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Add distinctness assumption to OT #5

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merged 2 commits into from
Aug 15, 2024
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Add distinctness assumption to OT #5

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cb6af7b
Add distinctness assumption to OT
vEnhance Aug 13, 2024
9ccb9b3
OK we'll run with this
vEnhance Aug 15, 2024
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10 changes: 8 additions & 2 deletions easy/src/ot.typ
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Original file line number Diff line number Diff line change
Expand Up @@ -4,10 +4,15 @@
<ot>

Alice has $n$ messages $x_1, dots, x_n$.
We'll assume the messages are essentially unrelated to each other
(since we could always pad them with random bits).
Bob wants to request the $i$-th message,
without letting Alice learn anything about the value of $i$.
Alice wants to send Bob $x_i$,
without letting him learn anything about the other $n-1$ messages. An _oblivious transfer (OT)_ allows Alice to transfer a single message to Bob, but she remains oblivious as to which message she has transferred. We'll see two simple protocols to achieve this.
without letting him learn anything about the other $n-1$ messages.
An _oblivious transfer (OT)_ allows Alice to transfer a single message to Bob,
but she remains oblivious as to which message she has transferred.
We'll see two simple protocols to achieve this.

(In fact, for two-party computation,
we only need "1-of-2 OT":
Expand Down Expand Up @@ -51,7 +56,8 @@ by working in a finite group (for example $FF_p^times$, or an elliptic curve).

Our first oblivious transfer protocol is built on the commutative encryption we just described.

Alice has $n$ messages $x_1, dots, x_n$, which we may as well assume are elements of the group $G$. Alice chooses a secret key $a$, encrypts each message, and sends all $n$ ciphertexts to Bob:
Alice has $n$ messages $x_1, dots, x_n$, which we may as well assume are elements of the group $G$.
Alice chooses a secret key $a$, encrypts each message, and sends all $n$ ciphertexts to Bob:
$
Enc_a (x_1), dots, Enc_a (x_n).
$
Expand Down
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