# Tyco

One RSA key, two messages a known distance apart. The lab had the plaintext in under three minutes.

HI Cyber Con CTF 2026. Cryptography. Published 2 November 2026. Challenge by Tsumiiiiiiii.

## The brief

> 🫠🤖

- tyco.zip, 690 bytes

## In short

The flag was encrypted twice under one RSA key, once as r and once as r + d, and d was printed with the results. Both ciphertexts give polynomials with the same root, and their greatest common divisor hands that root back without factoring N.

## One flag, encrypted twice

The description was two emoji. The script encrypts the flag r under a 511 bit RSA key with e = 56,263, then encrypts r + d under the same key and prints d next to both results.

## The distance between them was public

Textbook RSA has no padding, so the two plaintexts keep their exact relation. With d known, the second message is the first one shifted by a known amount, and that is all the Franklin-Reiter attack needs.

## Two polynomials, one shared root

Modulo N, x^e minus t1 and (x + d)^e minus t2 are both zero at x = r. So both contain the factor x minus r, and a common factor survives in their greatest common divisor.

## From degree 56,263 down to 1

Both polynomials have degree 56,263. The lab took their gcd modulo N without ever factoring N, and in about 17 seconds it came back linear, Ax + B.

## The root is the flag

The root is r = minus B over A modulo N, a 223 bit number. It encrypts back to t1 exactly, r + d encrypts back to t2, and its 28 bytes spell the flag.

## The insight

RSA without padding keeps the relation between two messages. Encrypt r and r + d under one key, print d, and a polynomial gcd hands back r.

## The flag

hiCTF{your_ai_slop_bores_me}

## More from this benchmark

[HI Cyber Con CTF 2026](https://p4ndora.ai/benchmarks/hi-cyber-con-2026)
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