Table 3 Performance comparison
From: Group signature with time-bound keys and unforgeability of expiry time for smart cities
Schemes | Signature size | Sign cost | Verify cost |
|---|---|---|---|
[34] | 12\({\mathbb{G}}_{{1}}\) + 4\({\mathbb{Z}}_{p}\) | 28\({{\rm mul}}{\mathbb{G}}_{{1}}\) + 2\({{\rm exp}}{\mathbb{G}}_{{2}}\) + 4\({\text{P }}\) | 20\({{\rm mul}}{\mathbb{G}}_{{1}}\) + 12\({{\rm exp}}{\mathbb{G}}_{{2}}\) + 2\({{\rm mul}}{\mathbb{G}}_{T}\) + 4\({\text{P }}\) |
[23] | 12\({\mathbb{G}}_{{1}}\) + 4\({\mathbb{Z}}_{p}\) | 32\({{\rm exp}}{\mathbb{G}}_{{1}}\) + 10\({\text{P}}\) + 5\({{\rm exp}}{\mathbb{G}}_{T}\) | 10\({{\rm exp}}{\mathbb{G}}_{{1}}\) + 20\({\text{P}}\) + 7\({{\rm exp}}{\mathbb{G}}_{T}\) |
[24] | 20\({\mathbb{G}}_{{1}}\) + 4\({\mathbb{Z}}_{p}\) | 18\({{\rm exp}}{\mathbb{G}}_{{1}}\) + 2\({\text{P}}\) + 15\({{\rm exp}}{\mathbb{G}}_{T}\) | 14\({{\rm exp}}{\mathbb{G}}_{{1}}\) + 4\({\text{P}}\) + 17\({{\rm exp}}{\mathbb{G}}_{T}\) |
[29] | 5\({\mathbb{G}}_{{1}}\) + 8\({\mathbb{Z}}_{p}\) | 2\({{\rm mul}}{\mathbb{G}}_{{1}}\) + 7\({{\rm exp}}{\mathbb{G}}_{T}\) + 2\({\text{P}}\) | 5\({{\rm mul}}{\mathbb{G}}_{{1}}\) + 7\(exp{\mathbb{G}}_{T}\) + 5\({\text{P}}\) |
Our scheme | 10\({\mathbb{G}}_{{1}}\) + 3\({\mathbb{G}}_{{2}}\) + 4\({\mathbb{Z}}_{p}\) | 16\({{\rm mul}}{\mathbb{G}}_{{1}}\) + 3\({{\rm mul}}{\mathbb{G}}_{{2}}\) | 4\({{\rm mul}}{\mathbb{G}}_{{1}}\) + 12\({\text{P}}\) |