Superencryption
Superencryption refers to a situation where an encrypted message is then encrypted again using the same encryption system or a different system. This is also called cascading encryption. Superciphers built this way are also called cascade ciphers.
Independent keys If you choose any couple of ciphers, and if you use the same key for both ciphers, the second cipher could undo (a part of) the work of the first cipher. To prevent that risk, you can use keys that are statistically independents for each layer (e.g. independent RNGs).
References A "way to combine multiple block algorithms" so that "a cryptanalyst must break both algorithms" in §15.8 of Applied Cryptography, Second Edition: Protocols, Algorithms, and Source Code in C by Bruce Schneier. Wiley Computer Publishing, John Wiley & Sons, Inc. S. Even and O. Goldreich, On the power of cascade ciphers, ACM Transactions on Computer Systems, vol. 3, pp. 108–116, 1985. M. Maurer and J. L. Massey, Cascade ciphers: The importance of being first, Journal of Cryptology, vol. 6, no. 1, pp. 55–61, 1993.
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