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In the process of trying to understand the effects of segwit on Bitcoin I started watching this:

https://www.youtube.com/watch?v=NOYNZB5BCHM

Which are the cases in which the receiver does not need the signatures? (minute 6.20)

Am I right, saying that signatures for segwit outputs will never be relayed to old clients?

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Yes and no: this is a presentation from 2015, and you are referencing a section which Pieter described as "assume we can redesign bitcoin". So bitcoin hasn't been redesigned, and not everything has been implemented as described in 6:20.

How it is handled today is part of a discussion with Andrew in bitcointalk (read down to page end). Older nodes don't get to see the witness data. They get just tx data, in an "anyone can spend" way, so it is recognized as valid tx by older nodes. Newer nodes get the witness data (of course).

Am i right saying that signatures for segwit outputs will never be relayed to old clients?

yes.

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When nodes connect, they introduce themselves to each other by telling each other their service flags. One of these service flags, NODE_WITNESS, informs their counterpart whether a node is segwit-capable. Only nodes that set NODE_WINESS will receive the full transaction, other peers will be sent the stripped transaction without the witness data.

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