Why is this DES key considered weak?

I understand the premise of weak keys in DES and cryptography. From searching online, I understand that keys that are comprised of all zeroes / all ones / alternating ones and zeroes / alternating zeroes and ones are considered weak and should not be used. If I was to use the following key: 0110 0110 0001 0001, would this be considered weak; and if so, how come?

• Please fix the question. The key $\mathtt{0110011000010001_h}$ is not a DES key because it comprises two bytes at $\mathtt{00_h}$, and these do not have the required odd parity. Changing these two bytes to $\mathtt{01_h}$ (by adjusting the low-order bit for odd parity, as customary), the key becomes $K=\mathtt{0110011001010101_h}$ and is not one of the four DES weak keys. Correspondingly, it does not hold that for any 8-byte block $X$ we have $\text{DES}_K(\text{DES}_K(X))=X$, which is a common characterization of a weak key $K$. Is the key you consider $\mathtt{0101010101010101_h}$ ?
– fgrieu
Jun 11 '21 at 16:15
• DES takes 56-bit keys. 3DES takes 112-bit keys. Anything less than 100 bits or so is weak in practice, though not as weak as a true "weak key". What you posted isn't even a valid DES key. Jun 11 '21 at 16:18
• Notice that It does not make sense to consider a single key as weak or strong. It's more relevant to consider a procedure to generate the key as strong or weak (and as a first trivial condition, this procedure should have enough entropy to avoid brute-force attack). Jun 11 '21 at 16:47

First, DES keys are considered to be weak because they are only 56 bit keys giving only $$2^{56}$$ possible keys. That small of a key space is searchable by brute force by even fairly low-capability attackers.