Using Transcendental Number to Encrypt BlackBerry Video

Jun Steed Huang

19920 Pacific Heights Boulevard, San Diego, CA 92121, USA

Suqian College, 399 South Huanghe Road, 223800, China

161 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada

October 18th, 2015

International Conference on Computer Science and Technology, October 17-18, 2015, WuhanInternational Conference on Computer Science and Technology, October 17-18, 2015, Wuhan

www.researchgate.net/profile/Jun_Huang38

Smart Car, S

mart Road, Smart H

ome

Keynote Speaking: 9:10-9:50

Number Matters.

Agenda

1. Introduction

2. Encryption Method

3. M2M Encryption Schemes

4. Simulations and Experiments

5. Conclusion and Future Work

ICCST, October 17-18, 2015, Wuhan

Number Matters.

1. Introduction

There are four different ways to explain M2M video streaming:

� Machine2Man (for road security applications),

� Man2Man (for fast home delivery services),

� Man2Machine (for mining and oil industries) and

� Machine2Machine (for environmental protections).

The IP through WiFi, WiMax, WiGig, LiFi, LTE or Terahertz-wave;

We focus on the end-to-end encryption aspect of the latest system.

1. Analog video monitoring system is the first generation.

2. Digital Video Recorder is the second generation.

3. The third generation is based on Internet Protocol (IP).

Number Matters.

911 After 2001 Effects

� In the law enforcement and homeland security, with third generatio

n solution, greater numbers of sensitive road sites can be

monitored in less bandwidth than can be covered with conventional

video techniques. In the event of a major occurrence, small low-

bandwidth drop-off cameras provide the command post with real

time video of the event scene, through the machine-to-man remote

settings.

� Knowing the exact situation is crucial for mining rescue authorities.

First responder mine worker can carry miniature video systems on-

site to provide data center server with all sensor readings for the co

mputer to summarize the CO density map, to allow decision-maker

s to call action plans. This is the man-to-machine quick sensor data

gathering system.

Number Matters.

Backup Cloud After That

� The hand held cameras send real-time video back to the courier

center over existing radio channels, can be used for potential users

range from online fast home delivery to just in time of rapid inventory

control and other emergency logistics situations. This is mainly for

man-to-man verification video communications.

� Flood-prone streams and rivers can be monitored for rising water lev

els with the machine-to-machine settings. The extreme portability, lo

w bandwidth and low power requirements of such live video system

supports rapid temporary deployment of video monitoring, for examp

le in late winter and early spring when ice jams can cause water flow

s to reach dangerous levels with little or no warning.

Number Matters.

BlackBerry Mobile is Going Everywhere

� The advanced digital wireless camera, overcomes the

disadvantages of the analogue one, and brings advantages of longer

distance reach, better penetration through obstacles, light weight,

easy set up, added encryption feature, flexible storage formats

(MPEG4/H265, MJPEG/JPEG or proprietary) and flexible

transportation formats (native or IP).

� The typical M2M network configuration for wireless camera is shown

in Fig. 1. The first block is the video capture end, transmitter (Tx). It

transmits encrypted video to the receiver, and at the same time it

can also receive commands from the laptop, tablet or BlackBerry

through the cloud. The transmitter (on robot) can also transmit the

sensor data along with the scrambled video signal to mac book etc.

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Figure 1. Our Sample M2M Network Configuration

Tx Rx BB Server

Black

Berry

CDMA/

GSM

M2M

Scra

mblin

g

400 M H z

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Each Blocks

� The receiver (Rx), relays bi-directional signal between transmitter and the

laptop. The interface between receiver and the laptop is USB interface. The

link between transmitter is a licensed 400MHz FHSS (Frequency Hopping

Spread Spectrum) radio. The third block can be a tablet, laptop or mac book.

� The transmitter transmits the video signal from a remote site to the control

center (software installed on any machine). Control Center (CC) transmits

commands back to the remote camera site, such as turn on hazard flashing

light etc.

� The next two blocks are CDMA (or GSM) network and handheld devices such

as BlackBerry or WinCE device. When BlackBerry is used, push server can be

set up to introduce more inter-activities between a handheld and a camera.

When Android phone is used, P2P protocol is preferred, this will simplify the

server construction. 　

