Paper 2022/1274
Self Masking for Hardering Inversions
Abstract
The question whether one way functions (i.e., functions that are easy to compute but hard to invert) exist is arguably one of the central problems in complexity theory, both from theoretical and practical aspects. While proving that such functions exist could be hard, there were quite a few attempts to provide functions which are one way "in practice", namely, they are easy to compute, but there are no known polynomial time algorithms that compute their (generalized) inverse (or that computing their inverse is as hard as notoriously difficult tasks, like factoring very large integers). In this paper we study a different approach. We provide a simple heuristic, called self masking, which converts a given polynomial time computable function $f$ into a self masked version $[{f}]$, which satisfies the following: for a random input $x$, $[{f}]^{1}([{f}](x))=f^{1}(f(x))$ w.h.p., but a part of $f(x)$, which is essential for computing $f^{1}(f(x))$ is masked in $[{f}](x)$. Intuitively, this masking makes it hard to convert an efficient algorithm which computes $f^{1}$ to an efficient algorithm which computes $[{f}]^{1}$, since the masked parts are available to $f$ but not to $[{f}]$. We apply this technique on variants of the subset sum problem which were studied in the context of one way functions, and obtain functions which, to the best of our knowledge, cannot be inverted in polynomial time by published techniques.
Metadata
 Available format(s)
 Category
 Foundations
 Publication info
 Preprint.
 Keywords
 One way functions Subset sum Complexity
 Contact author(s)

cyprysp @ gmail com
dolev @ cs bgu ac il
moran @ cs technion ac il  History
 20221009: last of 4 revisions
 20220926: received
 See all versions
 Short URL
 https://ia.cr/2022/1274
 License

CC0
BibTeX
@misc{cryptoeprint:2022/1274, author = {Paweł Cyprys and Shlomi Dolev and Shlomo Moran}, title = {Self Masking for Hardering Inversions}, howpublished = {Cryptology ePrint Archive, Paper 2022/1274}, year = {2022}, note = {\url{https://eprint.iacr.org/2022/1274}}, url = {https://eprint.iacr.org/2022/1274} }