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Is the G of the elliptic curve the same for Bitcoin and Ethereum? If yes, then why can't we send bitcoin and ether to same public address? If no, then what's the reason behind implementing it like that? If they use the same method, then one can send both coins to same public address, right?

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Is the G in elliptical curve same for bitcoin and ethereum?

Yes Ethereum also uses the secp256k1 curve that is defined using the generator point:

Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8

If yes then why can't we send bitcoin and ethereum to same public address?

For a number of reasons. Firstly, Bitcoin and Ethereum define addresses differently. Bitcoin uses the bech32 format starting bc1 and Ethereum uses a hexadecimal string starting 0x. Secondly, Bitcoin addresses contain a checksum at the end of the address (to flag incorrectly typed addresses) whilst Ethereum addresses don't. Thirdly, Ethereum only encodes the last 20 bytes of the public key into the address. Fourthly it is not just a raw public key that is encoded in a Bitcoin address. Bitcoin uses a scripting language "Script" that it uses to outline the conditions needed for the coins to move which generally includes requiring at least one signature associated with a particular public key. These conditions are baked into the address.

So yes don't try sending Bitcoin and Ethereum to the same address, you will lose your coins.

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    The most important reason is that they are simply separate unconnected systems. Even if they used the same addresses, and the same scripting system, separate systems can't interact. They're just different currencies, protected by similar cryptography. Jul 26, 2022 at 12:14
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    The way I understood the question was he wanted to send Bitcoin and Ether to the same address so the Bitcoin system told him his Bitcoin "balance" on that address and the Ethereum system told him is Ether "balance" on that address. That is theoretically possible (assuming addresses were defined exactly the same on both systems) if the Bitcoin system wasn't aware of the Ethereum system and vice versa? Jul 26, 2022 at 12:22
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    Ah, that's fair. I had interpreted the question as "why can't I send my BTC to my ETH wallet, or vice verse, if they use the same cryptography?", but your interpretation may make more sense. We'll need to wait for OP. Jul 26, 2022 at 12:25
  • Another reason why BTC/ETH transactions can't be intermingled: Bitcoin has a UTXO-based system, but Ethereum doesn't use UTXOs at all and just hardcodes the address balance into the blockchain. May 22, 2023 at 6:42
  • @Zenul_Abidin The difference in accounting models does introduce interoperability challenges but is not specifically related to the Elliptic Curve Generator point relevant to this question.
    – Poseidon
    May 22, 2023 at 20:26
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According to the other answer they do share the same G, however there is a slight difference between the term address and the term public key. An address generally is derived from a public key. The public key is a pair of coordinates that we get from multiplying with the curve Generator. Because that is the case, technically it may be possible for you to use the same public key on both Bitcoin and Ethereum, but this does not imply you can use the same address. That is because an address takes a public key runs it through somewhat of a one-way function. This one-way function is fundamentally different on Bitcoin and Ethereum, because neither network should have to build software to support all the upgrades for the opposing network.

Since they are completely different networks and scripting systems, simply sending Bitcoin to an ETH address will not succeed. Furthermore since interoperability between the two systems is also not a fundamental focus, there is little effort to create a wallet that would represent a valid address for both chains derived from the same public key, even though it might technically be possible.

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