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### Why is double encryption that's equivalent to single encryption no better than single encryption?

This is simply saying that if a cryptosystem has a functional composition that is $$h_{k}(x) = f_{k_1}(g_{k_2}(x))$$ then you can find a key for single encryption that works as the double encryption....
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Accepted

If you combine two affine ciphers, you obtain one affine cipher. Say the first cipher is $e_1(x) = a_1x+b_1$ and the second is $e_2(x) = a_2x+b_2$. Then $e_1(e_2(x)) = a_1(a_2x+b_2)+b_1 = (a_1a_2)x+(... • 7,914 13 votes Accepted ### Can double-encrypting be easier to break then either algorithm on its own? Can double-encrypting (with either the same or separate algorithms) weaken security? If you do not assume that the algorithms and keys are independent, then it certainly can. The example of ROT13 ... • 31.3k 12 votes Accepted ### Combining several symmetric ciphers using XOR The usual method to do this is to turn the block cipher into a stream cipher. In that way the ciphertext is generated by XOR'ing the plaintext with a generated key stream. This key stream in turn is ... • 85.9k 9 votes ### Can double-encrypting be easier to break then either algorithm on its own? The answers and comments here are good, but I think that it's worth tidying it all up a bit. The question is broad, and this is exactly expressed in the answers. There are multiple questions here. ... 7 votes ### Is a 4DES or 5DES system possible? There is a very interesting paper that relates to this exact question (but you wouldn't guess it from the title). The paper is titled Efficient Dissection of Composite Problems, with Applications to ... 7 votes Accepted ### Encryption-Decryption-Encryption EEE and EDE are effectively the same in terms of security. EDE is used because it is "backwards compatible:" by setting all three keys to be the same, it becomes equivalent to just single encryption (... • 5,662 6 votes ### Why are we not using multiple ciphers per message? I don't know about computing things in parallel, so I will ignore that part of the question. First, please note that the encryption algorithm is rarely the the weak point of the security. It is far ... • 1,124 6 votes ### Is an invulnerable code possible (including brute force attack)? No, If we assume that the mythical computer can brute force the multiple AES encryptions and there are many ciphertexts available which are encrypted under the same key and their corresponding ... • 43.5k 5 votes Accepted ### Order of multiple encryption algorithms Yes, in case of VeraCrypt there is a difference, but it is negligible in practice. First we need to consider how VeraCrypt actually performs the cascading of the encryption algorithms which is (... • 44.7k 5 votes ### Can Grover's Algorithm be combined with a meet-in-the-middle attack? You could be able to reduce the space required for a meet-in-the-middle attack, if you follow a similar idea as the application of Grover's algorithm on collisions. Suppose you have two layers of$n$-... • 31.3k 5 votes ### Regarding Key Strength with DES and Blowfish I won't say someone would be able to break it 'easily'; however it won't be anywhere as difficult as with a true 128 bit cipher (or even 120 bit cipher; your construction ignores 8 of the key bits). ... • 134k 5 votes ### Encrypting messages for multiple recipients Yes, this is possible. The most natural option is to look at identity-based encryption (I point to the wikipedia page, as it gather some links to various schemes), such as the Boneh-Franklin IBE. An ... • 16.9k 5 votes Accepted ### Is there a system where multiple people can encrypt a message and then decrypt it in any order? Yes, systems that allow this have a name: commutative encryption. In practice, there are two varieties: If A, B, C just xor in a keystream, it all commutes. Of course, anyone seeing the ... • 134k 5 votes ### Does the double-hash H(H(x)) have greater collision probability than H(x)? I'm not sure what the question here is, but obviously applying the hash function twice can never decrease the number/probability of collision as all collisions in the first invocation are maintained. ... • 10.6k 5 votes ### double encryption - One Time Pad The answer is we cannot improve the security of the one-time pad in this manner. Intuitively the reason is that the double one-time pad is just a less efficient one time pad. The security of the ... • 1,343 4 votes ### How strong can multiple encryption be? If the ciphers are different, with independent keys, you can say that it is at least as strong as the first cipher. If the ciphers commute, like with stream ciphers, you can even say that it is at ... • 31.3k 4 votes Accepted ### Is super encryption (aka “multiple encryption”) always good? Since you are deriving the key from a password, there is generally not a security advantage to using multiple encryption in the way you described. The entropy of key material generated is less than ... • 12.7k 4 votes ### Is there any way to have a coded string such that it can be decoded in multiple ways? Maybe this example is only remotely related to the question, but anyway: VeraCrypt application for encrypting computer's disks has an ability to offer part of the disk capacity to reach the plausible ... • 219 4 votes Accepted ### "Double Encryption" using the same cipher? When I think of encryption and doubling it, I believe the strength of encryption, in the case of AES, as being tied to the number of rounds through the algorithm. I don't believe that's the best way ... • 134k 4 votes Accepted ### Multisignature or Multi-password File This is precisely the domain of secret sharing, of which there are various popular schemes like Shamir's secret-sharing scheme, and there are many widely available implementations of it in various ... 3 votes Accepted ### Combining a block cipher with a (pseudo) OTP There's quite a few things wrong with this. For starters, a block cipher does not imply authentication. Common block cipher modes such as CTR, CBC, and (god forbid) ECB provide nothing but pure ... • 2,347 3 votes Accepted ### Can Grover's Algorithm be combined with a meet-in-the-middle attack? The combination of Grover algorithm and man in the middle attack is the main subject of a paper (arXiv:1410.1434) published last year by Marc Kaplan (Full disclosure: Marc is a friend of mine.) In ... 3 votes ### Adding dummy bytes to ciphertext If you're using a real encryption scheme then no it cannot weaken or strengthen the system because the encryption scheme's security is supposed to be independent the actual data being encrypted. The ... • 7,338 3 votes ### Playfair Cipher + Vigenère Cipher? The short answer is yes. It would be considerably more secure. But nowadays, classical encryption methods like Playfair and Vigenère are so easily broken by computer analysis that they offer next to ... • 2,013 3 votes ### Combining several symmetric ciphers using XOR There is a very simple, completely generic solution, that unlike the other solution doesn't assume anything about how the two encryption schemes work internally (e.g., that they are built from block ... • 5,662 3 votes ### Regarding Key Strength with DES and Blowfish The actual security would probably be about 65 bits. A meet-in-the-middle attack can be used to find the keys of both ciphers in less time than naive brute force. The attack would decrypt the ... • 31.3k 3 votes ### Regarding Key Strength with DES and Blowfish What you propose is called Double Encryption. With two independent keys, it is vulnerable to meet-in-the-middle attacks as described in another comment. I just add that this attack can be performed ... • 5,547 3 votes Accepted ### Repeated NONCE in CTR mode This would be better than simply CTR if your nonces do collide, but it is still not very good. Suppose you use the same IV for two messages$m_0||m_1||...m_n$and$m_0'||m_1'||...m_n'$where all the$...
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This is a well studied problem in cryptography; what you're looking for is known as a Secret Sharing Scheme. This is a scheme where we take a master secret, and from that generate $N$ shares, and ...