The compact key sizes and the low computational latency of the Elliptic Curve Cryptography (ECC) family of curves sparked high interest in their integration into network protocols. The recently suggested Curve448, assuring 224-bit security, is an ideal curve choice for integrating into cryptographic libraries according to a late study on backdoors on other ECC instances compromising their security, which results in the integration of Curve448 into the TLS1.3 protocol. Curve448 and its birationally equivalent untwisted Edwards curve Ed448, used for key exchange and authentication, respectively, present a perfect fit for low-end embedded cryptographic libraries due to their minimal memory requirements. In this work, we deploy optimized Montgomery Ladder point multiplication into the widely employed IoT-focused cryptographic library wolfSSL and present side-channel robust and efficient ECDH and EdDSA based on Curve448 and Ed448. We evaluate the performance of the newly integrated architectures against the NIST recommended CortexM4 STM32F407-DK ARM-based platform. We perform thorough side-channel evaluation of the proposed Montgomery Ladder implementation via powerful TVLA analysis revealing DPA data leakage. We integrate countermeasures to protect our design, evaluate their effectiveness and analyze the latency overhead. We achieve SCA robust Curve448 and Ed448 at the cost of around 1.2MCC(1.36× the execution time). Finally, we report the performance of our fully SCA protected Curve448 and Ed448 as part of TLS1.3 wolfSSL, reporting 1.04× performance compared to the original wolfSSL code.
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Side-Channel Analysis and Countermeasure Design for Implementation of Curve448 on Cortex-M4
The highly secure Curve448 cryptographic algorithm has
been recently recommended by NIST. While this algorithm
provides 224-bit security over elliptic curve cryptography,
its implementation may still be vulnerable to physical sidechannel
attacks. In this paper, we present a speed-optimized
implementation on a 32-bit ARM Cortex-M4 platform achieving
more than 40% improvement compared to the best previous
work. Our design can perform 43 scalar multiplications
per second on an STM32F4 working at 168 MHz. At 24 MHz,
our proposed implementation takes only 3,740k clock cycles.
On the other hand, the security of Curve448 is thoroughly
evaluated to have a trade-off between performance and required
protection. We apply different effective countermeasures
to prevent a subset of side-channel and fault injection
attacks at the cost of 8%-22% overhead.
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- Award ID(s):
- 2101085
- PAR ID:
- 10425459
- Date Published:
- Journal Name:
- Hardware and Architectural Support for Security and Privacy (HASP’22)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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