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I need an encryption algorithm that works fast on large files and doesn't increase the file...

I need an encryption algorithm that works fast on large files and doesn't increase the file size. It should use a key to encrypt/decrypt data. The files will be sent using REST and over HTTPS, but a good encryption/decryption method with a key is mandatory (to be used in a website).

The files will be saved on a 3rd party servers, and although the files are sent through HTTPS, they must be stored encrypted on the remote servers and decrypted when retrieved. The key will not be distributed. The key will be stored on my trusted server, as it is also the receiver! I want to encrypt the file, put it on the 3rd party server, then when I need it I can retrieve it and decrypt it.

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