Improved Perceptual Video Encryption Technique using Residue Number System

In this paper, we propose an enhanced perceptual video encryption technique to speed-up and secure cipher video transmitted across networks using Residue Number System (RNS). The technique proposes a new reverse converter with smaller dynamic range using the moduli set { } 1 2 , 2 , 1 2 + − n n n that is integrated into our previous work of [2]. After encryption, cipher video is encoded into three residual videos that have smaller pixel values and ideal for transmission across networks. Instead of transmitting the three (3) residual videos, the technique effectively transmits and decodes only two (2) of them back into the original video with same visual quality. Experimental results show that the technique enhances transmission speed and security of cipher video across networks.


Introduction
Perceptual video encryption techniques have received overwhelming attention by researchers in recent times leading to the development of varied cryptographic  [3,4,7,11,13,15,30,31]. These offer content providers the opportunity to reach more viewers while securing the high quality versions of their videos. Potential consumers can preview the degraded videos before acquiring the high quality ones. However, little has been done by previous techniques to enhance the transmission speed of cipher videos transmitted across networks. Owing to large bit representations, big numbers transmit slower than small ones across network. Small numbers can be achieved with the adoption of RNS where residues of the huge and redundant video data are used. Among many inherent features, RNS offers high computational and transmission speeds. In this proposed technique, RNS is employed to split cipher videos in to three shares (residual videos) that have smaller values. Two of the shares are then transmitted and deciphered at the receiver's end without loss of any information. The shares add extra layer of security and enhance transmission speed to the cipher videos. The rest of the paper is presented as follows; residue number system is presented in Section 2. Section 3 presents detail explanation of the proposed reverse converter while Section 4 presents the proposed integrated crytosystem of the scheme of [2] and RNS. Analysis of results is in Section 5 and finally we conclude in Section 6.

Residue Number System
Residue number system is described as a non-weighted number system having numerous benefits in numerical computations. The inherent features in RNS such as the digit-to-digit computations, parallelism, fault tolerance, high computational speed and low power dissipation make it ideal for implementation in fields of communication [9,10], Digital Signal Processing (DSP) [14,26,32], intensive computations such as digital filtering, correlations, convolutions, direct digital frequency synthesis [6], Discrete Fourier Transform (DFT) computations [24], Fast Fourier Transform (FFT) computations, image processing [1,10,20,25,28] and cryptography [27,33]. RNS are based on the congruence relation. Two integers x and y are said to be congruent modulo m if m divides exactly the difference of x and y; mathematically [20] . m y x ≡ If q and r are the quotient and remainder, respectively of the integer division of Y by m that is, , then, by definition, we have .
The relationship between r; Y and m is given by [20]. ( With this, every integer Y in [ ]

RNS to binary conversion
Two traditional techniques are widely used for RNS to binary reverse conversion; the Chinese Remainder Theorem (CRT) and the Mixed Radix Conversion (MRC).

The mixed radix conversion (MRC)
Suppose the moduli compose of positive pairwise relative prime integers is being ordered as for all i [17,19,20]. Apart from the traditional techniques, other researchers have proposed much faster and efficient RNS to binary reverse converter for particular moduli sets [5,8,12,16,18,34]. However, most of them are simple modification of the CRT or MRC techniques [21][22][23].

Proposed Technique
In this section, a new reverse converter with smaller dynamic range is proposed for fast decoding of cipher video. The quotient technique is used to convert numbers in RNS to their equivalent binary (weighted) number system. The dynamic range adopted for this technique is [ ].
Thus, two moduli in the moduli set are used in the reverse conversion process while one modulus is made redundant.

Proposed reverse converter for dynamic range [ ]
x x x X can be represented as in the following three different ways; 2 q can be represented as; , 3 2 where Z d ∈ and . 0 ≥ d Illustration 1.

Hardware implementation
The binary representations of the respective residues are as follows: Equation (11) can be simplified as ( ) and, ( )

Hardware realization
The hardware of the proposed scheme applicable to values of , 4 ≤ n can be realized with a simple modulo carry propagate adder (MCPA) and an inverter. Equation (16) is a concatenation of bits, which would not require any hardware resource for that operation. Equation (17) would only require a bit inverter, which is not expensive and at the same time, does not impose undue delay on the scheme. It is only in Equation (15) that an MCPA of length 2n-bits would be required to add the results of (16) and (17). Thus, the hardware resources in this regard are 2n-bits wide whiles the delay imposed by such an adder is 4n-bits. The delay for an inverter is usually unity; therefore, the total delay that would be imposed on the scheme is ( ) The block diagram for the reverse conversion is shown in Figure 1.

Enhanced encryption algorithm
The proposed enhancement to the encryption algorithm of [2] is obtained by modifying the last step to include the RNS encoder. This is presented as; • Input video file V, number of iteration I, block size blkSize, angle of rotation θ, unit-anti-diagonal matrix K and the number of bits n. • Compute the residual videos x2 and x3 from E V modulus n 2 and , 1 2 + n respectively.

Enhanced decryption algorithm
The proposed enhancement to the decryption algorithm of [2] is obtained by modifying the initial steps to include the RNS decoder. The proposed enhancement is presented as; • Input cipher videos x2 and x3, number of iteration I, block size blkSize, angle of rotation θ, anti-diagonal matrix K and the number of bits n.
• Decrypt cipher frames as follows: o Decode x2 and x3 back into cipher frames E V using equation (11).   The MATLAB Simulink system to test the proposed integrated scheme is shown in Figure 3. RNS is integrated with the work of [2]. After encryption with 'Encryption Algorithm1' sub-block, the cipher video is passed through the sub-block 'RNSEncoder' to be encoded into two residual videos x2 and x3 for transmission. Since residual values are less than that of the originals, transmission is much easier and faster. At the receiver's end, residual videos are decoded by the 'RNSDecoder' sub-block into the cipher video followed by decryption into the plain video using the 'Decryption Algorithm1' sub-block.   Figure 4 shows experimental results of the residual videos after encoding a cipher frame using .
The dark pictures of parts (b) and (c) confirm the smaller values achieved through the RNS encoder. Any adversary receiving these will need extra efforts to decode them to the cipher state before efficient decryption can occur.

Procession time
The average processing time (in seconds) for ten (10) simulations of the encryption and decryption processes are summaries in Table 1. The results indicate that the 'RNSEncoder' consumes about 9% of the average encryption time while 25% of the average decryption time is consumed by the 'RNSDecoder'. Thus, RNS constitutes about 34% of the total processing time of any given encryption and decryption operation. Also, the increase in the decryption time enhances security especially against Bruce-force

Encoding analysis
Video data is made up of several frames(images) arranged over time. The elements of these frames are called pixels. The weight of a pixel for the Red-Green-Blue (RGB) format of video span 0 to 2 8 . Thus, 8-bits are required to encode and transmit each pixel.
However, the introduction of RNS reduces this to 4-bits when 4 = n is used for the 'RNSEncoder'. This saves half of the bits required to encode and transmit cipher videos. Consequently, transmission speed is enhanced by the introduction of RNS.

Conclusion
This paper proposes an enhancement to the perceptual video encryption and decryption algorithms proposed in [2] using RNS. Analysis of simulated results shows that the enhanced scheme increases transmission speed and adds extra security to cipher video.