What happens if such solution is found?
Nothing. Anybody finding it would keep silent. The incentive to not spill out the secret is just too big.
Is there any alternatives to replace ECC?
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
| Name | PrivK | PubK | Sig | Security | PubK | Sig | block | average |
| | bytes | bytes | bytes | bits | *secp | *secp | *secp | block MB |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
| secp256k1 | 32 | 32 | 64 | 128 | 1.0 | 1.0 | 1.0 | 1.3 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
| RSA 2048 | 512 | 256 | 256 | 112 | 8.0 | 4.0 | 6.0 | 7.8 |
| RSA 3072 | 768 | 384 | 384 | 128 | 12.0 | 6.0 | 9.0 | 11.7 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
| Dilithium2 | 2528 | 1312 | 2420 | 128 | 41.0 | 37.8 | 39.4 | 51.2 |
| Dilithium3 | 4000 | 1952 | 3293 | 192 | 61.0 | 51.5 | 56.2 | 73.1 |
| Dilithium5 | 4864 | 2592 | 4595 | 256 | 81.0 | 71.8 | 76.4 | 99.3 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
| Falcon-512 | 1281 | 897 | 666 | 128 | 28.0 | 10.4 | 19.2 | 25.0 |
| Falcon-1024 | 2305 | 1793 | 1280 | 256 | 56.0 | 20.0 | 38.0 | 49.4 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
| Sphincs+ | 64 | 32 | 7856 | 128 | 1.0 | 122.8 | 61.9 | 80.5 |
| Sphincs+ | 96 | 48 | 16224 | 192 | 1.5 | 253.5 | 127.5 | 165.8 |
| Sphincs+ | 128 | 64 | 29792 | 256 | 2.0 | 465.5 | 233.8 | 303.9 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|