Can you encrypt your plugin files? Yes, ("yes" meaning that it is "possible" - not "permissible")
Should you? No.
Let's start with the obvious. WordPress is licensed under GPL - GNU General Public License.
What does that mean? It means that WordPress and any derivative work needs to be "open source." In other words, the source needs to be "open," readable, and available. The interpretation as far as WordPress is concerned (linked above) is that any "derivative work" must also be GPL or GPL compatible (as not all open source licensing is compatible with GPL). A plugin is considered "a derivative work" because it relies on WordPress to operate (it cannot run by itself), and therefore must be GPL compatible. Encrypting your code is NOT GPL compatible.
Since there was some commentary on legality, it should be noted that encrypting your plugin files is not "illegal" in the sense that a SWAT team will kick in your door with a warrant for your arrest. But it could result in a lawsuit (although that's unlikely). The more likely outcome is that few users buy your plugin, since it would not be open source (I'm presuming you're looking to sell it - otherwise, why would you encrypt it in the first place).
For plugins and themes in WordPress, this debate has been something that has gone on back-and-forth for as long as I've been involved with WP (2004); and it will likely continue. But the bottom line is this - if you encrypt or otherwise obfuscate your code, you go against everything that GPL and open source software stands for. The entire reason WordPress is as successful as it is is because it is open source.
If you obfuscate your code, it will certainly be rejected by wordpress.org for inclusion in the repository. It would also be rejected by any reputable aggregator (such as CodeCanyon). Your distribution options would mostly be limited to managing it through your own site.
So to summarize, can you encrypt it? Yes, insofar as it is possible. But that doesn't mean you should. (Also, it doesn't mean you can from a strictly legal sense.) If you find that you need to encrypt, then you shouldn't be developing something for an open source platform.
Then, the last thing you mentioned also needs to be addressed:
We dont want to spend money to buy any tool for the encryption. Hence
could you please provide me any suggestions on how to encrypt a plugin
at free of cost?
Presumably, you're looking at this as a commercial venture - selling a plugin to a base of users. Otherwise, why would it be necessary to obfuscate the code?
If that's the case, why would you chintz on investing in that process? You want to commercialize your plugin, but you don't want to spend any money on it? Quite frankly, that's absurd. It's like a bright neon sign flashing overhead that says, "Welcome to Amateur Night." I don't mean that to insult you, but rather to point out how it makes things look from a business perspective.
If you're going to venture out commercially, make appropriate investments in the tools you need (although that is not suggesting to invest in encrypting your code).
Perhaps what you really need to look at is your business model and what needs to change in order to grow and compete in a 21st Century economy. I recommend that you read "Free: The Future of a Radical Price" by Chris Anderson to wrap your head around how you monetize something that is "free" (regardless of whether that item is "free as in speech" or "free as in beer," which is the essence of the GPL).
