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I implement a webshop, basically it is more than a wehshop a marketplace and I would offer Bitcoin payment. There are 3 roles: buyer, seller, and the marketplace.

The procedure I imagined, that that seller has the private key. Seller derive adresses, where one would epxect the incomes. Seller hands those addresses to marketplace.

When buyer comes and want to purchase a product, marketplace return an address. Marketplace record in DB which buyer and address belongs together. Later Maketplace pull Blockchain, and check wether amount appeared in the specified address. If so, than pruduct can be shipped.

So:

Is it possible derive pathes without prive key? If so in which wallet?

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Yes, you can use a hierarchical key ("xpub") to do that. The seller will generate a wallet and provide you with their wallet's "xpub" public key, and they keep the corresponding private key "xprv". You can use the "xpub" to generate addresses for their wallet, and the seller can use their "xprv" private key to spend from those addresses.

I believe most wallet software supports this by default.

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