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

Presentation outline

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

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.

• 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.

Applications

• Use of wireless devices for multimedia retrieval

• Video email

• Video-on-demand

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.

MPEG encoding and decoding• Compression procedure:

1. Transform the image into a suitable color space: the RGB space is usually transform into the luminance/chrominance color space (YCbCr)

2. Discrete Cosine Transform (DCT)

3. Group the pixel values for each component into 8x8 blocks, then map each 8x8 block into another 8x8 block through DCT.

4. Quantization

5. Zig-zag scan

6. Entropy coding (e.g. Run Length Encoding)

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.

1. I frame (intra coded) frame: coded without any reference to other frames

2. P (predictive coded) frame: coded using motion-compensated prediction from the last I or P frame, which happens to be closest.

3. 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.

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.

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.

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.

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.

Examples of Error Preserving Functions

Sample Isometries

Theoretical Results on Error Preserving Encryption Functions

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.

Lemma 1: The Number of error preserving functions (0, 1)n -> (0, 1)n is n! * 2n

(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.

(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

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.

(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.

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).