NonMalleable Coding Against Bitwise and SplitState Tampering
Nonmalleable coding, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), aims for protecting the integrity of information against tampering attacks in situations where errordetection is impossible. Intuitively, information encoded by a nonmalleable code either decodes to the original message or, in presence of any tampering, to an unrelated message. Nonmalleable coding is possible against any class of adversaries of bounded size. In particular, Dziembowski et al. show that such codes exist and may achieve positive rates for any class of tampering functions of size at most 22αn, for any constant α ∈ [0, 1). However, this result is existential and has thus attracted a great deal of subsequent research on explicit constructions of nonmalleable codes against natural classes of adversaries.
In this work, we consider constructions of coding schemes against two wellstudied classes of tampering functions; namely, bitwise tampering functions (where the adversary tampers each bit of the encoding independently) and the much more general class of splitstate adversaries (where two independent adversaries arbitrarily tamper each half of the encoded sequence). We obtain the following results for these models.

For bittampering adversaries, we obtain explicit and efficiently encodable and decodable nonmalleable codes of length n achieving rate 1 − o(1) and error (also known as “exact security”) exp(−Ω~(n1/7)). Alternatively, it is possible to improve the error to exp(−Ω~(n)) at the cost of making the construction Monte Carlo with success probability 1−exp(−Ω(n)) (while still allowing a compact description of the code). Previously, the best known construction of bittampering coding schemes was due to Dziembowski et al. (ICS 2010), which is a Monte Carlo construction achieving rate close to .1887.

We initiate the study of seedless nonmalleable extractors as a natural variation of the notion of nonmalleable extractors introduced by Dodis and Wichs (STOC 2009). We show that construction of nonmalleable codes for the splitstate model reduces to construction of nonmalleable twosource extractors. We prove a general result on existence of seedless nonmalleable extractors, which implies that codes obtained from our reduction can achieve rates arbitrarily close to 1/5 and exponentially small error. In a separate recent work, the authors show that the optimal rate in this model is 1/2. Currently, the best known explicit construction of splitstate coding schemes is due to Aggarwal, Dodis and Lovett (ECCC TR13081) which only achieves vanishing (polynomially small) rate.