# Research Reading
[TOC]

---
## I. Steganography
:::info Keywords
- **Network Steganography**
- **Information Hiding**
- **Secret Sharing**
:::
### 1. [Vice Over IP: The VoIP Steganography Threat](https://ieeexplore.ieee.org/abstract/document/5397787?casa_token=iQVVuPWz0wYAAAAA:lnuEk53qg2JNjuYD-0FCseRRtwspyJdPADAEtxEvdqHg2zCi3YODjVdOT0MBKz3NggV4dHCjJqY)
> J. Lubacz, W. Mazurczyk and K. Szczypiorski, "Vice over IP," in **IEEE Spectrum**, vol. 47, no. 2, pp. 42-47, February 2010, doi: 10.1109/MSPEC.2010.5397787.
- Summary
- [My note](https://hackmd.io/@Phoebe61G/ViceOverIP)

### 2. [Principles and overview of network steganography](https://ieeexplore.ieee.org/document/6815916?partnum=6815916)
> J. Lubacz, W. Mazurczyk and K. Szczypiorski, "Principles and overview of network steganography," in **IEEE Communications Magazine**, vol. 52, no. 5, pp. 225-229, May 2014, doi: 10.1109/MCOM.2014.6815916.
- Summary
- [My note]()

### 3. [Network Steganography Using Extension Headers in IPv6](http://ms15.voip.edu.tw/~phoebe/files/Papers_reading/Recently/Network%20Steganography%20Using%20Extension%20Headers%20in%20IPv6.pdf)
> Bedi, P., Dua, A. (2020). Network Steganography Using Extension Headers in IPv6. In: Badica, C., Liatsis, P., Kharb, L., Chahal, D. (eds) Information, Communication and Computing Technology. ICICCT 2020. Communications in Computer and Information Science, vol 1170. Springer, Singapore.
> https://doi.org/10.1007/978-981-15-9671-1_8
- Summary
- 利用 IPv6 四種 Extention Header 及 Transport Layer 的存在與否(0/1)去傳遞隱藏訊息。
- The bit-order
- Hop-by-Hop Extension Header
- Destination Extension Header
- Routing Extension Header
- Fragmentation Extension Header
- Transport Layer Header (TCP/UDP)
- Transfer 5 bits/per packet

### 4. [Covert Channel in IPv6](http://ms15.voip.edu.tw/~phoebe/files/Papers_reading/Recently/Covert%20Channels%20in%20IPv6.pdf)
> Lucena, N.B., Lewandowski, G., Chapin, S.J. (2006). Covert Channels in IPv6. In: Danezis, G., Martin, D. (eds) Privacy Enhancing Technologies. PET 2005. Lecture Notes in Computer Science, vol 3856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11767831_10
- Summary

---
## II. Network Coding

### 1. [Network Information Flow](https://ieeexplore.ieee.org/document/850663)
> R. Ahlswede, Ning Cai, S. . -Y. R. Li and R. W. Yeung, "Network information flow," in IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1204-1216, July 2000, doi: 10.1109/18.850663.
- Summary
- [My note](https://hackmd.io/@Phoebe61G/Syx50qR9K)

---
## III. Frequency Hopping

### 1. [Hedy Lamarr: Not just a pretty face](https://www.scientificamerican.com/article/hedy-lamarr-not-just-a-pr/)
- Summary
- Hedy Lamarr devised it.
- Transmitting radio signals along rapidly changing, or "hopping," frequencies.
> The radio-guided weapons won't being detected or jammed.
> The sequence of frequencies would be known by both the transmitter and receiver ahead of time.
- Frequency hopping spread spectrum is based on a musical concept. The frequencies are carried in waves through space like melodies.

