1-2 Oblivious Transfer
In a 1-2 oblivious transfer protocol, the sender has two messages m0 and m1, and the receiver has a bit b, and the receiver wishes to receive mb, without the sender learning b, while the sender wants to ensure that the receiver receives only one of the two messages. The protocol of Even, Goldreich, and Lempel (which the authors attribute partially to Silvio Micali), is general, but can be instantiated using RSA encryption as follows.
| Alice | Bob | |||||
|---|---|---|---|---|---|---|
| Secret | Public | Calculus | Secret | Public | Calculus | |
| Messages to be sent | ||||||
| Generate RSA key pair and send public portion to Bob | Receive public key | |||||
| Generate two random messages | Receive random messages | |||||
| Choose, and generate random | ||||||
| Compute the encryption of, blind with and send to Alice | ||||||
| One of these will equal, but Alice does not know which. | ||||||
| Send both messages to Bob | Receive both messages | |||||
| Bob decrypts the since he knows which he selected earlier. | ||||||
- Alice has two messages, and wants to send exactly one of them to Bob, but does not want to know which one Bob receives.
- Alice generates a RSA key pair, comprising the modulus, the public exponent and the private exponent
- She also generates two random values, and sends them to Bob along with her public modulus and exponent.
- Bob picks to be either 0 or 1, and selects either the first or second .
- He generates a random value and blinds by computing, which he sends to Alice.
- Alice doesn't know which of and Bob chose, so she attempts to unblind with both of her random messages and comes up with two possible values for : and . One of these will be equal to since it will correctly decrypt, while the other will produce another random value that does not reveal any information about .
- She blinds the two secret messages with each of the possible keys, and, and sends them both to Bob.
- Bob knows which of the two messages can be unblinded with, so he is able to compute exactly one of the messages
Read more about this topic: Oblivious Transfer
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