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 -