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Efficient finite field basis conversion involving a dual basis
Efficient finite field basis conversion involving a dual basis
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机译:涉及双重基础的高效有限域基础转换
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摘要
The invention provides apparatus and methods for use in basis conversion involving a dual basis, such as a dual of a polynomial basis or dual of a normal basis. The invention in an illustrative embodiment includes basis generators for generating elements of a dual of a polynomial or a normal basis of a finite field GF(qm), where q is a prime number or power of a prime number and m is an integer greater than or equal to 2. The basis generators can be used in “import” basis conversion, such as converting a representation in an external basis to a representation in an internal dual of a polynomial basis or dual of a normal basis, as part of a generate-accumulate algorithm, or in “export” basis conversion, such as converting a representation in an internal dual of a polynomial basis or dual of a normal basis to a representation in an external basis, as part of a generate-evaluate algorithm. The invention also includes basis shifters which generate a shifted version of a representation in an internal polynomial or normal basis. The basis shifters may be used in import basis conversion as part of a shift-insert algorithm, or in export basis conversion as part of a shift-extract algorithm. The basis shifters may also be used to provide alternative shift-based basis generators. The basis conversion techniques of the invention significantly increase the storage and computational efficiency of dual basis operations in cryptographic systems and other applications.
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机译:本发明提供了用于涉及双重基础的多项变换的装置和方法,所述双重基础例如是多项式基础的对偶或正常基础的对偶。在说明性实施例中,本发明包括基数生成器,该基数生成器用于生成有限域GF(q m Sup>)的多项式或正规基的对偶的元素,其中q是质数或质数的幂数字和m是大于或等于2的整数。基数生成器可用于“导入”。基本转换,例如将外部表示形式转换为多项式内部对偶形式或普通对偶形式的表示形式,作为生成累加算法的一部分,或“导出”形式。基本转换,例如将多项式内部对偶或普通对偶的表示形式转换为外部对表示形式,作为生成评估算法的一部分。本发明还包括基数移位器,其以内部多项式或正态基数生成表示的移位版本。基础移位器可在导入基础转换中用作移位插入算法的一部分,或在导出基础转换中用作移位提取算法的一部分。基础移位器还可用于提供替代的基于移位的基础生成器。本发明的基础转换技术显着提高了密码系统和其他应用中的双基础运算的存储和计算效率。
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