In reality, even the full 256 bits range and beyond work For Example,  using 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, we get the address that is valid. The fact that you can derive a public address from a private key which is outside of valid range of 78win Trang private keys doesn't make it valid or useful. Normally a properly programmed wallet should reject such private keys. You can try with 78win Trang Testnet3 or Testnet4 how far you get. At least that way you don't risk loosing valuable coins. A quick test at bitaddress.org makes it reject above cited invalid private key. I agree. A clear example is that BIP32 or BIP39 don't use mod n; they simply invalidate it. Any numerical key greater than N (the order of the curve) is modified by mod n to always remain within the curve. This is what I explained to the OP in my clock analogy. Technically, there is no number greater than N on the elliptic curve; it is only an illusion. example: python r: 432420386565659656852420866394968145598 Pk: 432420386565659656852420866394968145598 Pk HEX: 0x000000000000000000000000000000014551231950b75fc4402da1732fc9bebe wif: KwDiBf89QgGbjEhKnhXJuH7grrzmjVFJVSqqLimWN6cB6k6v8AAF cPub: 039166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606af uPub: 049166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606aff181eb966be4a cb5cff9e16b66d809be94e214f06c93fd091099af98499255e7 H160: f5f5c490b6d86d83fda2143ebfab443f51bd3ebd C_Addr: Although trying to import the private key into many software programs will give you an error because it's larger than the order (it's just a redundant representation of a much smaller one), it's always possible to recover the real private key by applying the modulo. Most wallets don't allow you to do this because you could accidentally generate a very long private key whose modulo n is a vulnerable private key of just a few bits, like the one in the example.
In reality, even the full 256 bits range and beyond work For Example,  using 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, we get the address that is valid. The fact that you can derive a public address from a private key which is outside of valid range of 78win Trang private keys doesn't make it valid or useful. Normally a properly programmed wallet should reject such private keys. You can try with 78win Trang Testnet3 or Testnet4 how far you get. At least that way you don't risk loosing valuable coins. A quick test at bitaddress.org makes it reject above cited invalid private key. I agree. A clear example is that BIP32 or BIP39 don't use mod n; they simply invalidate it. Any numerical key greater than N (the order of the curve) is modified by mod n to always remain within the curve. This is what I explained to the OP in my clock analogy. Technically, there is no number greater than N on the elliptic curve; it is only an illusion. example: python r: 432420386565659656852420866394968145598 Pk: 432420386565659656852420866394968145598 Pk HEX: 0x000000000000000000000000000000014551231950b75fc4402da1732fc9bebe wif: KwDiBf89QgGbjEhKnhXJuH7grrzmjVFJVSqqLimWN6cB6k6v8AAF cPub: 039166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606af uPub: 049166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606aff181eb966be4a cb5cff9e16b66d809be94e214f06c93fd091099af98499255e7 H160: f5f5c490b6d86d83fda2143ebfab443f51bd3ebd C_Addr: Although trying to import the private key into many software programs will give you an error because it's larger than the order (it's just a redundant representation of a much smaller one), it's always possible to recover the real private key by applying the modulo. Most wallets don't allow you to do this because you could accidentally generate a very long private key whose modulo n is a vulnerable private key of just a few bits, like the one in the example.

In reality, even the full 256 bits range and beyond work For Example,  using 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, we get the address that is valid. The fact that you can derive a public address from a private key which is outside of valid range of 78win Trang private keys doesn't make it valid or useful. Normally a properly programmed wallet should reject such private keys. You can try with 78win Trang Testnet3 or Testnet4 how far you get. At least that way you don't risk loosing valuable coins. A quick test at bitaddress.org makes it reject above cited invalid private key. I agree. A clear example is that BIP32 or BIP39 don't use mod n; they simply invalidate it. Any numerical key greater than N (the order of the curve) is modified by mod n to always remain within the curve. This is what I explained to the OP in my clock analogy. Technically, there is no number greater than N on the elliptic curve; it is only an illusion. example: python r: 432420386565659656852420866394968145598 Pk: 432420386565659656852420866394968145598 Pk HEX: 0x000000000000000000000000000000014551231950b75fc4402da1732fc9bebe wif: KwDiBf89QgGbjEhKnhXJuH7grrzmjVFJVSqqLimWN6cB6k6v8AAF cPub: 039166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606af uPub: 049166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606aff181eb966be4a cb5cff9e16b66d809be94e214f06c93fd091099af98499255e7 H160: f5f5c490b6d86d83fda2143ebfab443f51bd3ebd C_Addr: Although trying to import the private key into many software programs will give you an error because it's larger than the order (it's just a redundant representation of a much smaller one), it's always possible to recover the real private key by applying the modulo. Most wallets don't allow you to do this because you could accidentally generate a very long private key whose modulo n is a vulnerable private key of just a few bits, like the one in the example.

In reality, even the full 256 bits range and beyond work For Example,  using 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF, we get the address that is valid. The fact that you can derive a public address from a private key which is outside of valid range of 78win Trang private keys doesn't make it valid or useful. Normally a properly programmed wallet should reject such private keys. You can try with 78win Trang Testnet3 or Testnet4 how far you get. At least that way you don't risk loosing valuable coins. A quick test at bitaddress.org makes it reject above cited invalid private key. I agree. A clear example is that BIP32 or BIP39 don't use mod n; they simply invalidate it. Any numerical key greater than N (the order of the curve) is modified by mod n to always remain within the curve. This is what I explained to the OP in my clock analogy. Technically, there is no number greater than N on the elliptic curve; it is only an illusion. example: python r: 432420386565659656852420866394968145598 Pk: 432420386565659656852420866394968145598 Pk HEX: 0x000000000000000000000000000000014551231950b75fc4402da1732fc9bebe wif: KwDiBf89QgGbjEhKnhXJuH7grrzmjVFJVSqqLimWN6cB6k6v8AAF cPub: 039166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606af uPub: 049166c289b9f905e55f9e3df9f69d7f356b4a22095f894f4715714aa4b56606aff181eb966be4a cb5cff9e16b66d809be94e214f06c93fd091099af98499255e7 H160: f5f5c490b6d86d83fda2143ebfab443f51bd3ebd C_Addr: Although trying to import the private key into many software programs will give you an error because it's larger than the order (it's just a redundant representation of a much smaller one), it's always possible to recover the real private key by applying the modulo. Most wallets don't allow you to do this because you could accidentally generate a very long private key whose modulo n is a vulnerable private key of just a few bits, like the one in the example.