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Trance-0
2025-10-27 11:56:32 -05:00
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content/CSE442T/CSE442T_L17.md
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@@ -32,7 +32,8 @@ Proof of the validity of the decryption: Exercise.
The encryption scheme is secure under this construction (Trapdoor permutation (TDP), Hardcore bit (HCB)).
Proof:
<details>
<summary>Proof</summary>
We proceed by contradiction. (Constructing contradiction with definition of hardcore bit.)
@@ -76,7 +77,7 @@ $$
This contradicts the definition of hardcore bit.
QED
</details>
### Public key encryption scheme (multi-bit)
@@ -144,7 +145,8 @@ Output: $m$
#### Security of El-Gamal encryption scheme
Proof:
<details>
<summary>Proof</summary>
If not secure, then there exists a distinguisher $\mathcal{D}$ that can distinguish the encryption of $m_1,m_2\in G_q$ with non-negligible probability $\mu(n)$.
@@ -155,5 +157,5 @@ $$
And proceed by contradiction. This contradicts the DDH assumption.
QED
</details>