Is there a Shortage of Primes for Cryptography?

Cryptographic algorithms often prescribe the use of primes whose length in bits is a power of 2. Recently, we proved that for m ＞ 1, there is no prime number with 2^m significant bits, exactly two of which are 0 bits. Here we generalize this theorem to impose many more restrictions on primes whose length in bits is a power of 2. No similar restrictions apply to primes of other lengths. We consider whether the restrictions on primes with length 2^m bits are so great that one should choose other lengths for primes to be used in cryptography.

並列關鍵字

Binary representation ； cryptography ； primes

被引用紀錄

Hsaio, W. H. (2015). 運用半監督式學習法之文件探勘研究 [doctoral dissertation, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2015.00317

林柏廷（2015）。基於在CIELAB色彩空間中進行模糊C均值聚類的模糊自動化對比度增強法的研發〔碩士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/CYCU.2015.00507

陳彥安（2015）。以藥物結構特性利用液相層析串聯質譜開發分析血漿中metolazone和fexofenadine濃度方法及藥動研究〔博士論文，臺北醫學大學〕。華藝線上圖書館。https://doi.org/10.6831/TMU.2015.00011

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Is there a Shortage of Primes for Cryptography?

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