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I understand how the Bitcoin core wallet communicates with the blockchain, but how do the lightweight wallets like Multibits, Electrum, etc, communicate with the blockchain?
Lightweight Wallets Communication with Blockchain
Answers
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You should have a look at the SPV (https://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29_Clients).
It was also mentioned by Satoshi in his paper at page 5 point 8: https://bitcoin.org/bitcoin.pdf
