1. Crypto for CTFs

2. In This Talk (I promise there won’t be any math)
Security Services
Classical (Substitution) Ciphers
Why those suck
Bitwise encodings
Random Number Generators
Entropy
Frequency Analysis

3. XKCD, “Security” available at https://xkcd
XKCD, “Security” available at under Creative Commons Attribution-NonCommercial 2.5 License

4. Security Keywords Give you hints as to what the question is asking
‘Plaintext’
‘Ciphertext’
‘Encrypt’
‘Decrypt’
‘Key’
‘Sign’

5. Security Services Confidentiality - ensure that data is hidden
Authentication - ensure that data comes from who it says it does
Integrity - ensure that data isn’t altered in transit
Non-repudiation - ensure that when Alice sends Bob data, Alice can’t take back later that she sent it

6. Encodings
Base64
Base32
Hex encoding - H(0xdeadbeef) => “deadbeef”

7. Substitution (classical) ciphers
Caesar Cipher - shift each letter by a constant amount
Atbash Cipher - Convert each letter to the l-26 % 26 letter
Vignere Cipher - shift each letter by a corresponding letter in the codeword
Oftentimes, non-alpha characters stay the same

8. How to solve: Atbash No key: A always maps to Z, etc
Ciphertext: R nfhg hzb, Nrgxs rh ollprmt tivzg glwzb!

9. How to solve: Caesar Key fact: There are only 26 possible shifts
Ciphertext: Hdoxc dn vi zsxzggzio ozvxczm
Try each possible key, see if ciphertext makes sense:
Key 1: Iepyd eo wj atyahhajp pawydan
Key 2: Jfqze fp xk buzbiibkq qbxzebo ….

10. How to solve: Vignere Short ciphertexts: brute force
Long ciphertexts: frequency analysis
Certain characters in the english alphabet are more common than others
2-character sequences…
3-character sequences…

11. Why substitution ciphers are bad
Kerckhoff's Principle - A cryptosystem should be secure even if an attacker knows everything about the system (other than a secret key)
In contrast to “Security through obscurity” (All three previous examples, Windows). You should assume attackers will gain access to system details
Modern ciphers combine Substitution and Permutation - if you change one number or input it completely, seemingly randomly changes occur throughout the new ciphertext

12. Why substitution ciphers are bad
Modern ciphers combine Substitution and Permutation - if you change one number or input it completely, seemingly randomly changes occur throughout the new ciphertext
Modern concept of “perfect secrecy” - none of these are perfectly secret - or even close

13. Perfect Secrecy Ciphertext conveys no information about the plaintext
Key length > plaintext length
Ex. vignere cipher with keyword longer than message (eh…)
Key: thisisakey, Message: hello, ciphertext: altdw
One-Time Pads

14. Bitwise Encoding
Messages are often represented as binary strings (ASCII, etc)
XOR encoding ⊕ A B
Result 1

15. Bitwise encoding continued (Need to know for interviews!)
Very nice mathematical properties!
A ⊕ 0 = A A ⊕ A = 0, A ⊕ B = R => A ⊕ R = B
Example: A=1100 B=1010
A ⊕ 0000 = A, A ⊕ A = 0000, A ⊕ B = 0110, A ⊕ 0110 = 1010
Critical for symmetric cryptography
Good for CTFs

16. One-Time Pad Random sequence of 1s and 0s Bitwise XOR encrypt
Ciphertext:
No way to get what the plaintext is without info on the key
Don’t use twice! (hence one-time)
Crib-drag: xor ciphertext with different offsets ciphertexts crib-drag.html

17. Random Number Generators
Goal: Create a stream of random numbers to create a one-time pad without needing to reuse any bits
Problem: How to implement this?
Problem: How to share this information secretly?

18. How to implement?

19. How to share this info?

20. Pseudo Random Number Generators (PRNG)
Idea: Create a “sharable” RNG
The only parameter you need to share for reproducibility is a key and/or seed
Goal: It should be practically impossible for attacker to guess the inner state or any future states from a subsequence of output
Goal: It should be practically impossible for an attacker to guess previous subsequence given an inner state
Subgoal: There should be about as many 0 bits as 1 bits

21. Pseudo Random Number Generators (PRNG)
Problem: PRNGs must have a finite state, introducing period of generated numbers
Problem: Mathematic difficulty creating a proper PRNG

22. PRNG Examples Linear Congruential Generator Mersenne Twister
Blum Blum Shub

23. Example: Blum Blum Shub
Generate two large primes p and q and a seed s (= x-1)
Calculate xn+1 = x2n mod M

24. Modular Arithmetic
science/cryptography/modarithmetic/a/what-is-modular-arithmetic

25. Entropy Entropy is a measure of the randomness of data
Many different ways to measure
Can you think of any?

26. Entropy
Let’s look at a random byte: “ ”

27. Look Closer:

28. Entropy
This byte may not seem random, but it has an equal probability of occuring in a truly random sequence of bytes as any other
This is why it is important to measure entropy over large sample sizes

29. Frequency Analysis
Fact: Each letter in the english language has a certain frequency of use
A simple computation will give us the frequencies - for each letter a through z, divide the total number of times it has been spoken or written and divide by the number of all letters ever spoken or written
In practice we use a representative sample to compute these frequencies
2004/cryptography/subs/frequencies.html
Why is this useful?

30. Frequency Analysis
Substitution Ciphers - Frequency of original letters unchanged, but transferred to new letters
I.e. If ‘x’ is the most frequent letter in the ciphertext, it is reasonable to assume this correlates with the plaintext letter ‘e’
Idea can be extended to Single-Byte XOR
Letter Bigram and Trigram frequencies can be more useful than single- letter frequencies
Idea can be extended to Multi-Byte XOR
HW will walk you through a FA problem