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7: Security against Chosen Plaintext Attacks

  • Page ID
    7382
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    Our previous security definitions for encryption capture the case where a key is used to encrypt only one plaintext. Clearly it would be more useful to have an encryption scheme that allows many plaintexts to be encrypted under the same key.

    Fortunately we have arranged things so that we get the "correct" security definition when we modify the earlier definition in a natural way. We simply let the libraries choose a secret key once and for all, which is used to encrypt all plaintexts. More formally:

    Definition 7.1 (CPA security)

    Let \(\Sigma\) be an encryption scheme. We say that \(\Sigma\) has security against chosen-plaintext attacks (CPA security) if \(\mathcal{L}_{\text {cpa-L }}^{\Sigma} \approx \mathcal{L}_{\text {cpa-R }}^{\Sigma}\), where:

    Notice how the key \(k\) is chosen at initialization time and is static for all calls to Enc. CPA security is often called "IND-CPA" security, meaning "indistinguishability of ciphertexts under chosen-plaintext attack."


    This page titled 7: Security against Chosen Plaintext Attacks is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Mike Rosulek (Open Oregon State) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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