Number Matters.

BlackBerry Push

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2. Encryption Method - Mathematics Background

� When the network cloud is a private system, the existing

encryption might be sufficient; however when the

network cloud includes public network, a better

encryption based on whitening becomes necessary.

� Maintaining several passwords across a number of wired

and wireless networks can be cumbersome. An end-to-

end pass phrase mixed with time stamp based

encryption in this case is highly desirable for most end

users.

Number Matters.

Fibonacci Polynomial Mixing

Fibonacci was born 1170, a wealthy Italian merchant

A Fibonacci polynomial is defined as the

next number in the sequence being made

from the weighted summation of previous

two numbers,

Fn+1(x,y)=xFn(x,y)+ yFn-1(x,y)

If the very first two weights x=y=1, then

it is called original Fibonacci sequence,

otherwise, called Extended Fibonacci

sequence.

Number Matters.

Fibonacci Sequence Properties

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Our Fibonacci Prime Theorem

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Proof of the Theorem

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Shang Gao (Pythagoras) Theorem

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Thue Theorem for Transcendental

Axel Thue (1863–1922), Norwegian, diophantine approximation, and combinatorics.

Diophantus (246—330), Greek, mathematician.

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Proof of Our Effective Lemma 1

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Proof of Our Effective Lemma 2

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Potential Transcendental Number Seeds

a transcendental number is a real or complex number that is not

algebraic—that is, it is not a root of a non-zero polynomial

equation with rational coefficients.p^(p^0.5)

Number Matters.

3. M2M Encryption Schemes

� There are two types of encryption, symmetrical or asymmetrical.

� An asymmetric encryption has keys come in a pairs. One is for encryption, the other

for decryption.

� The symmetrical method uses the same key to encrypt and to decrypt the message.

� Since the same key is used, it is important to safe guard that key. The

recommended method for exchanging the key is through a secured

communication system,

� where asymmetric encryption or quantum encryption shall be used.

� In this paper we focus on generating the good symmetrical key.

� Where the key matches with the scrambling Motion JPEG or swapping MPEG, in

the sense that the spectrum of the key is white enough, once applied to the

image frame, it will alter the spectrum of the frame, and make it also white.

Number Matters.

Why not AES

� For a small number of cameras or a single camera case, the key

generation is not that complicated, however for M2M network, the

number of cameras can be large, as such we use administrator

pass phrase with the time stamp that contains the camera

identification or GPS location to generate the key, through the use

of the Extended Fibonacci sequence with transcendental number.

� There are two main encryption algorithms on the market. They are

DES (Data Encryption Standard) and AES (Advanced Encryption

Standard). We are not using anyone of them due to the

computation burden. The method we used is SES (Swapping

Encryption System), it is a convolution based scrambling algorithm,

on top of the swapping based algorithm, if necessary.

Number Matters.

National Institute of Standards 2001

1. KeyExpansions — round keys are derived from the

cipher key using Rijndael's key schedule, AES requires

a separate 128-bit round key block for each round.

2. InitialRound 1. AddRoundKey—each byte of the state is combined

with a block of the round key using bitwise xor.

3. Rounds 1. SubBytes — a non-linear substitution step where each

byte is replaced with another according to a lookup table.

4. ShiftRows — a transposition step where the last three rows of the

state are shifted cyclically a certain number of steps.

5. MixColumns — a mixing operation which operates on the columns

of the state, combining the four bytes in each column.

6. AddRoundKey, SubBytes, ShiftRows, AddRoundKey.

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What Special for Video – Narrower Space

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Need Productive rather than Additive

� MJPEG based video compression has compressed the information so

hard that the resulted code word has a very strong pattern (small vector

space) that is vulnerable to attack. Either DES or AES shuffles the data

too much rounds, which may make the pattern more obvious, while

consume a lot of energy.

� This is fine for uncompressed or lightly compressed data, but not good

for heavily compressed data like MJPEG or MPEG. The problem is very

much like when you zip a zipped file, the file size will become even

larger. For such data, we just need a good white key to do few rounds

scrambling or swapping, to balance out the spectrum, increase the

vector space.

Number Matters.

