TY - GEN
T1 - Limits to non-malleability
AU - Ball, Marshall
AU - Dachman-Soled, Dana
AU - Kulkarni, Mukul
AU - Malkin, Tal
N1 - Publisher Copyright:
© Marshall Ball, Dana Dachman-Soled, Mukul Kulkarni, and Tal Malkin.
PY - 2020/1
Y1 - 2020/1
N2 - There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question: When can we rule out the existence of a non-malleable code for a tampering class F? First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes: Functions that change d/2 symbols, where d is the distance of the code; Functions where each input symbol affects only a single output symbol; Functions where each of the n output bits is a function of n − log n input bits. Furthermore, we rule out constructions of non-malleable codes for certain classes F via reductions to the assumption that a distributional problem is hard for F, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P 6⊆ NC.
AB - There have been many successes in constructing explicit non-malleable codes for various classes of tampering functions in recent years, and strong existential results are also known. In this work we ask the following question: When can we rule out the existence of a non-malleable code for a tampering class F? First, we start with some classes where positive results are well-known, and show that when these classes are extended in a natural way, non-malleable codes are no longer possible. Specifically, we show that no non-malleable codes exist for any of the following tampering classes: Functions that change d/2 symbols, where d is the distance of the code; Functions where each input symbol affects only a single output symbol; Functions where each of the n output bits is a function of n − log n input bits. Furthermore, we rule out constructions of non-malleable codes for certain classes F via reductions to the assumption that a distributional problem is hard for F, that make black-box use of the tampering functions in the proof. In particular, this yields concrete obstacles for the construction of efficient codes for NC, even assuming average-case variants of P 6⊆ NC.
KW - Average-case hardness
KW - Black-box impossibility
KW - Non-malleable codes
KW - Tamper-resilient cryptogtaphy
UR - http://www.scopus.com/inward/record.url?scp=85078052827&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85078052827&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ITCS.2020.80
DO - 10.4230/LIPIcs.ITCS.2020.80
M3 - Conference contribution
AN - SCOPUS:85078052827
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 11th Innovations in Theoretical Computer Science Conference, ITCS 2020
A2 - Vidick, Thomas
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 11th Innovations in Theoretical Computer Science Conference, ITCS 2020
Y2 - 12 January 2020 through 14 January 2020
ER -