Encryption and decryption using multiple different keys

Question

I want to encrypt files, wich can be decrypted and encrypted by multiple different keys. Is there any algorithm which can accomplish this?

Example (Each user has a different key):

• User 1 encrypts a file with his key
• User 2 decrypts the file, adds information and encrypts it with his key
• User 3 decrypts the file with his key

Answer 1

It seems that the similar problem was discussed here. The general approach was to encrypt the file with a random key and then encrypt copies of this key with users' keys.

However, if you'd like really different keys, check @ddddavidee's answer.