On Error Preserving Encryption Algorithms for Wireless Video Transmission

1. On Error Preserving Encryption Algorithms for Wireless Video Transmission Ali Saman Tosun and Wu-Chi Feng The Ohio State University Department of Computer and Information Science ACM Multimedia 2001

2. Presentation outline • Introduction • Applications • Objectives of this project • MPEG encoding and decoding • Video security • Forward error correction • Error preserving encryption functions • Conclusion

3. Introduction • The distribution of multimedia information, including video, to wireless devices present significant hurdles to both high quality content delivery as well as the preservation of digital rights management • Video data has unique characteristics: large size, large storage space, time requirements to present it in a continuous manner. • Current wireless devices have limited processor resources (limited CPU processing capacity, limited memory, etc.) and limited power.

4. Because MPEG encoding and decoding is a computationally intensive process, solutions is needed to add minimal complexity for encryption and decryption. • By taking advantage of the special properties of video coding, several techniques have been proposed to minimize the amount of overhead required to secure a video stream. However, they do not work well when used in wireless networks. • These methods do not preserve bit errors from the wireless transmission, resulting in streams that cannot survive the decryption process without significant error processing step.

5. Applications • Use of wireless devices for multimedia retrieval • Video email • Video-on-demand

6. Objectives of this project • To understand permutation-complementation based encryption algorithms that take advantage of the fact that compressed multimedia data is already random in byte distribution. • Several formal properties of such systems are presented • Application of these properties in securing video data is also described.

7. MPEG encoding and decoding • Compression procedure: • Transform the image into a suitable color space: the RGB space is usually transform into the luminance/chrominance color space (YCbCr) • Discrete Cosine Transform (DCT) • Group the pixel values for each component into 8x8 blocks, then map each 8x8 block into another 8x8 block through DCT. • Quantization • Zig-zag scan • Entropy coding (e.g. Run Length Encoding)

8. MPEG Motion Compensation • Exploits the fact that a frame is likely to be similar to its predecessor, so it can be nearly constructed from it. • I frame (intra coded) frame: coded without any reference to other frames • P (predictive coded) frame: coded using motion-compensated prediction from the last I or P frame, which happens to be closest. • B (bi-directionally predicted coded) frame: coded using motion-compensated prediction from the most recent P or I frame and the closest future P or I frame.

9. Video Security Algorithms • Historically, the straight forward applications of standard encryption algorithms (e.g. DES) to the entire video streams adds too much computational overhead. • New algorithms include: • Zig-zag permutation algorithm • Selective coding of I-frames • Secure MPEG encryption algorithm using DES, but encodes only half of the data in a stream using DES.

10. Forward Error Correction (FEC) • FEC is a common technique used to decrease losses when data is transmitted over noisy channels (e.g. wireless network). • This comes with additional overhead, which is linear in the number of errors it can correct. • We can design FEC code to correct k bits of errors. If the number of bit errors is more than k, the FEC code may not be able to correct the errors. • Bit errors left in data after decoding are left to the application.

11. Example to show intolerance of encrypted streams to bit errors • A text file is created and encrypted with PGP software. • A single bit error is introduced into the encrypted file. • For the decryption, a key phrase is entered by the user, which substitutes the key. • After the bit error is introduced, the file is not able to be decrypted. • PGP return an bad pass phrase error, did not decrypt the file and no text is returned.

12. Definition of Error Preserving Function • Let f be a function of the form f: (0, 1)n -> (0, 1)n , which means that f maps binary strings of length n to binary strings of length n. • A function is called error preserving if d(x,y)=d(f(x),f(y)) for all x, y. • In fact, a unction is error preserving if it preserves the shape of the hypercube. • In algebra, a transformation that preserve shape is called an isometry. • So, the number of error-preserving functions is equal to the number of of isometries of n dimensional hypercube.

13. Examples of Error Preserving Functions

14. Sample Isometries

15. Theoretical Results on Error Preserving Encryption Functions Lemma 1: The Number of error preserving functions (0, 1)n -> (0, 1)n is n! * 2n Lemma 2: All error-preserving functions can be generated using permutation and complementation. Permutation permutes the positions of bits and complementation complements a subset of the bits.

16. (Continue) Lemma 3: (P1C1)(P2C2) = (P3C3) Proof: Let f = (P1C1) and g = (P2C2) Since f and g are both error preserving, we have d( g(f(x)), g(f(y))) = d(f(x), f(y)) = d(x,y) Hence g.f is error preserving and it can be written as (P3C3) by Lemma 2.

17. (Continue) Lemma 4: (P1C1)-1(P2C2) = (P3C3) Lemma 5: (P1C1) (P2C2) -1 (P3C3) = (P4C4) Lemma 6: Number of permutations which map none of the bits to their original position is given by D, = n!(l - l/(1!) + l/(2!) - l/(3!) + … + (-l)n.1/(n!)). Such permutation is known as derangement . Lemma 7: Using the random Derangement Complementation (D-C) algorithm. The probability that k users will all have distinct (D-C) is , which is larger than

18. APPLICATIONS OF ERROR PRESERVINGENCRYPTION FUNCTIONS • Lemma 1 gives the expression for the number of error preserving functions. • Lemma 2 shows that all the error preserving functions can be enumerated using a permutation followed by complementation of a subset of bits. • Lemma 3 shows that for error preserving encryption double encryption does not help since there is a (P-C) that is equivalent to it.

19. (Continue) • Lemma 4 can be used for secure wireless video multicast in an ad-hoc network where users can be expelled from the group. • Lemma 5 shows that triple encryption is equivalent to a single encryption and therefore does not improve security. • Lemma 6 gives the expression for number of derangements. • Lemma 7 gives the probability that no collision occurs for k users. For n= 10 and k = 1000 second expression gives 0.99999994520261 which means that probability of collision is very low.

20. Conclusion • A theory is developed to build error preserving video encryption algorithms. • The scheme presented in this paper takes advantage of the fact that most multimedia applications are somewhat tolerable to bit errors. • All error preserving encryption algorithms can be implemented by permuting bits and complementing a subset of the bits, double and triple encryption do not improve security of the system. • The algorithm is very efficient (9-10 times faster than PGP).