Decrypting 3-DES with DES I have a ciphertext, that is encrypted using 3-DES.
I wondered, why is it possible to decrypt it using 1-DES.
1-DES key is shorter than 3-DES that is used. How does it work like that?
Triple DES (Wikipedia) is simply DES used three times, usually ciphertext = E(k3,D(k2,E(k1,plaintext))), although I have seen other arrangements such as E(k1,E(k2,E(K3,plaintext).  So just split the 3-DES key into three (sometimes two) parts k1, k2, and k3, and run 1-DES three times, using the appropriate key each time.

So, for example, if my 3-DES key is aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbcccccccccccccccc (hex), then the 1-DES keys would typically be aaaaaaaaaaaaaaaa, bbbbbbbbbbbbbbbb, and cccccccccccccccc, with the system documentation letting us know which one is k1, k2, and k3.  So assuming we encrypted using ciphertext = E(k3,D(k2,E(k1,plaintext))), then we can decrypt using 1-DES as follows:


temp1 = D(k3,ciphertext)
temp2 = E(k2,temp1)
plaintext = D(k1,temp2)


And of course if we are using something like Cipher Block Chaining, the whole sequence above would be considered one block cipher decryption.

Edit: 
1. If only two keys are used (the ABA mentioned in the comments), the general approach is the same, except instead of having a separate k3, we just set k3=k1 and do the same as before.


Just to be clear, E(k,p) is enciphering the plaintext p using the key k, and D(k,c) is decrypting the ciphertext c using the key k.  For this example, we are using plain DES for both E() and D().