Fault Injection Analysis is seen as a powerful attack against implementations of cryptographic algorithms. Over the last two decades, researchers proposed a plethora of countermeasures to secure such implementations. However, the design process and implementation are still error-prone, complex, and manual tasks which require long-standing experience in hardware design and physical security. Moreover, the validation of the claimed security is often only done by empirical testing in a very late stage of the design process. To prevent such empirical testing strategies, approaches based on formal verification are applied instead providing the designer early feedback.In this work, we present a fault verification framework to validate the security of countermeasures against fault-injection attacks designed for ICs. The verification framework works on netlist-level, parses the given digital circuit into a model based on Binary Decision Diagrams, and performs symbolic fault injections. This verification approach constitutes a novel strategy to evaluate protected hardware designs against fault injections offering new opportunities as performing full analyses under a given fault models.Eventually, we apply the proposed verification framework to real-world implementations of well-established countermeasures against fault-injection attacks. Here, we consider protected designs of the lightweight ciphers CRAFT and LED-64 as well as AES. Due to several optimization strategies, our tool is able to perform more than 90 million fault injections in a single-round CRAFT design and evaluate the security in under 50 min while the symbolic simulation approach considers all 2128 primary inputs.
BIKE is a Key Encapsulation Mechanism selected as an alternate candidate in NIST’s PQC standardization process, in which performance plays a significant role in the third round. This paper presents FPGA implementations of BIKE with the best area-time performance reported in literature. We optimize two key arithmetic operations, which are the sparse polynomial multiplication and the polynomial inversion. Our sparse multiplier achieves time-constancy for sparse polynomials of indefinite Hamming weight used in BIKE’s encapsulation. The polynomial inversion is based on the extended Euclidean algorithm, which is unprecedented in current BIKE implementations. Our optimized design results in a 5.5 times faster key generation compared to previous implementations based on Fermat’s little theorem.Besides the arithmetic optimizations, we present a united hardware design of BIKE with shared resources and shared sub-modules among KEM functionalities. On Xilinx Artix-7 FPGAs, our light-weight implementation consumes only 3 777 slices and performs a key generation, encapsulation, and decapsulation in 3 797 μs, 443 μs, and 6 896 μs, respectively. Our high-speed design requires 7 332 slices and performs the three KEM operations in 1 672 μs, 132 μs, and 1 892 μs, respectively.
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Physical attacks, including passive Side-Channel Analysis and active Fault Injection Analysis, are considered among the most powerful threats against physical cryptographic implementations. These attacks are well known and research provides many specialized countermeasures to protect cryptographic implementations against them. Still, only a limited number of combined countermeasures, i.e., countermeasures that protect implementations against multiple attacks simultaneously, were proposed in the past. Due to increasing complexity and reciprocal effects, design of efficient and reliable combined countermeasures requires longstanding expertise in hardware design and security. With the help of formal security specifications and adversary models, automated verification can streamline development cycles, increase quality, and facilitate development of robust cryptographic implementations.In this work, we revise and refine formal security notions for combined protection mechanisms and specifically embed them in the context of hardware implementations. Based on this, we present the first automated verification framework that can verify physical security properties of hardware circuits with respect to combined physical attacks. To this end, we conduct several case studies to demonstrate the capabilities and advantages of our framework, analyzing secure building blocks (gadgets), S-boxes build from Toffoli gates, and the ParTI scheme. For the first time, we reveal security flaws in analyzed structures due to reciprocal effects, highlighting the importance of continuously integrating security verification into modern design and development cycles.
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