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Showing content with the highest reputation on 07/06/24 in all areas

  1. Yes, the wealthy are always held accountable for their transgressions. </sarcasm>
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  3. That is, as far as I know, correct. There are some indirect applications in for instance ECC (Elliptic Curve Cryptography) and Elliptic Curve Digital Signature Algorithm (ECDSA). This may be of interest to OP since it is used, maybe on a daily basis, when browsing the internet; Elliptic Curve Cryptography (ECC) is of interest because it offers the same level of security with (much) smaller key sizes than for instance RSA. I did not find an open paper at this time** The following section is an attempt of a summary but it is outside my area of expertise and understanding, maybe @joigus or other experts can contribute: While Wiles' proof itself is not directly related to cryptographic applications, the deeper understanding and advanced techniques developed through his work have influenced fields that use elliptic curves. Without Wiles' Proof the theoretical framework supporting ECC would be less robust. The lack of proof of the Modularity Theorem* could leave gaps in understanding the deep properties of elliptic curves, potentially undermining confidence in their security properties and/or making them more vulnerable to sophisticated mathematical attacks. *) https://en.wikipedia.org/wiki/Modularity_theorem **) This seems interesting but I could only get the abstract: https://link.springer.com/chapter/10.1007/978-981-99-3758-5_5
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