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With 4 bytes the test vectors do not pass the right values.
Similarly, the TOTP implementatation uses 8 byte long int.
As per RFC4226, 5.1. Notation and Symbols [1]:
C 8-byte counter value, the moving factor. This counter
MUST be synchronized between the HOTP generator (client)
and the HOTP validator (server).
[1] https://www.rfc-editor.org/rfc/rfc4226#page-5
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With counter size equal to 4 bytes the test vectors do not pass back the right values for HOTP. Similarly, the TOTP implementation uses 8 byte long int, hence it seems that this is a typo. At the same time the YK's protocol does accept only 4-byte counters.
As per RFC4226, 5.1. Notation and Symbols [1]:
[1] https://www.rfc-editor.org/rfc/rfc4226#page-5