Convert Decimal Number 509559809 to a Message: Private Key and Public Key Explanation

How can you convert the decimal number 509559809 to a message using the private key and public key provided?

Private and Public Key Explanation

To convert the decimal number 509559809 to a message, you will need the private key and public key provided. The public key is represented as \( N=14781585251 \) and \( b=101 \), while the private key can be either 23 or 835393901. It is also mentioned that you may convert the decimal number to binary first or hexadecimal before proceeding with the conversion.

Conversion Steps

1. Convert Decimal Number to Binary:
- Divide the decimal number 509559809 by 2 and write down the remainder.
- Continue dividing the quotient by 2 and writing down the remainders until the quotient becomes 0.
- Read the sequence of remainders from the bottom up to get the binary representation of the decimal number.

Example:
Decimal number: 509559809
Binary representation: 11110000110001000000000000
2. Convert Binary Representation to Message:
- Split the binary representation into groups of 8 digits.
- Convert each group of 8 digits to its corresponding ASCII character.
- Concatenate the ASCII characters to form the message.

Example:
Binary representation: 11110000110001000000000000
Message: "4CP\0\0\1"
By following these steps, the decimal number 509559809 can be converted to the message "4CP\0\0\1" using the private key, public key, and the conversion process described above.

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