On the Information-theoretic Security of Combinatorial All-or-nothing Transforms

Yujie Gu, Sonata Akao, Navid Nasr Esfahani, Ying Miao, Kouichi Sakurai

研究成果: ジャーナルへの寄稿学術誌査読


All-or-nothing transforms (AONTs) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have numerous applications in cryptography and information security. Later the unconditionally secure AONTs and their combinatorial characterization were introduced by Stinson. Informally, a combinatorial AONT is an array with the unbiased requirements and its security properties in general depend on the prior probability distribution on the inputs s-tuples. Recently, it was shown by Esfahani and Stinson that a combinatorial AONT has perfect security provided that all the inputs s-tuples are equiprobable, and has weak security provided that all the inputs s-tuples are with non-zero probability. This paper aims to explore on the gap between perfect security and weak security for combinatorial (t, s, v)-AONTs. Concretely, we consider the typical scenario that all the s inputs take values independently (but not necessarily identically) and quantify the amount of information H(X|Y) about any t inputs X that is not revealed by any s – t outputs Y. In particular, we establish the general lower and upper bounds on H(X|Y) for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases. Furthermore, the discussions are extended for the security properties of combinatorial asymmetric AONTs.

ジャーナルIEEE Transactions on Information Theory
出版ステータス印刷中 - 2022

!!!All Science Journal Classification (ASJC) codes

  • 情報システム
  • コンピュータ サイエンスの応用
  • 図書館情報学


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