Non-malleable codes (NMCs) protect sensitive data against degrees of
corruption that prohibit error detection, ensuring instead that a corrupted
codeword decodes correctly or to something that bears little relation to the
original message. The split-state model, in which codewords consist of two
blocks, considers adversaries who tamper with either block arbitrarily but
independently of the other. The simplest construction in this model, due to
Aggarwal, Dodis, and Lovett (STOC'14), was shown to give NMCs sending k-bit
messages to O(k7)-bit codewords. It is conjectured, however, that the
construction allows linear-length codewords. Towards resolving this conjecture,
we show that the construction allows for code-length O(k5). This is achieved
by analysing a special case of Sanders's Bogolyubov-Ruzsa theorem for general
Abelian groups. Closely following the excellent exposition of this result for
the group F2n by Lovett, we expose its dependence on p for the
group Fpn, where p is a prime