# Appendix G Β· Exercises and Self-Test (with Answer Keys) > [🌐 δΈ­ζ–‡η‰ˆ](https://yukinoshita-lin.github.io/nsf5-steganography/zh/content/appG.html) This appendix gathers the most important takeaways into a set of self-test questions, covering "steganography vs encryption / LSB & statistical fingerprints / matrix embedding / nsF5 & wet paper / hash keying / ML evaluation". Answer them yourself first, then compare with the key; each question notes the relevant chapter, so revisit that chapter if you get stuck. > **How to use |** Read the question, write or compute your answer first, then read the > explanation. The code snippets below all run in the project. ## G.1 Steganography vs Encryption (Ch. 3) **Q1** In one sentence, what do "encryption" and "steganography" protect respectively, and why is "encrypt first, then hide" recommended?
Answer - **Encryption** protects the *content*: without the key you cannot read the plaintext. - **Steganography** protects the *existence*: nobody can tell there is a secret. - Encrypt first, then hide: the ciphertext looks like random bits, so it is less likely to stand out statistically. The two are usually combined (see 3.1).
**Q2** True or false, and why: "LSB steganography exploits visual redundancy but breaks statistical redundancy."
Answer True. The eye cannot notice a 1-level gray difference (visual redundancy), so changing the LSB is invisible; but LSB replacement flattens the even/odd counts of adjacent gray pairs and destroys the spatial structure of the LSB plane (statistical redundancy). That is exactly the fingerprint the chi-square test and RS analysis catch (see 3.3, 3.4).
## G.2 LSB and Statistical Fingerprints (Ch. 3) **Q3** After LSB replacement, what happens to the chi-square **p-value**? Why? Does "high p" mean safe?
Answer - LSB replacement forces the even/odd counts of adjacent pairs (2i, 2i+1) toward balance, so the chi-square statistic drops and the **p-value rises**. - **Not necessarily safe**: a naturally noisy photo already has a near-random LSB and a high p. So the project adds a "content background randomness" correction (gray difference entropy) to judge how random the image is before treating a high p as embedding evidence (see the tip at the end of 3.3).
**Q4** In RS analysis, what does $G_n$ tend toward for a clean image vs an embedded one, and why?
Answer A clean natural image has structured LSBs; applying the negative mask turns many groups from "regular" to "singular", so $G_n=(R_n-S_n)/n$ is clearly positive (commonly 0.3~0.7 for clean smooth images). LSB randomization collapses that structure, positive/negative masks behave alike, and $G_n$ approaches 0 (see 3.4).
## G.3 Matrix Embedding (Ch. 4) **Q5** For p=3, how many bits can be hidden and what is the block length? Explain why flipping one column achieves the target syndrome.
Answer For p=3 the block length is $n=2^p-1=7$ and it hides $p=3$ bits. Compute the syndrome of the current LSB block $s=Hx$, XOR with the target message $m$ to get the difference $d=s\oplus m$. Each column of $H$ is a 3-bit binary number; if $d$ equals one column (or the XOR of a few columns), flipping that column's pixel makes $Hx'=m$. Usually only one pixel needs flipping (see 4.1, 4.2).
**Q6** Why does matrix embedding hide more and change fewer pixels than naive LSB?
Answer Naive LSB hides 1 bit per pixel and changes 1 pixel. Matrix embedding spreads p message bits over an $n=2^p-1$-pixel LSB block and only expects to flip about $1-2^{-p}$ pixels. So the "bits carried per change" (embedding efficiency) rises sharply with p (see the efficiency figure 4-2).
## G.4 nsF5 and Wet Paper (Ch. 5) **Q7** How are "wet/dry" points defined in nsF5? Why does marking wet points first avoid shrinkage?
Answer Let $xv=$ pixel $-128$. A **wet point** has $|xv|\le1$ (pixels 127/128/129) - decrementing it can hit an illegal value/zero; a **dry point** has $|xv|>1$ (see 5.1). Embedding only solves on dry points (wet paper coding), so it never "hits zero halfway", every block embeds successfully, no retry, and no extra zero coefficients - hence **no shrinkage** (see 5.2, 5.3).
**Q8** What is the mathematical essence of "wet paper coding cannot find a solution"?
Answer We must solve $Hy=d$ using only dry columns. The dimension of the space spanned by the dry columns equals the rank $r$ of the dry-column matrix; when $r ## G.5 Hash Keying (Ch. 6) **Q9** What does image hash keying solve, and what is its limitation?
Answer Embedding positions are derived from the password and permuted (`permute_index`, splitmix64 + Fisher-Yates), so: - It solves: the decoder does not need to record where each block is; it can re-derive positions from the password ("self-synchronization", see 6.2). - Limitation: crypto strength depends on the password; a weak/leaked password makes positions predictable. Hash keying gives *unpredictable positions*, not "invisibility" (see the reading notes of Ch. 6).
## G.6 Machine Learning Evaluation (Ch. 7-8) **Q10** Why must data be split by `photo_id` (GroupKFold) instead of a random KFold?
Answer Variants of the same photo are highly similar; a random split puts "siblings" on both sides of train/test, causing **data leakage** and inflated scores. GroupKFold keeps all variants of a photo in the same fold, so the OOF score is honest (see 7.6, 7.7).
**Q11** Under class imbalance, why is "accuracy" misleading? Which metrics should you look at?
Answer If there are far more stego than clean samples, a model that labels everything "stego" achieves high accuracy while false-positiving every clean image. Look at AUC (ranking ability, threshold-independent), precision/recall, and F1 instead (see 7.7.3, 8.5).
**Q12** What does AUC=0.7 roughly mean, and why must you still pick a threshold for deployment?
Answer AUC=0.7 means: draw one stego and one clean image at random, and the model ranks the stego higher about 70% of the time - usually right, but not great (weak densities are hard; see 7.7.1). AUC is threshold-independent, but deployment needs one threshold: higher -> conservative (fewer false positives, more misses), lower -> aggressive (more detection, more false positives); it is a trade-off between false positives and misses (see 7.7.2, 8.6).
## G.7 Capstone (Ch. 10) **Q13** Design a minimal honest experiment to show your new feature actually helps, and name the consistency rules you must keep.
Answer Use `make_dataset.py` to build clean/stego variants of the same photos -> extract features (baseline vs your new feature) -> compare AUC with the **same test-photo groups + 5-fold GroupKFold OOF** -> evaluate the held-out test set exactly once. Key rules: separate train/calibrate/test; split a calibration set out of the training pool to pick the threshold; evaluate the test set only once (otherwise it becomes "dirty"). See 8.8 and the honest-evaluation pipeline of Ch. 10 (Fig. 10-1).
> **Grade yourself |** If you can answer all 13 with examples, you can already explain this body of knowledge to > someone else. For any you missed, go back to that chapter and read it again with the "Think about it / Try it" > blocks. Once you pass all of them, return to the intro's Section 0.4 and hand yourself a "certificate of completion".