Stuck on a cryptanalytical research project

This is not a technical question, but rather it seeks advice on what to do if cryptanalytical research goes wrong.

I've discovered a new attack that works great in theory, but in practice, it fails.

I don't know why. Haven't figured it out yet. Tried really hard. I work on this thing alone. Not sure If I could do this alone right now.

All the arithmetic of the attack works great with normal numbers, but in terms of cryptographical math, it doesn't work. I thought that If the attack works in terms of normal arithmetic properties / operations, then it should work in cryptographical math as well. It was false.

Anyway, as I'm stuck I have a few options to move forward:

1. Publish the question about it on a public forum.

But I am scared of revealing any details about the project itself to the public, as it'll gain public attention.

2. Publish a research paper on it, citing the failure.

3. Reach out some cryptography experts, with an offer to collaborate.

I know a few people who might help with the project, but the connection wise - they are total strangers to me. Not sure If I could trust them.

As of now, I don't have any friends / trusted people, who are able to help with the project.

4. Contact the National Security Agency.

5. Your suggestion?

I am open to any suggestion and ideas.

I am open to collaboration, but at the same time, don't want to be left out of the action. I wanna be in the game, participating in the full capacity.

The fact that your attack only works when you're using "normal math" and not "cryptographical math" (by which I assume you probably mean modular arithmetic, or perhaps arithmetic in a finite field or on an elliptic curve) probably means that it's not actually an effective attack. This also means that it's almost certainly safe to discuss publicly.

In particular, there are several arithmetic operations that are easy when using normal integers or real numbers, but (believed to be) hard on various mathematical systems used in cryptography. For example:

• Calculating the square root of a real number is easy. Calculating the discrete square root of an arbitrary number $x$ modulo the product of two primes $p$ and $q$ (i.e. a number $y$ such that $y^2 \equiv x \mod pq$) is as hard as factoring the modulus, which is believed to be hard as long as the primes are sufficiently large.

• Calculating $n$-th roots of real numbers for $n > 2$ is also easy. Calculating the discrete $n$-th root modulo the product of two primes is the RSA problem, which is also believed to be hard as long as the primes are sufficiently large.

• Calculating the logarithm of a real number is easy. Calculating the discrete logarithm of a number modulo a large safe prime is believed to be hard.

Also, to be honest, it's very unlikely that you've just happened to stumble across a cryptanalytic breakthrough as an amateur. Not only is cryptanalysis hard, but there are a lot of very talented and determined people doing it already, so all the low hanging fruit have already been picked. In particular, if there was a simple way to break some popular modern cryptosystem waiting to be discovered, someone would almost certainly have discovered it already.

That's not to say that you should give up on it, of course. Even if your attack doesn't work, figuring out why it doesn't work and how you might be able to improve it will be a great learning exercise. (It's also what even people who've made cryptanalysis their whole career spend most of their time doing, because the fact is that most attacks just don't work. You have to go through a lot of unsuccessful attempts just to — perhaps — eventually come up with one that does.)

What I'd suggest you do is first check out the Wikipedia articles I linked above. Then, if you're still not sure why your attack doesn't work with "crypto math", post a concise description of it (or, better yet, of the specific part that fails) e.g. here on Stack Exchange and ask why it doesn't work.

Most likely the reason will be something like the examples I mentioned above, i.e. some operation you're using is a lot harder using e.g. modular arithmetic than it would be in normal arithmetic. But the specific details may be illuminating.

There is already a good answer. In addition, if you think actual cryptosystems used today are at risk but you believe "clock arithmetic" works makes me think actual (public key) cryptosystems are not threatened by your attack.

This is written without knowledge of your mathematical background.

Beyond the question of the effect of using very large parameters in actual cryptosystems, whence attacks become impractical to impossible also consider the following.

For example textbook RSA or plain old RSA where a plaintext (say symmetric key) is input directly into RSA via modular arithmetic is not what's implemented. There is a padding scheme to obtain better security. See this question.

Of course if your break is a fast factoring algorithm then all bets are off. No padding scheme will survive such a fundamental breakthrough.