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A full client does not need to trust any individual node on the Ethereum network, as the full client can see the activity from all nodes and discard any inconsistencies caused by ill intentioned nodes

Does the same apply for a light client, or does the light client require a chain of trust towards some node (or set of nodes) on the Ethereum network?

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full security is only possible for a full node

https://github.com/ethereum/wiki/wiki/Light-client-protocol

One reason is that block headers show proof of work, but not proof of valididty. So a light node may receive an invalid block header and assume it is valid. Of course, invalid blocks are just as expensive to produce as valid blocks, without any block subsidty.

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Short answer: it does not.

Long answer: getting the correct header is the only critical part. Light clients cannot check every state transition, they rely on PoW/PoS. PoS will be a better protection against fraud since signing wrong blocks costs a lot, but PoW is also reliable if we wait a few "confirmation" blocks (light client will have that option).

No one except the attacker will ever mine on a fake block, so if the attacker has less hashpower than the rest of the network, it won't be able to create too many consecutive blocks on an alternative (fake) chain and also have a higher total difficulty than the canonical chain at any point.

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