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 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
If you look at the average block MB, I can at least guess why Satoshi chose the secp256k1 keypairs for including their signatures in transactions, as the rest of the cryptosystems have large block-sizes that resemble Bitcoin Cash and SV. This is most likely because of the ballooning sig-bytes sizes.
These two:
| 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 |
|-------------+-------+-------+-------+----------+-------+-------+-------+----------|
are the quantum algorithms, right? Or is Dilithium also one of them?
Is there any quantum digital signature algorithm that does
not make humongous signatures?