:::info
**FHSS(Frequency Hopping Spread Spectrum)**
- Hopping sequence
- FHSS radios use a predefined hop pattern comprising series of small frequencies in know as Frequency hopping sequence.
- GFSK (Gaussian frequency-shift keying)
- FHSS use GFSK to encode the data.
- [Wikipedia - FSK](https://en.wikipedia.org/wiki/Frequency-shift_keying)
:::

### 2. [Designing and Evaluation of Performance of a Spread Spectrum Technique for Audio Steganography](http://ijsetr.com/uploads/435162IJSETR2102-816.pdf)
> Malik, H. and Sandeep Singh Kang. “Designing and Evaluation of Performance of a Spread Spectrum Technique for Audio Steganography.” (2013).
- Summary
- Two commonly spread spectrum techniques are used **direct sequence spread spectrum (DSSS)** and **frequency hopped spread spectrum (FHSS)**.
- In DSSS, the secret message is spread out by a constant called the chip rate and then modulated with a pseudorandom signal. It is then interleaved with the cover signal.
- In FHSS, the audio file's frequency spectrum is altered so that it hops rapidly between frequencies.
> Implementation of steganography in audio data using Direct Sequence Spread Spectrum method has been presented in this paper.
- The message is transmitted through noiselike wave. This method can be applied to embed messages in audio data.
- A key is needed to embed messages into noise, this key is used to generate **pseudo-random key sequence**.
- **Watermarking**: original signal --> embedded signal (watermarked data)
- Embedding block
- Extraction block

### 3. [Frequency Hopping Method for Audio Watermarking](https://journal.telfor.rs/Published/Vol4No2/Vol4No2_A15.pdf)
> [IEEE - Audio watermarking using frequency hopping method](https://ieeexplore.ieee.org/document/6143863)
> A. Anastasijević, D. Čoja and J. Ćertić, "Audio watermarking using frequency hopping method," 2011 19thTelecommunications Forum (TELFOR) Proceedings of Papers, 2011, pp. 1586-1589, doi: 10.1109/TELFOR.2011.6143863.
- Summary
- The techniques result in perceptible or imperceptible watermarking, the level of content quality degradation.
> Perceptible audio watermarking in the spectral domain for adding copyright owner’s authentication to media is the main focus of this paper.
- Adding pseudo-noise (PN) into media has become a fairly common procedure in audio watermarking in the near past with the possibilities for adding PN in:
- time domain
- DCT (Discrete Cosine Transform) domain
- wavelet domain
- FFT (Fast Fourier Transform) coefficients
- It has to be pseudo-random noise so that the process of watermarking can be reversible.
- The positions (frequencies) for watermark embedding are chosen according to a pseudo-random sequence (the watermark key).
- 

### 4. [Spreadspectrum audio watermarking using frequency hopping and attack characterization](https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.126.3531&rep=rep1&type=pdf)
> Nedeljko Cvejic and Tapio Seppänen. 2004. Spread spectrum audio watermarking using frequency hopping and attack characterization. <i>Signal Process.</i> 84, 1 (January 2004), 207–213.
> ACM Digital Library: https://dl.acm.org/doi/10.1016/j.sigpro.2003.10.016
> DOI: https://doi.org/10.1016/j.sigpro.2003.10.016
- Summary

:::spoiler Related Reading
- [FHSS - Wikipedia](https://en.wikipedia.org/wiki/Frequency-hopping_spread_spectrum)
- [藍牙跳頻算法分析](https://www.itread01.com/content/1542207737.html)
- [Can I use frequency hopping spread spectrum technique for audio steganography?](https://dsp.stackexchange.com/questions/37746/can-i-use-frequency-hopping-spread-spectrum-technique-for-audio-steganography)
- [Blind Steganography using Direct Sequence/Frequency Hopping Spread Spectrum Technique](https://ieeexplore.ieee.org/document/1689229)
- [A Digital Audio Multi-Watermarking Algorithm Based on Improved Quantization](https://ieeexplore.ieee.org/document/5990187)
:::

