3.3 Key space
The security of an encryption algorithm is subtly related to the notion of key space. Simply put, a key space refers to encryption/decryption key pairs. The size of a key space determines how many of these pairs are available in a cryptographic algorithm (recall that in a symmetric algorithm, the encryption and decryption keys are the same, but in asymmetric cryptography they are different).
Clearly, the key space must be sufficiently large to prevent brute-force attacks (by means of an exhaustive search). But it would be very dangerous to assume an encryption algorithm is secure based on its key space size only.
A case in point: consider a simple type of cipher, the so-called polyalphabetic substitution ciphers, where the plaintext letters are substituted by ciphertext letters using multiple substitution alphabets. If the plaintext letters from the Roman alphabet are always substituted by a letter coming from the same alphabet, there are 26! possibilities for doing this...