Degenerate Fault Attacks on Elliptic Curve Parameters in OpenSSL

Abstract

In this paper, we describe several practically exploitable fault attacks against OpenSSL's implementation of elliptic curve cryptography, related to the singular curve point decompression attacks of Blömer and Günther (FDTC2015) and the degenerate curve attacks of Neves and Tibouchi (PKC 2016). In particular, we show that OpenSSL allows to construct EC key files containing explicit curve parameters with a compressed base point. A simple single fault injection upon loading such a file yields a full key recovery attack when the key file is used for signing with ECDSA, and a complete recovery of the plaintext when the file is used for encryption using an algorithm like ECIES. The attack is especially devastating against curves with j-invariant equal to 0 such as the Bitcoin curve secp256k1, for which key recovery reduces to a single division in the base field. Additionally, we apply the present fault attack technique to OpenSSL's implementation of ECDH, by combining it with Neves and Tibouchi's degenerate curve attack. This version of the attack applies to usual named curve parameters with nonzero j-invariant, such as P192 and P256. Although it is typically more computationally expensive than the one against signatures and encryption, and requires multiple faulty outputs from the server, it can recover the entire static secret key of the server even in the presence of point validation. These various attacks can be mounted with only a single instruction skipping fault, and therefore can be easily injected using low-cost voltage glitches on embedded devices. We validated them in practice using concrete fault injection experiments on a Rapsberry Pi single board computer running the up to date OpenSSL command line tools-a setting where the threat of fault attacks is quite significant.

Understanding the Impact of IoT Security Patterns on CPU Usage and Energy Consumption on IoT Devices

“…This was crucial in establishing an encrypted connection between the sensor nodes and the database, protecting the privacy and security of the collected data. To ensure confidential exchanges, we made use of a dual encryption method, generating SSL keys (both public and private) with the help of RSA-2048 48 . Additionally, AES-256 49 was implemented to guarantee a high level of security for stored information.…”

SoK

“…Nonetheless, the practical difference between the methods in IEEE and Dragonfly seems negligible given that the probability of an "invalid" output occurring by chance is negligible. (However, it is unclear if an attack action, e.g., fault injection [95], could significantly increase the probability of the "invalid" case. )…”

“…Following this path, IEEE 1363.2 [51] generalized its SPEKE spec to allow short exponents as in DSA groups, resulting in changing 𝑓 (as noted in §3.2) to 𝑓 = 𝐻 (𝑤) 𝑘 mod 𝑝; again 𝑝 = 𝑘 • 𝑞 + 1 and 𝑘 is a co-factor. Compared with a safe-prime modulus, the probability for getting an "invalid" output by chance in a DSA group (same modulus size) increases, but remains negligible (without considering attack actions like fault injection [95]). However, in a DSA group, it now requires one exponentiation to validate a received public key.…”

Differential Fault Attack on Montgomery Ladder and in the Presence of Scalar Randomization

“…The first model considered is the skip instruction that was applied successfully in practice on RSA exponentiation with a spike injection on a microcontroller to skip a squaring [31]. It was also recently applied in the elliptic curve point decompression algorithm to make a point lie on weak curve [5,36].…”