Study on Highly Sensitive Universal Randomness Test Based on the Shift of Probability Distribution

• Project/Area Number: 16K14263
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Communication/Network engineering
• Research Institution: Meiji University (2018); The University of Tokyo (2016-2017)
• Principal Investigator: Yamamoto Hirosuke 明治大学, 研究・知財戦略機構, 研究推進員 (30136212)
• Research Collaborator: LIU Qiqiang
• Project Period (FY): 2016-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 乱数検定 / ユニバーサル乱数検定 / Maurerの乱数検定法 / Coronの乱数検定法 / 乱数 / 擬似乱数 / Maurerの検定法 / Coronの検定法 / 情報理論 / 暗号 / 複雑度

Outline of Final Research Achievements

Known universal randomness tests are based on the characteristic of entropy such that the entropy of a binary sequence becomes maximum when the sequence is truly random. However, since the derivative of the entropy is zero at the maximum point, such universal randomness tests are not sensitive to detect deviations from true random sequences. In this study, we proposed a new universal randomness test with high sensitivity. In the new test, we first transform a given binary sequence to another binary sequence with the maximum sensitivity by changing bits ‘1’ to bits `0’ randomly in a specific ratio in the given sequence. Then, we test the transformed sequence by Coron’s universal statistical test. We showed by theory and simulation that the proposed universal randomness test is very sensitive and useful.

Academic Significance and Societal Importance of the Research Achievements

多くの情報セキュリティシステムの安全性は，乱数で生成される秘密鍵に依存している．真性乱数は生成コストが高く再現性がないため，多くの場合擬似乱数が用いられている．しかし，その擬似乱数に何らかの偏りがあると，情報セキュリティシステムの安全性が保証されないため，使用している擬似乱数に偏りがないかを判定する乱数検定法が重要となる．また，偏りには非常に多くの種類が存在するため，偏り方に依存しないユニバーサルで高感度な乱数検定法が必要とされている．本研究で提案した高感度なユニバーサル乱数検定法は，従来の検定法に比べて非常に感度がよく，学術的に重要であるだけでなく，社会的意義も大きな研究成果である．

Research Products

• [Presentation] 高感度ユニバーサル乱数検定法 (2019)
  • Author(s): 山本博資，Liu Qiqiang
  • Organizer: 第３回情報理論および符号理論とその応用ワークショップ (ICA2019)
• [Presentation] Highly sensitive universal statistical test (2016)
  • Author(s): Hirosuke Yamamoto and Qiqian Liu
  • Organizer: 2016 IEEE International Symposium on Information Theory
  • Place of Presentation: Barcelona, Spein
  • Year and Date: 2016-07-10
  • Int'l Joint Research