I'm trying to encrypt and decrypt a message bigger than the key size.
This is simply not possible using RSA. Most RSA crypto systems use a symmetric cypher (like AES) to encrypt the data with a cryptographically secure random key, and then encrypt that key using RSA.
WARNING The fact that you’re asking this question indicates that:
Your not a crypto expert, and
You’re designing your own crypto system
That’s a really bad combination. It’s very easy for inexperienced developers to create crypto systems that look right but contain vulnerabilities that are obvious to crypto experts (and hence to any attackers). For example, when combining RSA and AES as I’ve suggested above, you need to make sure you use authenticating encryption (either by using a fancy AES mode or by combining AES with a MAC) to avoid some gnarly exploits. I strongly recommend you either:
Implement a standard crypto system that’s generally considered secure (like CMS)
Or, if you must design a new crypto system from scratch, hire a crypto expert to review its security
On a personal note, while I dabble in crypto, and know some of these issues, I’m not a crypto expert and I would not attempt to design my own crypto system from scratch.
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