Weak key
From Academic Kids

In cryptography, a weak key is a key which when used with a specific cipher, makes the cipher behave in some undesirable way. Weak keys usually represent a very small fraction of the overall keyspace, which usually means that if one generates a random key to encrypt a message weak keys are very unlikely to give rise to a security problem. Nevertheless, it is considered desirable for a cipher to have no weak keys.
Weak keys in DES
The block cipher DES has a few specific keys termed "weak keys" and "semiweak keys". These are keys which cause the encryption mode of DES to act identically to the decryption mode of DES (albeit potentially that of a different key).
In operation, the secret 56bit key is broken up into 16 subkeys according to the DES key schedule; one subkey is used in each of the sixteen DES rounds. The weak keys of DES are those which produce sixteen identical subkeys. This occurs when the key bits are:
 all zeros
 all ones
 the first half of the entire key is all ones and the second half is all zeros
 vice versa
Since all the subkeys are identical, and DES is a Feistel network, the encryption function is selfinverting; that is, encrypting twice produces the original plaintext.
DES also has semiweak keys. These come in pairs K_{1} and K_{2}, and they have the property that:
 <math>E_{K_1}(M)=E_{K_2}(M)<math>
where E_{K}(M) is the encryption algorithm encrypting message M with key K. This means that both keys encrypt a plaintext to the same ciphertext. This is because these keys produce only two unique subkeys. There are six semiweak key pairs.
Are these weak and semiweak keys fatal flaws of DES? Not really. There are 2^{56} (7.21 × 10^{16}, about 72 quadrillion) possible keys for DES, of which four are weak and twelve are semiweak. This is such a tiny fraction of the possible keyspace that users do not need to worry. If they so desire, they can check for weak or semiweak keys when the keys are generated. They are very few, and easy to recognize. Note, however, that DES is not recommended for general use since all keys can be bruteforced in about a day for a onetime hardware cost on the order of some new cars.
List of algorithms with weak keys
 IDEA. IDEA's weak keys are identifiable in a chosenplaintext attack. They make the relationship between the XOR sum of plaintext bits and ciphertext bits predictable. There is no list of these keys, but they can be identified by their "structure".
 Blowfish. Blowfish's weak keys produce bad Sboxes, since Blowfish's Sboxes are keydependent. There is a chosen plaintext attack against a reducedround variant of Blowfish that is made easier by the use of weak keys. This is not a concern for full 16round Blowfish.
No weak keys as a design goal
The goal of having a 'flat' keyspace (ie, all keys equally strong) is always a cipher design goal. As in the case of DES, sometimes a small number of weak keys is acceptable, provided that they are all identified or identifiable. An algorithm that has weak keys which are unknown does not inspire much trust.
The two main countermeasures against inadvertently using a weak key:
 Checking generated keys against a list of known weak keys, or building rejection of weak keys into the key scheduling.
 When the number of weak keys is known to be very small (in comparison to the size of the keyspace), generating a key uniformly at random ensures that the probability of it being weak is a (known) very small number.
A large number of weak keys is a serious flaw in any cipher design, since there will then be a (perhaps too) large chance that a randomly generated one will be a weak one, compromising the security of messages encrypted under it. It will also take longer to check randomly generated keys for weakness in such cases, which will tempt shortcuts in interest of 'efficiency'.
However, weak keys are much more often a problem where the adversary has some control over what keys are used, such as when a block cipher is used in a mode of operation intended to construct a secure cryptographic hash function (eg DaviesMeyer)
Block ciphers edit (https://search.academickids.com:443/encyclopedia/index.php?title=Template:Block_ciphers&action=edit) 
Algorithms: 3Way  AES  Akelarre  Blowfish  Camellia  CAST128  CAST256  CMEA  DEAL  DES  DESX  FEAL  FOX  FROG  GDES  GOST  ICE  IDEA  Iraqi  KASUMI  KHAZAD  Khufu and Khafre  LOKI89/91  LOKI97  Lucifer  MacGuffin  Madryga  MAGENTA  MARS  MISTY1  MMB  NewDES  RC2  RC5  RC6  REDOC  Red Pike  S1  SAFER  SEED  Serpent  SHACAL  SHARK  Skipjack  Square  TEA  Triple DES  Twofish  XTEA 
Design: Feistel network  Key schedule  Product cipher  Sbox  SPN Attacks: Brute force  Linear / Differential cryptanalysis  Mod n  XSL Standardisation: AES process  CRYPTREC  NESSIE Misc: Avalanche effect  Block size  IV  Key size  Modes of operation  Pilingup lemma  Weak key 