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The LWE assumption I think we should start from the LWE assumption. Let $n$ and $q$ be integers and let $\chi$ be a distribution over $\mathbb{Z}_q$. We often take $\chi$ as a Gaussian with small variance. (We take an error $e$ from this distribution $\chi$ and assume that $|e| \ll q$.) The LWE assumption states that any efficient adversary cannot ...


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What if it could? What does this definition mean in practice? Consider $M_0=$ attack and $M_1=$ don't attack. If the adversary can distinguish which message you are sending to your troops, they can optimize their strategy to defeat you. Another example. Say you are casting a yes ($1$) no ($0$) vote for a proposed piece of legislation. If the adversary ...


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The initial notion of semantic security from Goldwasser and Micali has been shown to be euqivalent to what we call today indistinguishability under chosen plaintext attacks (IND-CPA). Yes that's only security against a passive adversary and actually the weakest reasonable security notion that we use today. The authors of the second paper you link seem to ...


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First, on the difference between perfect security and semantic security. Both definitions concern confidentiality, so let us first define what confidentiality means. Note first that an adversary as some a priori knowledge of the message. We can capture that by e.g. having the adversary choose two messages and then flipping a fair coin to decide which one to ...


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Here is the proof I came up with. Please let me know if you see any problems with it... Statement to prove: If an encryption scheme is secure in the IND\$-CPA sense, then it is secure in the IND-CPA sense as well. i.e. IND\$-CPA $\Rightarrow$ IND-CPA The contrapositive is easier to prove: $\neg$IND-CPA $\Rightarrow$ $\neg$IND\$-CPA. This statement is a ...


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That basically means 'an adversary running in a reasonable amount of time can (or cannot) distinguish one message from another once encrypted'. If we didn't care about that, there would be no point in using cryptography altogether. mikeazo gives a few good examples why this is important. Furthermore here's the definition for the security of an encryption ...



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