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My understanding is that when an e-mail is encrypted and sent to a recipient, the recipient's public key is used to encrypt the e-mail, and then only the recipient can decrypt it with their private key. However, how would this process work when sending an encrypted e-mail to multiple recipients?

My best guess would be that the e-mail program must "make copies" of the e-mail for each recipient, and then encrypt each with the recipient's public key, and then send it to each recipient. After this, each recipient could then decrypt their copy with their private key. Would this be correct? I have not yet been able to find an answer searching online.

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This is done as you say, except with an optimization. The email itself is encrypted with a newly generated random symmetric key; and that key is then encrypted with the public key of each recipient. This means that if you have a 2MB email and send it to 20 people, total size is a bit more than 2MB, not 40MB.

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