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椭圆曲线：密码学的核心工具

2025-12-18 分类：前沿哨所阅读(3) 评论(0) 赞(0)

智谱 GLM，支持多语言、多任务推理。从写作到代码生成，从搜索到知识问答，AI 生产力的中国解法。

椭圆曲线是数学中一种特殊曲线，在密码学中扮演关键角色。文章从非正式定义（y² = x³ + ax + b）到正式定义（光滑射影代数曲线），解释了椭圆曲线形成阿贝尔群，具有交换性和结合性。群运算通过几何方法（如两点连线交点反射）或代数公式实现，使椭圆曲线密码学（ECC）实际可行。ECC广泛应用于区块链、数字签名等领域，提供高效安全的加密方案。理解椭圆曲线有助于把握现代密码学的前沿发展，尤其对AI系统的安全通信至关重要。

原文链接：Hacker News

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