FPGA IMPLEMENTATION FOR ELLIPTIC CURVE CRYPTOGRAPHY OVER BINARY EXTENSION FIELD

Elliptic curve cryptography plays a crucial role in network and communication security. However, implementation of elliptic curve cryptography, especially the implementation of scalar multiplication on an elliptic curve, faces multiple challenges. One of the main challenges is side channel attacks (SCAs). SCAs pose a real threat to the conventional implementations of scalar multiplication such as binary methods (also called doubling-and-add methods). Several scalar multiplication algorithms with countermeasures against side channel attacks have been proposed. Among them, Montgomery Powering Ladder (MPL) has been shown an effective countermeasure against simple power analysis. However, MPL is still vulnerable to certain more sophisticated side channel attacks. A recently proposed modified MPL utilizes a combination of sequence masking (SM), exponent splitting (ES) and point randomization (PR). And it has shown to be one of the best countermeasure algorithms that are immune to many sophisticated side channel attacks [11]. In this thesis, an efficient hardware architecture for this algorithm is proposed and its FPGA implementation is also presented. To our best knowledge, this is the first time that this modified MPL with SM, ES, and PR has been implemented in hardware

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

MicroWalk: A Framework for Finding Side Channels in Binaries

Microarchitectural side channels expose unprotected software to information leakage attacks where a software adversary is able to track runtime behavior of a benign process and steal secrets such as cryptographic keys. As suggested by incremental software patches for the RSA algorithm against variants of side-channel attacks within different versions of cryptographic libraries, protecting security-critical algorithms against side channels is an intricate task. Software protections avoid leakages by operating in constant time with a uniform resource usage pattern independent of the processed secret. In this respect, automated testing and verification of software binaries for leakage-free behavior is of importance, particularly when the source code is not available. In this work, we propose a novel technique based on Dynamic Binary Instrumentation and Mutual Information Analysis to efficiently locate and quantify memory based and control-flow based microarchitectural leakages. We develop a software framework named \tool~for side-channel analysis of binaries which can be extended to support new classes of leakage. For the first time, by utilizing \tool, we perform rigorous leakage analysis of two widely-used closed-source cryptographic libraries: \emph{Intel IPP} and \emph{Microsoft CNG}. We analyze $15$ different cryptographic implementations consisting of $112$ million instructions in about $105$ minutes of CPU time. By locating previously unknown leakages in hardened implementations, our results suggest that \tool~can efficiently find microarchitectural leakages in software binaries

Using Modular Extension to Provably Protect Edwards Curves Against Fault Attacks

International audienceFault injection attacks are a real-world threat to cryptosystems, in particular asymmetric cryptography. In this paper, we focus on countermeasures which guarantee the integrity of the computation result, hence covering most existing and future fault attacks. Namely, we study the modular extension protection scheme in previously existing and newly contributed variants of the countermeasure on elliptic curve scalar multiplication (ECSM) algorithms. We find that an existing countermeasure is incorrect and we propose new " test-free " variant of the modular extension scheme that fixes it. We then formally prove the correctness and security of modular extension: specifically, the fault non-detection probability is inversely proportional to the security parameter. Finally, we implement an ECSM protected with test-free modular extension during the elliptic curve operation to evaluate the efficient of this method on Edwards and twisted Edwards curves

On Fault-based Attacks and Countermeasures for Elliptic Curve Cryptosystems

For some applications, elliptic curve cryptography (ECC) is an attractive choice because it achieves the same level of security with a much smaller key size in comparison with other schemes such as those that are based on integer factorization or discrete logarithm. Unfortunately, cryptosystems including those based on elliptic curves have been subject to attacks. For example, fault-based attacks have been shown to be a real threat in today’s cryptographic implementations. In this thesis, we consider fault-based attacks and countermeasures for ECC. We propose a new fault-based attack against the Montgomery ladder elliptic curve scalar multiplication (ECSM) algorithm. For security reasons, especially to provide resistance against fault-based attacks, it is very important to verify the correctness of computations in ECC applications. We deal with protections to fault attacks against ECSM at two levels: module and algorithm. For protections at the module level, where the underlying scalar multiplication algorithm is not changed, a number of schemes and hardware structures are presented based on re-computation or parallel computation. It is shown that these structures can be used for detecting errors with a very high probability during the computation of ECSM. For protections at the algorithm level, we use the concepts of point verification (PV) and coherency check (CC). We investigate the error detection coverage of PV and CC for the Montgomery ladder ECSM algorithm. Additionally, we propose two algorithms based on the double-and-add-always method that are resistant to the safe error (SE) attack. We demonstrate that one of these algorithms also resists the sign change fault (SCF) attack

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

Efficient Side-Channel Aware Elliptic Curve Cryptosystems over Prime Fields

Elliptic Curve Cryptosystems (ECCs) are utilized as an alternative to traditional public-key cryptosystems, and are more suitable for resource limited environments due to smaller parameter size. In this dissertation we carry out a thorough investigation of side-channel attack aware ECC implementations over finite fields of prime characteristic including the recently introduced Edwards formulation of elliptic curves, which have built-in resiliency against simple side-channel attacks. We implement Joye\u27s highly regular add-always scalar multiplication algorithm both with the Weierstrass and Edwards formulation of elliptic curves. We also propose a technique to apply non-adjacent form (NAF) scalar multiplication algorithm with side-channel security using the Edwards formulation. Our results show that the Edwards formulation allows increased area-time performance with projective coordinates. However, the Weierstrass formulation with affine coordinates results in the simplest architecture, and therefore has the best area-time performance as long as an efficient modular divider is available