Elliptic curve scalar multiplication (ECSM) is a fundamental element of
pre-quantum public key cryptography, which is the predominant choice for
public key cryptography. ECSM implementations on deeply-embedded
architectures and Internet-of-nano-Things have been vulnerable to both
permanent and transient errors, as well as fault attacks. Consequently,
error detection is crucial. In this work, we present a novel
algorithm-level error detection scheme on Montgomery ladder often used
for a number of elliptic curves featuring highly efficient point
arithmetic, known as Montgomery curves. Our error detection simulations
achieve high error coverage on loop abort and scalar bit flipping fault
model utilizing binary tree data structure. Assuming n is the size of
the private key, the overhead of our error detection scheme is O(n).
Finally, we conduct a benchmark of our suggested error detection scheme
on both ARMv8 and FPGA platforms to illustrate the implementation and
resource utilization. Deployed on Cortex-A72 processors, our proposed
error detection scheme maintains a clock cycle overhead of less than
3%. Additionally, integrating our error detection approach into FPGAs,
including AMD/Xilinx Zynq Ultrascale+ and Kintex Ultrascale+, results in
comparable throughput and less than 1% increase in area compared to the
original hardware implementation. We note that we envision using the
proposed architectures in the post-quantum cryptography (PQC) based on
elliptic curves.