-box offers 6.52% reduction in Slices, 5.68% reduction in LUTs, 2.24% reduction in delay and 6.15% reduction in power consumption than traditional Composite S-Box.Proposed Enhanced Composite-s-Box based AES Encryption offers 17.15% reduction in Slices, 17.87% reduction in LUTs, 5.77% reduction in Minimum Period delay and 11.73% reduction in power consumption than traditional AES Encryption.Similarly, Proposed Enhanced Composite S-Box based AES Decryption offers 3.62% reduction in Slices, 7.51% reduction in LUTs, 12.23% reduction in Minimum period delay and 9.14% reduction in power consumption than traditional AES Decryption.In future, Proposed Enhanced Composite S-Box based AES Encryption and Decryption Standard will be absolutely used in different types of wireless cryptography based applications for implementing with less hardware and high speed.