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If a hash-based signature schemes such as W-OTS is used, do we still need public key based certificates to prove ownership of a public key? I understand that hash-based signatures are one of the candidates for post-quantum signatures. However, if quantum vulnerable schemes such as RSA is used for certificates, it makes such system still vulnerable to quantum computing.

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However, if quantum vulnerable schemes such as RSA is used for certificates, it makes such system still vulnerable to quantum computing.

Well, yes, if one used conventional crypto in your certificates, things would be vulnerable. You'd need to use a certificate that used postquantum signatures.

BTW: generating a certificate for a one-time signature public key, such as W-OTS, would appear to be somewhat pointless, as you'd need to request a new certificate everytime you used your private key. What you'd want to do (assuming tracking state is not an issue) is to use a scheme that can sign multiple messages, such as XMSS or LMS.

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