---

## IV. Chi-square test
### What is Chi-square test?
- A statistical hypothesis test (統計假設)
- Bivariate table (雙變量表)
- 用途: 同時呈現出兩個不同變項間次數分配的情況
- 目的: 用來探索這兩個變項間是否有明顯的關係存在
- [Critical Values of the Chi-Square Distribution(table)](https://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm)
- Degrees of Freedom (df，自由度)
- Obtained Values of the Chi-Square Distribution
:::info
$χ^2(obtained)＝Σ(fo－fe)^2／fe$
:::

- 兩種常見測試用途
- **獨立性** (the test for **independence**)
- 每格中之次數（即一變項之某一類別與另一變項之某一類別間之交集的次數）是在random chance下發生的
- 這種虛無假設下所產生（或算出）之次數稱為「期待次數」(expected frequencies)或「理論次數」
- $df＝(r-1)(c-1)$
- **適合度** (the test of **goodness of fit**)
- 看一個變項之次數分配是否達到顯著水準(是否觀察到的次數分配和理論次數的差距很大)
- $df＝k-1$
- [Wikipedia - Goodness of fit](https://en.wikipedia.org/wiki/Goodness_of_fit)

- Results
- Null Hypothesis: 兩組分類之間沒有關係。
- Alternative Hypothesis: 兩組分類之間有一定關係。
:::info
If $χ^2(obtained)$ is close to $χ^2(critical)$, then it's **good fit**.
:::

#### Hands on code (Goodness of fit)
- Python [`scipy.stats.chisquare`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisquare.html)

scipy.stats.chisquare(f_obs, f_exp=None, ddof=0, axis=0)

> f_obs: Observed frequencies
> f_exp: Expected frequencies
> ddof: Delta degrees of freedom, $df=(k-1)-ddof$
> axis:
- Return values
- `chisq`: The chi-squared test statistic.
- `p-value`: The P-value is the probability of observing a sample statistic as extreme as the test statistic.
- Example

import numpy as np
from scipy import stats
chi2, p_value = stats.chisquare([31,19])
print(chi2)
print(p_value)

#### Online calculators
- [Social Science Statistics](https://www.socscistatistics.com/tests/chisquare2/default2.aspx)
- [Graph Pad](https://www.graphpad.com/quickcalcs/chisquared1/?Format=C)
- [Microsoft - CHISQ.TEST function](https://support.microsoft.com/en-us/office/chisq-test-function-2e8a7861-b14a-4985-aa93-fb88de3f260f)
- [Example](https://www.educba.com/chi-square-test-in-excel/)

#### Chi-square in Cryptography

:::spoiler Related Articles
- [The chi-square test for cryptography](https://crypto.stackexchange.com/questions/87600/the-chi-square-test-for-cryptography)
- [Using Chi Squared to Crack Codes](https://ibmathsresources.com/2014/06/15/using-chi-squared-to-crack-codes/)
- [Decrypt Caesar with Chi-squared Algorithm](https://python.algorithmexamples.com/web/ciphers/decrypt_caesar_with_chi_squared.html)
- [Chi-squared Statistic](http://practicalcryptography.com/cryptanalysis/text-characterisation/chi-squared-statistic/)
:::
#### Chi-square in Steganography

### 1. [An Evaluation of the Robustness Chi-Square Steganalysis Method on Wav Audio Files with Various Content](https://dergipark.org.tr/tr/download/article-file/517396)
> Durdu, Ali. (2020). An Evaluation of the Robustness Chi-Square Steganalysis Method on Wav Audio Files with Various Content. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 36. 178-192.
- Summary
- Evaluate the performance of the chi-square method for steganalysis purposes on audio files through three types of audio input files: music, human voice, animal sounds.
### 2. [Pairs of Values and the Chi-squared Attack](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.146.5017&rep=rep1&type=pdf)
> Stanley, Christy A., “Pairs of Values and the Chi-squared Attack.” ,2005.
- Summary
- Details about Chi-squared method(on images).