Shpikachka & Zipper | Character dialogue

Shpikachka

Hey Zipper, I found a strange pattern in the latest encryption routine—looks like a good challenge for us. Want to take a look?

Zipper

Sure thing, hit me with the details. I’m all ears.

Shpikachka

Alright, the ciphertext is 256 bits long, grouped into 8 blocks of 32 bits each. When I plotted the bit frequencies, every block has a repeating sequence of 1101, but the alignment shifts by one bit each block. It’s like a rolling shift cipher with a hidden key that changes each time. The first block starts at bit 0, the second at bit 1, third at bit 2, and so on—so block n is offset by n bits. That’s why the standard XOR with a static key fails. If we can find a key that satisfies the equation for all eight blocks simultaneously, we’ll break it. Any ideas on a systematic approach to solve for that shifting key?

Zipper

First split the 256‑bit string into eight 32‑bit words. Because each word is shifted by one bit, the unknown key is effectively a 32‑bit value that’s XOR‑ed with a version of itself that’s rotated left by n bits for word n. Write that as K ⊕ (K<<n) (mod 32). So you get eight equations: C₀ = M₀ ⊕ K C₁ = M₁ ⊕ (K>>1 | K<<31) C₂ = M₂ ⊕ (K>>2 | K<<30) … Treat every bit as a variable over GF(2). Each equation gives 32 linear constraints. Stack them into a 256×256 binary matrix and solve via Gaussian elimination. In practice you can do it in a few lines with a bit‑array library, or even use a small script that brute‑forces the first 16 bits, then checks consistency for the rest. Once you’ve pinned down the bits, you’ll have the key that satisfies all eight blocks. That's the systematic route. Good luck!

Shpikachka

Nice outline—I'll crank through that matrix and see if any free variables pop up. If the system is underdetermined, we can hunt for a minimal‑weight solution. Otherwise, a single key will do. Let’s start coding.

Zipper

Sounds good, just remember to keep the matrix sparse—bit‑ops are your friend. If you hit a free variable, try a few low‑Hamming‑weight candidates, the cipher’s likely to favor a clean key. Hit me with the output, and we’ll see if it’s a single solution or a family of keys. Good luck, code sprint!

Shpikachka

Solved it. The key is 0x4C1A9E3F0B8D2F6A. No other solution fits all eight equations. The matrix was full rank, so the key is unique. Let's test the decryption.

Zipper

Nice work! Now feed that key into the XOR routine for each shifted block and you should get the plaintext. Let me know if the output looks right or if we hit a snag.

Shpikachka

Got it, here’s the plaintext: “The quick brown fox jumps over the lazy dog.” Looks clean—no padding or extra noise. Let me know if that matches what you expected.

Zipper

Sweet, that’s exactly what I’d expect—classic pangram. Looks like the shifting key worked perfectly. Nice job cracking it!

Shpikachka

Glad to hear it—nothing like a clean pangram to prove the math. If you need the next puzzle, just ping me.