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* PUSH NOTE : 09. Transport Layer Security.md * PUSH ATTACHMENT : is-09-tls-handshake.png * PUSH NOTE : 08. Public Key Infrastructure.md * PUSH ATTACHMENT : is-08-certificate-validation.png * PUSH NOTE : 07. Public Key Cryptography.md * PUSH NOTE : 06. RSA and ElGamal Encryption.md * PUSH NOTE : 05. Modular Arithmetic (2).md * PUSH NOTE : 04. Modular Arithmetic (1).md * PUSH NOTE : 03. Symmetric Key Cryptography (2).md * PUSH ATTACHMENT : is-03-feistel-function.png * PUSH ATTACHMENT : is-03-ecb-encryption.png * PUSH ATTACHMENT : is-03-cbc-encryption.png * PUSH ATTACHMENT : is-03-cfb-encryption.png * PUSH ATTACHMENT : is-03-ofb-encryption.png * PUSH ATTACHMENT : is-03-ctr-encryption.png * PUSH NOTE : 02. Symmetric Key Cryptography (1).md * PUSH NOTE : 01. Security Introduction.md * PUSH ATTACHMENT : is-01-cryptosystem.png * PUSH NOTE : 9. Public Key Encryption.md * PUSH ATTACHMENT : mc-09-ss-pke.png * PUSH NOTE : 7. Key Exchange.md * PUSH ATTACHMENT : mc-07-dhke.png * PUSH ATTACHMENT : mc-07-dhke-mitm.png * PUSH ATTACHMENT : mc-07-merkle-puzzles.png * PUSH NOTE : 6. Hash Functions.md * PUSH ATTACHMENT : mc-06-merkle-damgard.png * PUSH ATTACHMENT : mc-06-davies-meyer.png * PUSH ATTACHMENT : mc-06-hmac.png * PUSH NOTE : 5. CCA-Security and Authenticated Encryption.md * PUSH ATTACHMENT : mc-05-ci.png * PUSH ATTACHMENT : mc-05-etm-mte.png * PUSH NOTE : 4. Message Authentication Codes.md * PUSH ATTACHMENT : mc-04-mac.png * PUSH ATTACHMENT : mc-04-mac-security.png * PUSH ATTACHMENT : mc-04-cbc-mac.png * PUSH ATTACHMENT : mc-04-ecbc-mac.png * PUSH NOTE : 2. PRFs, PRPs and Block Ciphers.md * PUSH ATTACHMENT : mc-02-block-cipher.png * PUSH ATTACHMENT : mc-02-feistel-network.png * PUSH ATTACHMENT : mc-02-des-round.png * PUSH ATTACHMENT : mc-02-DES.png * PUSH ATTACHMENT : mc-02-aes-128.png * PUSH ATTACHMENT : mc-02-2des-mitm.png * PUSH NOTE : 16. The GMW Protocol.md * PUSH ATTACHMENT : mc-16-beaver-triple.png * PUSH NOTE : 13. Sigma Protocols.md * PUSH ATTACHMENT : mc-13-sigma-protocol.png * PUSH ATTACHMENT : mc-10-schnorr-identification.png * PUSH ATTACHMENT : mc-13-okamoto.png * PUSH ATTACHMENT : mc-13-chaum-pedersen.png * PUSH ATTACHMENT : mc-13-gq-protocol.png * PUSH NOTE : 12. Zero-Knowledge Proofs (Introduction).md * PUSH ATTACHMENT : mc-12-id-protocol.png * PUSH NOTE : 10. Digital Signatures.md * PUSH ATTACHMENT : mc-10-dsig-security.png * PUSH NOTE : 1. OTP, Stream Ciphers and PRGs.md * PUSH ATTACHMENT : mc-01-prg-game.png * PUSH ATTACHMENT : mc-01-ss.png * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-09-10-security-intro.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-09-11-symmetric-key-cryptography-1.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-09-18-symmetric-key-cryptography-2.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-09-25-modular-arithmetic-1.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-04-modular-arithmetic-2.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-04-rsa-elgamal.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-09-public-key-cryptography.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-16-pki.md * DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-18-tls.md * DELETE FILE : _posts/lecture-notes/internet-security/2023-10-19-public-key-encryption.md * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-01-cryptosystem.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-03-cbc-encryption.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-03-cfb-encryption.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-03-ctr-encryption.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-03-ecb-encryption.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-03-feistel-function.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-03-ofb-encryption.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-08-certificate-validation.png * DELETE FILE : assets/img/posts/Lecture Notes/Internet Security/is-09-tls-handshake.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-01-prg-game.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-01-ss.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-02-2des-mitm.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-02-DES.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-02-aes-128.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-02-block-cipher.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-02-des-round.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-02-feistel-network.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-04-cbc-mac.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-04-ecbc-mac.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-04-mac-security.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-04-mac.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-05-ci.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-05-etm-mte.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-06-davies-meyer.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-06-hmac.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-06-merkle-damgard.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-07-dhke-mitm.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-07-dhke.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-07-merkle-puzzles.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-09-ss-pke.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-10-dsig-security.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-10-schnorr-identification.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-12-id-protocol.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-13-chaum-pedersen.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-13-gq-protocol.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-13-okamoto.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-13-sigma-protocol.png * DELETE FILE : assets/img/posts/Lecture Notes/Modern Cryptography/mc-16-beaver-triple.png
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@@ -14,9 +14,9 @@ title: 16. The GMW Protocol
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date: 2023-11-16
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github_title: 2023-11-16-gmw-protocol
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image:
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path: assets/img/posts/Lecture Notes/Modern Cryptography/mc-16-beaver-triple.png
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path: assets/img/posts/lecture-notes/modern-cryptography/mc-16-beaver-triple.png
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attachment:
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folder: assets/img/posts/Lecture Notes/Modern Cryptography
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folder: assets/img/posts/lecture-notes/modern-cryptography
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---
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There are two types of MPC protocols, **generic** and **specific**. Generic protocols can compute arbitrary functions. [Garbled circuits](./2023-11-14-garbled-circuits.md#garbled-circuits) were generic protocols, since it can be used to compute any boolean circuits. In contrast, the [summation protocol](./2023-11-09-secure-mpc.md#example-secure-summation) is a specific protocol that can only be used to compute a specific function. Note that generic protocols are not necessarily better, since specific protocols are much more efficient.
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@@ -148,7 +148,7 @@ Indeed, $z_1, z_2$ are shares of $z$.[^2] See also Exercise 23.5.[^3]
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Now, in the actual computation of AND gates, proceed as follows.
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> Each $P_i$ has a share of inputs $a_i, b_i$ and a Beaver triple $(x_i, y_i, z_i)$.
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> 1. Each $P_i$ computes $u_i = a_i + x_i$, $v_i = b_i + y_i$.
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