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Oblivious transfer is mostly studied as a theoretic construction, as it is an important component in achieving interesting protocols (like secure two-party computation and secure function evaluation). The interest in 1-2 OT is that it is a minimal definition theoretically, and most results that limit themselves to 1-2 are designed to improve some basic ...

the securty of 1-n OT is a function of the security of a 1-2 OT. So in analysis it is easy to use 1-2 OT for security proofs. A 1-n OT is essentially a multiple run of a 1-2 OT. (somewhat like a byte is made of 8 bits) So IMO the question is like asking why use bits when you can use bytes for communication. [it depends on the application]

Yao's garbled circuit is simple to understand. First of all, note that if we can securely compute $\mathsf{NAND/NOR}$ of two input bit, we can perform any boolean operation. Yao's garbled circuit tries to achieve the same. Lets look at scrambled $\mathsf{OR}$ gate. Alice creates a set of four keys, $K_{x=0},K_{x=1},K_{y=0},K_{y=1}$ She then creates 4 ...

As discovered by D.W., this is in fact part of recommended IDEA implementation. IDEA uses $a\cdot b \bmod (2^{16}+1)$, with a special case of handling $0$ as $2^{16}$. From the Handbook of Applied Cryptography, note 7.016: Note (implementing $ab \bmod 2^{n}+1$) Multiplication $\bmod 2^{16}+1$ may be efficiently implemented as follows, for $0 \leq a, ...

At first glance, it doesn't look like that interesting of a function. If we define: f(b, c) = (b*c)%k - (b*c)/k then we always have: f(b, c) == b*c (mod k+1) In other words, largely it's just an odd way of doing a modular multiplication. Of course, f(b, c) is not always (b*c) % (k+1); sometimes it is negative. At first glance, I don't see any ...