Explicit Construction of Global Function Fields with Many Rational Places

具有许多合理位置的全局函数域的显式构造

• 批准号: DP0558891
• 负责人: Prof John Cannon
• 金额: $ 11.09万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2005
• 资助国家: 澳大利亚
• 起止时间: 2005-04-27 至 2008-04-26
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0558891
• 关键词: Explicit; Construction; Global; Function; Fields

The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.

纠错码和密码系统的使用对我们日常生活中所依赖的许多技术设备的安全和可靠运行至关重要。本质上看不见，编码理论和密码学对于银行(ATM机、电子银行)、商业(电子商务)、国防(密码学)和娱乐(数字电视和收音机、音乐CD、DVD)都是必不可少的。虽然可以由抽象理论保证其存在的特定函数域来构造某些族的“好的”码和密码系统，但目前通常还不知道函数域的实际构造。我们的目标是缩小这一差距，使更多的“好”代码和密码系统可用于实际应用。