Cryptology ePrint Archive: Report 2017/627

Sliding right into disaster: Left-to-right sliding windows leak

Daniel J. Bernstein and Joachim Breitner and Daniel Genkin and Leon Groot Bruinderink and Nadia Heninger and Tanja Lange and Christine van Vredendaal and Yuval Yarom

Abstract: It is well known that constant-time implementations of modular exponentiation cannot use sliding windows. However, software libraries such as Libgcrypt, used by GnuPG, continue to use sliding windows. It is widely believed that, even if the complete pattern of squarings and multiplications is observed through a side-channel attack, the number of exponent bits leaked is not sufficient to carry out a full key-recovery attack against RSA. Specifically, 4-bit sliding windows leak only 40\% of the bits, and 5-bit sliding windows leak only 33\% of the bits.

In this paper we demonstrate a complete break of RSA-1024 as implemented in Libgcrypt. Our attack makes essential use of the fact that Libgcrypt uses the left-to-right method for computing the sliding-window expansion. We show for the first time that the direction of the encoding matters: the pattern of squarings and multiplications in left-to-right sliding windows leaks significantly more information about exponent bits than for right-to-left. We show how to incorporate this additional information into the Heninger-Shacham algorithm for partial key reconstruction, and use it to obtain very efficient full key recovery for RSA-1024. We also provide strong evidence that the same attack works for RSA-2048 with only moderately more computation.

Category / Keywords: left-to-right sliding windows, cache attack, Flush+Reload, RSA-CRT

Original Publication (in the same form): IACR-CHES-2017

Date: received 26 Jun 2017, last revised 28 Jun 2017

Contact author: authorcontact-slidingright at box cr yp to

Available format(s): PDF | BibTeX Citation

Version: 20170628:083856 (All versions of this report)

Short URL: ia.cr/2017/627