# Elliptic Curve Cryptography: Inverses and Group Structure

Page: https://stenobird.com/podcast/magic-internet-math-7652323/elliptic-curve-cryptography-inverses-and-group-structure
Text version: https://stenobird.com/podcast/magic-internet-math-7652323/elliptic-curve-cryptography-inverses-and-group-structure.md
Podcast: [Magic Internet Math](https://stenobird.com/podcast/magic-internet-math-7652323)
Published: 2026-03-02T12:22:37+00:00
Episode link: https://magicinternetmath.com
Audio file: https://serve.podhome.fm/episode/68bd541f-7118-40ad-47f7-08dd33f04393/639136107900912589a4ef36cb-7591-4af0-8174-a851e53b148dv1.mp3
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JSON: https://stenobird.com/v1/public/podcasts/magic-internet-math-7652323/episodes/elliptic-curve-cryptography-inverses-and-group-structure
Duration seconds: 5536

## Resource

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode of the Magic Internet Math Podcast, the hosts continue their exploration of elliptic curve cryptography, focusing on the inverse problem and the mathematical structures that ensure its existence, as part of their series on Bitcoin security. Key Topics: Inverse Problem Modular Arithmetic Groups and Fields Euclidean Algorithm Fermat's Little Theorem LibSecP Library Summary: The hosts emphasize the importance of understanding the mathematical foundations of Bitcoin, specifically the inverse problem, where a public key can be inverted back into its corresponding private key. They highlight that the existence of an inverse is crucial for the security of Bitcoin, ensuring that transactions can be verified and private keys remain secure. This is supported by the mathematical structures of groups and fields, which guarantee the existence of an inverse for every element under certain operations.

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## Transcript

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