# Aggregatable Subvector Commitment with Efficient Updates
## 5 Experimental Evaluations  
This section analyzes the performance of variable commitment schemes. We implemented the above algorithms in Python and chose the BLS12-381 curve on the py-ecc library, which is a pairing-friendly elliptic curve and an elliptic curve for polynomial commitments that provides 128-bit security. For the hardware device on which the algorithm is implemented, we use a 12 th Gen Intel (R) core (TM) i5-124000 processor, which operates at a frequency of 2.5 GHz, 16 GB of RAM.  
Comparison. Figure 2 shows a performance comparison experiment between the commitment scheme proposed in Section 3 and aSVC [3]. To ensure the fairness of the experiments, both schemes run on the same hardware platform and both use the BLS12-381 elliptic curve parameters. In the experiments, we obtained the source code of aSVC from GitHub, and also evaluated the computational efficiency of the two schemes in Python environment to obtain objective performance data. The experimental results show the performance of the two schemes in terms of time overhead for different vector lengths (i.e., \(2^{4},2^{5},2^{6},\ldots,2^{10}\)).  
**UpdateAllProofs**. The experimental results shown in Figure 2 indicate that, in terms of updating all proofs, the aSVC [3] approach exhibits superior time efficiency across various vector lengths compared to our proposed scheme. This discrepancy stems from the fact that our scheme directly invokes the OpenAll algorithm, resulting in a higher computational complexity. Therefore, improving the efficiency of proof-updating in our scheme is the aim of our future work.  
**Aggregation**. Figure 2 shows the efficiency of proof aggregation. We fixed the number of aggregated proofs at eight, and the report the time efficiency across various vector lengths. By employing the Karatsuba algorithm, our scheme significantly reduced the time overhead of the aggregation process. The results show that the time overhead for the aggregation algorithm in aSVC is approximately 2.13\(\times\) higher than that in our scheme. This significant reduction highlights the practical benefits of our scheme.  
**Verification**. Figure 2 presents the comparative performance metrics between our scheme and aSVC [3] during the verification phase of aggregated proofs. By integrating the Karatsuba algorithm into the verification process, the proposed approach significantly improves verification efficiency. Experimental results reveal that the time overhead for the verification algorithm in aSVC is approximately 1.73\(\times\) higher than that in our scheme. The results show that this significant reduction highlights the practical benefits of our scheme.  
**AddAllProofs**. Figure 2 depicts the time overhead incurred when updating all proofs after adding a vector node across different vector lengths. The results demonstrate that the time efficiency of our scheme is significantly better than that of aSVC. This is due to the fact that the aSVC scheme uses Fast Fourier Transform and Lagrange interpolation algorithms,which are closely related to the length of the vectors, and this feature implies that when adding a new vector node, the aSVC has to call the OpenAll algorithm to recalculate all the existing proofs. In contrast, our scheme uses an incremental vector node construction method, i.e., when adding a new vector node, only the incremental portion needs to be computed to achieve incremental updating of the proofs, without having to call the OpenAll algorithm to recompute all the proofs. This design reduces the computational overhead of the proof updating process and can greatly reduce the consumption of computational resources in practical applications.