RSA signature attack check on lowest 16 bytes - Implementation

Question

I am referring to solution given in this question

I need help to implement Poncho hint in this comment:

As the first question i have an RSA signature of 1024 bit applied on an hash (MD5) of the message.

I am trying to get a valid result coding it in Java but i don't get any result from my iterations.

Can someone help me to find out why i don't get results as mentioned by @Poncho?

Example of hash: 0xCC844F9AF903BCB3CB0A7F0433AF70D3 Decimal representation: 271849508914011436342484527734062018771

Thanks a lot.

Answer 1

if(checkValue.compareTo(resultOfModulus) == 0)

Here's your problem; you're checking if $y^3 = (md5BigInteger \bmod 2^i)$; that's wrong (as $md5BigInteger \bmod 2^i$ won't typically be a cube).

Instead, what you want is to check if $y^3 \equiv md5BigInteger \pmod{2^i}$; or, in other words (thinking less like a mathematician, and more like a programmer) if $(y^3 \bmod 2^i) = (md5BigInteger \bmod 2^i)$

Also, don't forget to check if $md5BigInteger$ is odd (or more generally, $8^k w$ for integer $k$ and odd $w$); if it's not of that form, no such simple cube will exist.