Performing client independent update of hash with Argon2

Question

I'm trying to perform a hash update with updated parameters using argon2. According to Argon spec v3 (2.2.3 Client-indepentend Update, p. 9) the client independent update is executed as follows:

$$ Tag_{new} = \Pi(Tag_{old},S,m_{new},R_{new},\tau_{new}) $$

I'm assuming $\Pi$ to be our hash fn Argon2i/Argon2d (as used in 2.4.4 Security of Argon2 to generic attacks, p. 15) and $R_{new}$ the parallelism param.

Now, using the online tool https://argon2.online/ , I performed the following attempt:

input asdf as plain text input
input salt11chars as salt
leave params as default (mode=argon2i, parallelism=1, $m=16, $$t=2$, $\tau=16$)
calculate hash
input calculated hash as plain text input
increase parallelism by 1
calculate hash
verify if asdf matches the hash

$\rightarrow$ verification fails

So why is that and what am I doing wrong here? Thanks in advance.

For client independent updates with Argon2 is possible only for iteration and you need to store full output size ( 512-bit). If you look at the image at this answer, you will see why or page 6 see the initial hash and the first final hash. — kelalaka, Jun 14 '22 at 10:37
See discussion here Password hashing algorithms that can transform an existing hash to a different cost setting without knowledge of the password — kelalaka, Jun 14 '22 at 11:22
Thanks for your hints. Would it be possible for you to give me an example? And where have I access to the full output, given the final tag is actually a composite hash a ccording to the figure? — prohit, Jun 14 '22 at 12:00
I don't think that Argon2 has a true client-independent update. — kelalaka, Jun 14 '22 at 12:03
FYI: According to OWASP Best Practices for Password Storage, one should hash the old hashed password with a new hash, generated by a newer hashing algorithm. After the user enters the original password, one can hash it using only the newer hashing algorithm and store its' hash. I assume this 2 step hashing has to be included for backwards compatibility, until all users have input their original passwords at least once and generated a hash with the newer hashing algorithm. — prohit, Jun 22 '22 at 13:13
This is not client independent, but the recommended way to update legacy hashes . — prohit, Jun 22 '22 at 13:14

Performing client independent update of hash with Argon2

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