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Cryptographic Hardware and Embedded Systems - CHES 2013

Volume 8086 of the series Lecture Notes in Computer Science pp 435-452

Using Bleichenbacher”s Solution to the Hidden Number Problem to Attack Nonce Leaks in 384-Bit ECDSA

  • Elke De MulderAffiliated withCryptography Research, Inc.
  • , Michael HutterAffiliated withCryptography Research, Inc.Institute for Applied Information Processing and Communications (IAIK), Graz University of Technology
  • , Mark E. MarsonAffiliated withCryptography Research, Inc.
  • , Peter PearsonAffiliated withCryptography Research, Inc.

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Abstract

In this paper we describe an attack against nonce leaks in 384-bit ECDSA using an FFT-based attack due to Bleichenbacher. The signatures were computed by a modern smart card. We extracted the low-order bits of each nonce using a template-based power analysis attack against the modular inversion of the nonce. We also developed a BKZ-based method for the range reduction phase of the attack, as it was impractical to collect enough signatures for the collision searches originally used by Bleichenbacher. We confirmed our attack by extracting the entire signing key using a 5-bit nonce leak from 4000 signatures.

Keywords

Side Channel Analysis ECDSA Modular Inversion Hidden Number Problem Bleichenbacher FFT LLL BKZ