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My understanding is that an ICAP address will have 33 characters for Direct or 35 characters for Basic, thus I've generated some 34 characters long ICAP addresses using: 

helpeth keyGenerate

In these cases, the Ethereum Addresses starts with 0x0. Is that correct? What's this kind of ICAP address?

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The idea is to generate addresses that fits in the convention of IBAN (to have a checksum in the address itself). This is the IBAN format:

  • {country} {2 digit checksum } { 30 free characters } ==> total 34 chars

30 characters is usually too short to fit an ethereum address, in which case 31 characters are used (and is not fully compliant to IBAN). However if the address happens to starts with a few zero's it does fit.

These are the formats:

  • Direct: {XE} {2 digit checksum } { 30 free characters } ==> total 34 chars
  • Basic: {XE} {2 digit checksum } { 31 free characters } ==> total 35 chars

When you run "helpeth keyGenerate" a couple of times you can get a 34 char (direct) address:

Address: 0x063f6ad9039562f0bbc3b660819322b08ce301d3
Address (checksum): 0x063f6aD9039562f0BbC3b660819322B08Ce301D3
ICAP: XE09 Q9TQ 98HI APKD TMG6 CQY2 OZDO 6LQZ 83
Public key: 0xcfbe85959ab86421f7f5e9d0ad2fcd673ba253da24341d9b736dc40b387f93fb2a53a1295c6215b334cf7bbcad234da4b538b08a047fd9cabd37f93decbc33e3
Private key: 0x2d370faa059aefc2d64aa50ee3cfb2e6f1019604a06d01379603c59c1ead35ee

See also:

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