# Secure ECDSA SRAM-PUF Based on Universal Single/Double Scalar Multiplication Architecture
## Appendix A Soft-Decision SRAM-PUF Based on Reed-Muller Codes
Subsequently, the main loop is initiated and is entirely controlled based on these flag signals to execute PA and PD. Each round of iteration involves two PAs and one PD. Therefore, the iteration process is completely uniform, making it resilient against some power analysis attacks. Moreover, since the differential relationships always hold throughout each round of iteration, the simplified forms in Equations (A9) and (A10) can consistently be utilized. ## Appendix D Custom ECDSA Signature and Verification
```
0:\(d\), \(m\) and \(n\). 0:\(x_{p}\) and \(s^{-1}\) mod \(n\). 1:while\(s^{-1}\) mod \(n\
eq 0\)do
2:while\(x_{p}\
eq 0\)do
3: Select \(k\) from 1 to \(n-1\) randomly;
4:\(P=kG=(x_{p},y_{p})\);
5:endwhile
6:\(Z=HASH(m)\);
7:\(s^{-1}\) mod \(n=k(z+rd)^{-1}\) mod \(n\);
8:endwhile Return:\(x_{p}\) and \(s^{-1}\) mod \(n\). ```
**Algorithm A6** Custom ECDSA Signature \(cusECDSA\_SIG\)
```
0:\(x_{p}\), \(x_{p}z\) mod \(p\), \(s^{-1}\) mod \(n\), \(m\), \(H\). 0: Verification results, \(X\), \(Z\). 1:\(z=HASH(m)\);
2:\(u_{1}=s^{-1}z\) mod \(n\);
3:\(u_{2}=s^{-1}x_{p}\) mod \(n\);
4:\(P=u_{1}G+u_{2}H=(X,Z)\);
5:if\(X=x_{p}Z\)then
6: The verification passes. 7:else
8: The verification fails. 9:endif
0:\(X\) and \(Z\). ```

**Algorithm A7** Custom ECDSA Verification \(cusECDSA\_VER\)

## References

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