Paper 2015/516

Key-Recovery Attacks on ASASA

Brice Minaud, Patrick Derbez, Pierre-Alain Fouque, and Pierre Karpman


The ASASA construction is a new design scheme introduced at Asiacrypt 2014 by Biryukov, Bouillaguet and Khovratovich. Its versatility was illustrated by building two public-key encryption schemes, a secret-key scheme, as well as super S-box subcomponents of a white-box scheme. However one of the two public-key cryptosystems was recently broken at Crypto 2015 by Gilbert, Plût and Treger. As our main contribution, we propose a new algebraic key-recovery attack able to break at once the secret-key scheme as well as the remaining public-key scheme, in time complexity 2^63 and 2^39 respectively (the security parameter is 128 bits in both cases). Furthermore, we present a second attack of independent interest on the same public-key scheme, which heuristically reduces the problem of breaking the scheme to an LPN instance with tractable parameters. This allows key recovery in time complexity 2^56. Finally, as a side result, we outline a very efficient heuristic attack on the white- box scheme, which breaks instances claiming 64 bits of security under one minute on a laptop computer.

Note: Added IACR/Springer copyright

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Publication info
A major revision of an IACR publication in ASIACRYPT 2015
ASASAAlgebraic CryptanalysisMultivariate CryptographyLPN
Contact author(s)
brice minaud @ gmail com
2015-11-02: last of 2 revisions
2015-05-29: received
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      author = {Brice Minaud and Patrick Derbez and Pierre-Alain Fouque and Pierre Karpman},
      title = {Key-Recovery Attacks on ASASA},
      howpublished = {Cryptology ePrint Archive, Paper 2015/516},
      year = {2015},
      note = {\url{}},
      url = {}
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