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10.1109-TIT.2022.3174008 |
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|a 00189448 (ISSN)
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|a On the Information-theoretic Security of Combinatorial All-or-nothing Transforms
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|b Institute of Electrical and Electronics Engineers Inc.
|c 2022
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|a 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. IEEE
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|a All or nothings
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|a Brute-force attack
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|a Cryptography
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|a Electronic mail
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|a Information security
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|a Information- theoretic securities
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|a Information theory
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|a Perfect securities
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|a Pre-processing techniques
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|a Probability distribution
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|a Probability distributions
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|a Probability: distributions
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|a Random variables
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|a Security
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|a Security
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|a Security of data
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|a Security properties
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|a Transforms
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|a Unconditionally secure
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|a Upper bound
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|a Upper Bound
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|a Akao, S.
|e author
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|a Esfahani, N.N.
|e author
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|a Gu, Y.
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|a Miao, Y.
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|a Sakurai, K.
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|t IEEE Transactions on Information Theory
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|z View Fulltext in Publisher
|u https://doi.org/10.1109/TIT.2022.3174008
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