As Paŭlo Ebermann says, this is (apparently) a homophonic cipher.
Ciphers that obscure single-letter frequencies, such as homophonic ciphers, the Alberti cipher, Vigenère cipher, the Playfair cipher, etc. are impossible to crack using single-letter frequency analysis, which is the only cryptanalysis technique published before 1863.
However, other cryptanalysis techniques that have been developed since then.
Given enough ciphertext, you can discover other patterns and decrypt the message.
Several of these techniques are mentioned in Stahl's proposal for a homophonic cipher that attempts to resist those techniques:
F. A. Stahl.
"A homophonic cipher for computational cryptography"
Ciphertext-only cryptanalysis techniques that can be applied to homophonic ciphers include:
- Some words (and word fragments) are very common. If we find a near-repeat -- "aBcde" in one place, and "aXcde" in another -- we begin to suspect that B and X both refer to the same plaintext letter.
- When encrypting a plaintext letter that could be represented by several ciphertext symbols, one way to guarantee that all those ciphertext symbols have exactly the same frequency is for the writer to cycle through them -- when encrypting the first plaintext "h", the writer writes "M", the next plaintext "h" becomes ")", the next "M", then ")", etc. Later when the cryptanalyst sees that 2 symbols that always occur in the order (neglecting all other symbols) "M)M)M)M)" in the ciphertext, or 3 symbols that always occur in order "tr\tr\tr\tr\", we begin to suspect that M and ) both refer to one plaintext letter, and that t, r, and \ all refer to one other plaintext letter.
- many bigram frequencies in English are significantly different than what we might predict from the underlying single-letter frequencies alone. Some enciphered letters might have a next-cipher-letter frequency that is relatively flat (all other ciphertext letters follow it), so perhaps it is a vowel, while other enciphered letters have a very spiked next-letter frequency (the next letter is nearly always one of a small set of ciphertext letters), so perhaps it is a consonant -- if extremely spiked, perhaps it is the 'q'.
- And other cryptanalysis techniques.
This type of cryptographic system would not withstand modern computer-based cryptanalysis.
However, certain ciphertexts from such a system have withstood modern attempts at decoding because:
With a homophonic cipher message where every symbol is unique (and we have no other messages that use the same ciphertext-to-plaintext mapping) -- imagine if we only had the first 2 rows of the 340 Cipher -- every possible message is a plausible message, much like every possible message is a plausible message with a one-time pad, and such a "entirely unique" message is impossible to decrypt.
With messages that contain some repeats, we can rule out some possible messages, but if the message is short enough, there may be a huge number of plausible deciphered plaintexts (using different homophonic encryption alphabets), much like the one-time pad gives a huge number of plausible deciphered plaintexts (using different keypads). One of them is the original message, but even an infinite amount of computer power won't help you figure out which one it is.