Non-malleable Reductions and Applications
Divesh Aggarwal, Yevgeniy Dodis, Tomasz Kazana, Maciej Obremski · 2015
Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs [DPW10], provide a useful message integrity guarantee in situations where traditional error-correction (and even error-detection) is impossible; for example, when the attacker can completely overwrite the encoded message. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely "unrelated value". Although such codes do not exist if the family of "tampering functions" cF allowed to modify the original codeword is completely unrestricted, they are known to exist for many broad tampering families cF. The family which received the most attention [DPW10,LL12,DKO13,ADL14,CG14a,CG14b] is the family of tampering functions in the so called (2-part) split-state model: here the message x is encoded into two shares L and R, and the attacker is allowed to arbitrarily tamper with each L and R individually. Despite this attention, the following problem remained open: Build efficient, information-theoretically secure non-malleable codes in the split-state model with constant encoding rate: |L|=|R|=O(|x|).