Cryptography on an's security blog

rotation

Mon, 04 May 2026 21:50:16 +0800

First, calculate the shift amount. Then for each alphabetical character in the ciphertext, subtract that shift amount with the current character, rotate back to z/Z if went overboard

cipher = "xqkwKBN{z0bib1wv_l3kzgxb3l_555957n3}"
diff = ord(cipher[0]) - ord('p')
plain = ""

for c in cipher:
 ch = ord(c) - diff
 
 if c.islower():
 if chr(ch).islower():
 plain += chr(ch)
 else:
 plain += chr(ch + 26)
 
 elif c.isupper():
 if chr(ch).isupper():
 plain += chr(ch)
 else:
 plain += chr(ch + 26)
 
 else:
 plain += c
 
print(plain)

Note that this Python implemention is not exactly the prettiest in the world. And I struggled quite a bit because I thought digits are also rotated (its not lol)

basic-mod2

Mon, 04 May 2026 21:36:16 +0800

Take each number mod 41 and find its modular inverse using Fermat’s little theorem, then map it to the following character set: 1-26 is the alphabet (uppercase), 27-36 are the decimal digits, else an underscore.

cipher = [432, 331, 192, 108, 180, 50, 231, 188, 105, 51, 364, 168, 344, 195, 297, 342, 292, 198, 448, 62, 236, 342, 63]
plain = ""

for n in cipher:
 n = n % 41
 n = pow(n, 41 - 2, 41)
 if 1 <= n <= 26:
 plain += chr(n - 1 + 65)
 elif 27 <= n <= 36:
 plain += chr(n - 27 + 48)
 else:
 plain += '_'
 
print(plain)

basic-mod1

Mon, 04 May 2026 21:25:16 +0800

Take each number mod 37 and map it to the following character set: 0-25 is the alphabet (uppercase), 26-35 are the decimal digits, and 36 is an underscore.

encoded = [350, 63, 353, 198, 114, 369, 346, 184, 202, 322, 94, 235, 114, 110, 185, 188, 225, 212, 366, 374, 261, 213]
plain = ""

for n in encoded:
 n = n % 37
 if 0 <= n <= 25:
 plain += chr(n + 65)
 elif 26 <= n <= 35:
 plain += chr(n - 26 + 48)
 else:
 plain += '_'
 
print(plain)

Cryptography

Mon, 04 May 2026 21:23:16 +0800

Modular Arithmetic

Mon, 04 May 2026 11:58:16 +0800

Modular Arithmetic

This module (no pun intended) introduces modular arithmetic, which is a critical mathematical edge for cryptography. Here are my important remarks:

Euclidean Algorithm

This is a very famous algorithm designed to calculate the GCD of two integers. I initially struggled trying to understand the intuition, but the following analogy helps:

You are a carpenter. You have two wooden planks of different lengths, say Plank A is 105 inches long, Plank B 24. Our goal is to find a “ruler” that measures perfectly both plank from end-to-end.

CryptoHack

Mon, 04 May 2026 07:23:16 +0700

Introduction to CryptoHack

Mon, 27 Apr 2026 07:23:16 +0700

Introduction to CryptoHack

Since this is an introduction, these are pretty straightforward stuffs. But there are a few notes to consider:

Base64

This allows us to represent binary data as an ASCII string using an alphabet of 64 characters. One character of a Base64 string encodes 6 binary digits (bits), and so 4 characters of Base64 encode three 8-bit bytes.

There is also padding introduced when the number of bits is not divisible by 6. Read more here: https://en.wikipedia.org/wiki/Base64#Examples