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@ -890,7 +890,7 @@ communicate his public key to her. Like that problem, where
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public keys can be fairly large, the constraints Bob uses can also be
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quite large—potentially thousands of bytes. That's not only thousands
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of bytes that need to be communicated to Alice, but thousands of bytes
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for which she needs to pay transaction fees every time she wants to spend money to Bob. However, the solution of using hash functions to create
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for which she needs to pay transaction fees every time she wants to send money to Bob. However, the solution of using hash functions to create
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small commitments to large amounts of data also applies here.
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</p>
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++++
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@ -218,7 +218,7 @@ network.
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Public child key derivation can produce a linear sequence of keys
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similar to the previously seen <<Type1_wallet>>, but modern wallet
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applications use one more trick to provide a tree of keys instead a
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applications use one more trick to provide a tree of keys instead of a
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single sequence, as described in the((("wallets", "key generation", "public child key derivation", startref="wallet-keygen-public-child")))((("key generation", "public child key derivation", startref="keygen-public-child")))((("public child key derivation", startref="public-child-derive")))((("child key pair derivation", startref="child-key-pair"))) following section.
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[[hd_wallets]]
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