| Title | On the Security Properties of Combinatorial All-or-nothing Transforms |
| Publication Type | Conference Paper |
| Year of Publication | 2022 |
| Authors | Gu, Yujie, Akao, Sonata, Esfahani, Navid Nasr, Miao, Ying, Sakurai, Kouichi |
| Conference Name | 2022 IEEE International Symposium on Information Theory (ISIT) |
| Keywords | Collaboration, combinatorial all-or-nothing transform, composability, compositionality, conditional entropy, cryptography, Entropy, Human Behavior, human factors, Information security, information theoretic security, Metrics, perfect security, policy-based governance, Probability distribution, pubcrawl, resilience, Resiliency, Scalability, security, Transforms, Upper bound, weak security |
| Abstract | All-or-nothing transforms (AONT) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have many applications in cryptography and information security. Later the unconditionally secure AONT 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(\textbackslashmathcalX\textbackslashmid \textbackslashmathcalY) about any t inputs \textbackslashmathcalX that is not revealed by any st outputs \textbackslashmathcalY. In particular, we establish the general lower and upper bounds on H(\textbackslashmathcalX\textbackslashmid \textbackslashmathcalY) for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases. |
| DOI | 10.1109/ISIT50566.2022.9834366 |
| Citation Key | gu_security_2022 |
On the Security Properties of Combinatorial All-or-nothing Transforms