user98008: We know that: S(Secret-Scalar) x G(Generater Point-Point(X,Y)) = Public Key
In bitcoin, what is the range of that secret can be? What can it be at most and at least? Is there a limit to it like 2^256? If yes what is the logic behind that too?

user48884: The maximum and minimum private key possible is defined by ECDSA and the curve being used. In ECDSA, the private key is an integer between 1 and n - 1, where n is the order of the generator point G. Bitcoin uses the secp256k1 curve whose generator has an order n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141, which is almost 2^256.
This means that the minimum value for a private key is 1 and the maximum is 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140. If you use an integer outside of this range, taking the modulo n of that integer will give you a value that is in the valid range (except for multiples of n for which the modulo is zero).

98008: <p>We know that: <strong>S(Secret-Scalar) x G(Generater Point-Point(X,Y)) = Public Key</strong></p>
<p>In bitcoin, what is the range of that secret can be? What can it be at most and at least? Is there a limit to it like 2^256? If yes what is the logic behind that too?</p>
 48884: <p>The maximum and minimum private key possible is defined by ECDSA and the curve being used. In ECDSA, the private key is an integer between <code>1</code> and <code>n - 1</code>, where <code>n</code> is the order of the generator point <code>G</code>. Bitcoin uses the secp256k1 curve whose generator has an order <code>n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141</code>, which is almost <code>2^256</code>.</p>
<p>This means that the minimum value for a private key is <code>1</code> and the maximum is <code>0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140</code>. If you use an integer outside of this range, taking the modulo <code>n</code> of that integer will give you a value that is in the valid range (except for multiples of <code>n</code> for which the modulo is zero).</p>
