Breaking Ed25519 in WolfSSL

Ed25519 is an instance of the Elliptic Curve based signature scheme EdDSA that was recently introduced to solve an inconvenience of the more established ECDSA. Namely, both schemes require the generation of a random value (scalar of the ephemeral key pair) during the signature generation process and the secrecy of this random value is critical for security: knowledge of one such a random value, or partial knowledge of a series of them, allows reconstructing the signer\u27s private key. In ECDSA it is not specified how to generate this random value and hence implementations critically rely on the quality of random number generators and are challenging to implement securely. EdDSA removes this dependence by deriving the secret deterministically from the message and a long-term auxiliary key using a cryptographic hash function. The feature of determinism has received wide support as enabling secure implementations and in particular deployment of Ed25519 is spectacular. Today Ed25519 is used in numerous security protocols, networks and both software and hardware security products e.g. OpenSSH, Tor, GnuPG etc. In this paper we show that in use cases where power or electromagnetic leakage can be exploited, exactly the mechanism that makes EdDSA deterministic complicates its secure implementation. In particular, we break an Ed25519 implementation in WolfSSL, which is a suitable use case for IoT applications. We apply differential power analysis (DPA) on the underlying hash function, SHA-512, requiring only 4000 traces. Finally, we present a tweak to the EdDSA protocol that is cheap and effective against the described attack while keeping the claimed advantage of EdDSA over ECDSA in terms of featuring less things that can go wrong e.g. the required high-quality randomness. However, we do argue with our countermeasure that some randomness (that need not be perfect) might be hard to avoid

Double Public Key Signing Function Oracle Attack on EdDSA Software Implementations

EdDSA is a standardised elliptic curve digital signature scheme introduced to overcome some of the issues prevalent in the more established ECDSA standard. Due to the EdDSA standard specifying that the EdDSA signature be deterministic, if the signing function were to be used as a public key signing oracle for the attacker, the unforgeability notion of security of the scheme can be broken. This paper describes an attack against some of the most popular EdDSA implementations, which results in an adversary recovering the private key used during signing. With this recovered secret key, an adversary can sign arbitrary messages that would be seen as valid by the EdDSA verification function. A list of libraries with vulnerable APIs at the time of publication is provided. Furthermore, this paper provides two suggestions for securing EdDSA signing APIs against this vulnerability while it additionally discusses failed attempts to solve the issue

A modern signature scheme with message recovery: Abe--Okamoto signatures with EdDSA elements

This paper revisits the Abe--Okamoto signature scheme to present a version of their signature scheme augmented with modern best practices, with major influences taken from EdDSA. Implementation guidance is given on how to reuse existing Ed25519 code

Attacking Deterministic Signature Schemes using Fault Attacks

Many digital signature schemes rely on random numbers that are unique and non-predictable per signature. Failures of random number generators may have catastrophic effects such as compromising private signature keys. In recent years, many widely-used cryptographic technologies adopted deterministic signature schemes because they are presumed to be safer to implement. In this paper, we analyze the security of deterministic ECDSA and EdDSA signature schemes and show that the elimination of random number generators in these schemes enables new kinds of fault attacks. We formalize these attacks and introduce practical attack scenarios against EdDSA using the Rowhammer fault attack. EdDSA is used in many widely used protocols such as TLS, SSH and IPSec, and we show that these protocols are not vulnerable to our attack. We formalize the necessary requirements of protocols using these deterministic signature schemes to be vulnerable, and discuss mitigation strategies and their effect on fault attacks against deterministic signature schemes

SoK: SCA-secure ECC in software – mission impossible?

This paper describes an ECC implementation computing the X25519 keyexchange protocol on the Arm Cortex-M4 microcontroller. For providing protections against various side-channel and fault attacks we first review known attacks and countermeasures, then we provide software implementations that come with extensive mitigations, and finally we present a preliminary side-channel evaluation. To our best knowledge, this is the first public software claiming affordable protection against multiple classes of attacks that are motivated by distinct real-world application scenarios. We distinguish between X25519 with ephemeral keys and X25519 with static keys and show that the overhead to our baseline unprotected implementation is about 37% and 243%, respectively. While this might seem to be a high price to pay for security, we also show that even our (most protected) static implementation is at least as efficient as widely-deployed ECC cryptographic libraries, which offer much less protection

The Side-Channel Metrics Cheat Sheet

Side-channel attacks exploit a physical observable originating from a cryptographic device in order to extract its secrets. Many practically relevant advances in the field of side-channel analysis relate to security evaluations of cryptographic functions and devices. Accordingly, many metrics have been adopted or defined to express and quantify side-channel security. These metrics can relate to one another, but also conflict in terms of effectiveness, assumptions and security goals. In this work, we review the most commonly used metrics in the field of side-channel analysis. We provide a self-contained presentation of each metric, along with a discussion of its limitations. We practically demonstrate the metrics on examples of relevant implementations of the Advanced Encryption Standard (AES), and make the software implementation of the presented metrics available to the community as open source. This work, being beyond a survey of the current status of metrics, will allow researchers and practitioners to produce a well-informed security evaluation through a better understanding of its supporting and summarizing metrics

Fault attacks on RSA and elliptic curve cryptosystems

This thesis answered how a fault attack targeting software used to program EEPROM can threaten hardware devices, for instance IoT devices. The successful fault attacks proposed in this thesis will certainly warn designers of hardware devices of the security risks their devices may face on the programming leve

Side-Channel Analysis and Cryptography Engineering : Getting OpenSSL Closer to Constant-Time

As side-channel attacks reached general purpose PCs and started to be more practical for attackers to exploit, OpenSSL adopted in 2005 a flagging mechanism to protect against SCA. The opt-in mechanism allows to flag secret values, such as keys, with the BN_FLG_CONSTTIME flag. Whenever a flag is checked and detected, the library changes its execution flow to SCA-secure functions that are slower but safer, protecting these secret values from being leaked. This mechanism favors performance over security, it is error-prone, and is obscure for most library developers, increasing the potential for side-channel vulnerabilities. This dissertation presents an extensive side-channel analysis of OpenSSL and criticizes its fragile flagging mechanism. This analysis reveals several flaws affecting the library resulting in multiple side-channel attacks, improved cache-timing attack techniques, and a new side channel vector. The first part of this dissertation introduces the main topic and the necessary related work, including the microarchitecture, the cache hierarchy, and attack techniques; then it presents a brief troubled history of side-channel attacks and defenses in OpenSSL, setting the stage for the related publications. This dissertation includes seven original publications contributing to the area of side-channel analysis, microarchitecture timing attacks, and applied cryptography. From an SCA perspective, the results identify several vulnerabilities and flaws enabling protocol-level attacks on RSA, DSA, and ECDSA, in addition to full SCA of the SM2 cryptosystem. With respect to microarchitecture timing attacks, the dissertation presents a new side-channel vector due to port contention in the CPU execution units. And finally, on the applied cryptography front, OpenSSL now enjoys a revamped code base securing several cryptosystems against SCA, favoring a secure-by-default protection against side-channel attacks, instead of the insecure opt-in flagging mechanism provided by the fragile BN_FLG_CONSTTIME flag