places, although banks in Switzerland and many other countries require a six-digit PIN. PIN validation There are several main methods of validating PINs. The operations discussed below are usually performed within a hardware security module (HSM). IBM 3624 method One of the earliest ATM models was the IBM 3624, which used the IBM method to generate what is termed a natural PIN. The natural PIN is generated by encrypting the primary account number (PAN), using an encryption key generated specifically for the purpose. This key is sometimes referred to as the PIN generation key (PGK). This PIN is directly related to the primary account number. To validate the PIN, the issuing bank regenerates the PIN using the above method, and compares this with the entered PIN. Natural PINs cannot be user selectable because they are derived from the PAN. If the card is reissued with a new PAN, a new PIN must be generated. Natural PINs allow banks to issue PIN reminder letters as the PIN can be generated. IBM 3624 + offset method To allow user-selectable PINs it is possible to store a PIN offset value. The offset is found by subtracting natural PIN from the customer selected PIN using modulo 10. For example, if the natural PIN is 1234, and the user wishes to have a PIN of 2345, the offset is 1111. The offset can be stored either on the card track data, or in a database at the card issuer. To validate the PIN, the issuing bank calculates the natural PIN as in the above method, then adds the offset and compares this value to the entered PIN. VISA method The VISA method is used by many card schemes and is not VISA-specific. The VISA method generates a PIN verification value (PVV). Similar to the offset value, it can be stored on the card's track data, or in a database at the card issuer. This is called the reference PVV. The VISA method takes the rightmost eleven digits of the PAN excluding the checksum value, a PIN validation key index (PVKI, chosen from one to six, a PVKI of 0 indicates that the PIN cannot be verified through PVS) and the required PIN value to make a 64-bit number, the PVKI selects a validation key (PVK, of 128 bits) to encrypt this number. From this encrypted value, the PVV is found. To validate the PIN, the