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Flaw in Enigma

One of the Enigma machine's flaw was the derangement (fixed-point free permutation) of the produced ciphertext, or simply put: No plaintext-letter can be enciphered to itself. See this example from Wikipedia of how this text (in German) "Keine besonderen Ereignisse" can or can't be encrypted:

More modern encryption algorithms used during WW2, such as the Enigma-alike Typex machine used by the British, eliminated this flaw, meaning that a plaintext-letter sometimes could indeed be encrypted to itself.

And as far as I know most modern encryption algorithms (i.e. AES) also allow for the possibility of plaintext-letters being encrypted to themselves.

Questions

My questions are:

1. Are all encryption algorithms with fixed-point free permutations inherently flawed?
2. Can it be mathematically proven that all fixed-point free permutation algorithms can be broken with a "faster-than-brute-force" attack?

Flaw in Enigma

One of the Enigma machine's flaw was the derangement (fixed-point free permutation) of the produced ciphertext, or simply put: No plaintext-letter can be enciphered to itself. See this example from Wikipedia of how this text (in German) "Keine besonderen Ereignisse" can or can't be encrypted:

More modern encryption algorithms used during WW2, such as the Enigma-alike Typex machine used by the British, eliminated this flaw, meaning that a plaintext-letter sometimes could indeed be encrypted to itself.

And as far as I know most modern encryption algorithms (i.e. AES) also allow for the possibility of plaintext-letters being encrypted to themselves.

Questions

My questions are:

1. Are all encryption algorithms with fixed-point free permutations inherently flawed?
2. Can it be mathematically proven that all fixed-point free permutation algorithms can be broken with a "faster-than-brute-force" attack?

###Flaw in Enigma###

One of the Enigma machine's flaw was the derangement (fixed-point free permutation) of the produced ciphertext, or simply put: No plaintext-letter can be enciphered to itself. See this example from Wikipedia of how this text (in German) "Keine besonderen Ereignisse" can or can't be encrypted:

More modern encryption algorithms used during WW2, such as the Enigma-alike Typex machine used by the British, eliminated this flaw, meaning that a plaintext-letter sometimes could indeed be encrypted to itself.

And as far as I know most modern encryption algorithms (i.e. AES) also allow for the possibility of plaintext-letters being encrypted to themselves.

###Questions###

My questions are:

1. Are all encryption algorithms with fixed-point free permutations inherently flawed?
2. Can it be mathematically proven that all fixed-point free permutation algorithms can be broken with a "faster-than-brute-force" attack?

Flaw in Enigma

One of the Enigma machine's flaw was the derangement (fixed-point free permutation) of the produced ciphertext, or simply put: No plaintext-letter can be enciphered to itself. See this example from Wikipedia of how this text (in German) "Keine besonderen Ereignisse" can or can't be encrypted:

More modern encryption algorithms used during WW2, such as the Enigma-alike Typex machine used by the British, eliminated this flaw, meaning that a plaintext-letter sometimes could indeed be encrypted to itself.

And as far as I know most modern encryption algorithms (i.e. AES) also allow for the possibility of plaintext-letters being encrypted to themselves.

Questions

My questions are:

1. Are all encryption algorithms with fixed-point free permutations inherently flawed?
2. Can it be mathematically proven that all fixed-point free permutation algorithms can be broken with a "faster-than-brute-force" attack?

###Flaw in Enigma###

One of the Enigma machine's flaw was the derangement (fixed-point free permutation) of the produced ciphertext, or simply put: No plaintext-letter can be enciphered to itself. See this example from Wikipedia of how this text (in German) "Keine besonderen Ereignisse" can or can't be encrypted:

More modern encryption algorithms used during WW2, such as the Enigma-alike Typex machine used by the British, eliminated this flaw, meaning that a plaintext-letter sometimes could indeed be encrypted to itself.

And as far as I know most modern encryption algorithms (i.e. AES) also allow for the possibility of plaintext-letters being encrypted to themselves.

###Questions###

My questions are:

• Are all encryption algorithms with fixed-point free permutations inherently flawed?
• Can it be mathematically proven that all fixed-point free permutation algorithms can be broken with a "faster-than-brute-force" attack?

###Flaw in Enigma###

One of the Enigma machine's flaw was the derangement (fixed-point free permutation) of the produced ciphertext, or simply put: No plaintext-letter can be enciphered to itself. See this example from Wikipedia of how this text (in German) "Keine besonderen Ereignisse" can or can't be encrypted:

More modern encryption algorithms used during WW2, such as the Enigma-alike Typex machine used by the British, eliminated this flaw, meaning that a plaintext-letter sometimes could indeed be encrypted to itself.

And as far as I know most modern encryption algorithms (i.e. AES) also allow for the possibility of plaintext-letters being encrypted to themselves.

###Questions###

My questions are:

1. Are all encryption algorithms with fixed-point free permutations inherently flawed?
2. Can it be mathematically proven that all fixed-point free permutation algorithms can be broken with a "faster-than-brute-force" attack?