Our SES vs their AES

Key 1 2 3 4

Text a b c d

Convolution

d1+c2+

b3+a4

d2+c3+

b4+a1

d3+c4+

b1+a2

d4+c1+

b2+a3

SES b a d c

AES c3 d4 a1 b2

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Extend Pass word to Pass phrase

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Goldbach and Chandra partitions

1690-1764

1923-1983

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Goldbach Circle Concentration

Subhash Kak

Number Matters.

Camera with GPS Time and Location

The GPS uses a constellation of 24 satellites that orbit the earth

at about 11,000 nautical miles (1.852km), once every 12 hours.

Each satellite has a very accurate clock, 0.000000003 seconds.

Number Matters.

Video Time Stamps

MPEG has two timestamps that are inserted into the packet header,

the DTS or decoding timestamp, and

the PTS, or presentation timestamp.

The decoder will read the packets and use the DTS to know when to

decode the frame.

The PTS will be used to know when to display the frame.

Gary Joseph Sullivan

Number Matters.

Map with Integer Complexity – F26

Professor Emeritus, at the University of Calgary.

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Our definitions of IUD and ILD

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Map the GPS Identity with IC-ID

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Detail Algorithm

� Here is the pseudo code of the key generation algorithm.

� 1.Initialize the code

� 2.Get frame size and image size

� 3.Determine the encryption key size: root(frameSize/16)/(width mod (height))

� 4.Find the largest Fibonacci prime that is within root(frameSize) iterations as seed Key(1)

� 5.Convert a transcendental number to vector format, as seed Key(2), and compute the spectrum

� 6.Obtain the user pass word, extend to pass phrase with Goldbach circle numbers

� 7.Obtain the video time stamp and GPS, convert with integer complexities

� 8.Mix them with Extended Fibonacci polynomial formula:

Key(n) = Key(n-1)*passPhrase + Key(n-2)*timeStamp

� 9.Compute the spectrum and its standard deviation (std)

� 10.If std is small enough to white out the frame, stop, otherwise go back to step 8.

Number Matters.

4.Simulations and Experiments

� We have done a number of trials with customers across the world.

� The trial band runs from 300MHz all the way to 2.4GHz.

� The distance range from 200 meters underground to 1000 meters for an

open pit area.

� Three typical MJPEG files are captured from the field and simulated in

Matlab. They are

– 1. VGA Tx-Rx Color frame, 640x480 pixels size, 62515 bytes frame size;

– 2. HD Rabbit frame, 1280x960 pixels size, 117745 bytes frame size;

– 3. VGA Night vision frame, 640x480 pixels size, 16806 bytes frame size. Following figures show the actual pictures and the spectrum for each of them before and after the convolution with the key.

Number Matters.

Figure 2: VGA Frame Head and its Spectrum with the Key

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Figure 3: HD Frame Tail and its Spectrum with the Key

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Figure 4: Night-Vision Middle Frame and its Spectrum with the Key

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5. Conclusion

� The main information we offered here is that the transcendental

number in general will provide very white base spectrum, that is

needed to cover up the video information. The best number we

have found so far is e^pi.

� As such, we mixed the two numbers to generate the Fibonacci like

sequence, using pass phrase as the current weight, and use the

time stamp as the weight. With this extended way, we inherit the

white spectrum, use it to scramble the MJPEG.

ICCST, October 17-18, 2015, Wuhan

Number Matters.

and future work

� For MPEG, we get back to the original story: the extended rabbit

family now starts from more than two rabbits, and when they grow

their family numbers along the Fibonacci like way, there is a chance

that the twin babies are expected, also there is a chance that the

bobcat may eat some of their babies very unfortunately!

� The example code is available from Matlab file exchange server:

http://www.mathworks.com/matlabcentral/profile/authors/6205312-steed-huang

ICCST, October 17-18, 2015, Wuhan

Number Matters.

Acknowledgment

� This research was financially supported by

� GenieView subsidiaries and partners.

� Thanks go to Prof. Yuhui Shi, Qing Zou,

� Oliver Yang, Qi Chen, Helen Liu, Botao Zhu,

� Hongwei Shi, Mi Zhou, Guangqian Lu, Moran Huang for discussions.

ICCST, October 17-18, 2015, Wuhan