Let G be a cyclic group of order n and let g be a generator of G. The El Gamal encryption scheme AEEG = (K, E, D) associated to G, g is the asymmetric encryption scheme whose constituent algorithms are depicted below: Algorithm K x ←$ Zn X ← gx Return (X, x) Algorithm EX(M) If M ∈ G then return ⊥ y ←$ Zn ; Y ← gy K ← Xy ; W ← KM Return (Y,W) Algorithm Dx((Y,W)) K ← Y x M ← WK−1 Return M The plaintext-space associated to a public key X ∈ G is G itself, and if M is not in this set then the encryption algorithm returns ⊥.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Let G be a cyclic group of order n and let g be a generator of G. The El Gamal encryption scheme AEEG = (K, E, D) associated to G, g is the asymmetric encryption scheme whose constituent algorithms are depicted below:
Algorithm K
x ←$ Zn
X ← gx
Return (X, x)
Algorithm EX(M)
If M ∈ G then return ⊥
y ←$ Zn ; Y ← gy
K ← Xy ; W ← KM
Return (Y,W)
Algorithm Dx((Y,W))
K ← Y x
M ← WK−1
Return M
The plaintext-space associated to a public key X ∈ G is G itself, and if M is not in this set then the encryption algorithm returns ⊥.

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