As Sarad said, the operations are different, XOR compared with multiply. In encryption, you can use multiplication instead of XOR if you want to. It works. The problem is, the encrypted messages will become longer than the plaintext message.

And then in decryption, if you used multiplication to encrypt, you have to use division to decrypt. Whereas if you used XOR to encrypt, you would decrypt using that same XOR operation on the encrypted text.

If you encrypt by multiplying the plaintext by a secret key of 3, let's say, then you would decrypt by dividing the encrypted symbol by 3. Instead, if you encrypt by doing x XOR 3, then you would decrypt by doing (encrypted x) XOR 3.

XOR and multiplication are different operations that are used for different purposes in encryption. XOR is used to scramble the plaintext by mixing it with a key, while multiplication is used to generate the keys and manipulate them in some encryption algorithms.

Clearly they are not. However, it is worth noting that in binary, multiplication and division can be accomplished by logical shifting. That is dependent on the modulo being used (in the normal computer case - modulo 2). Makes one want to explore other modulo cases, which are not even factors of 2. I am interested in the fractional and irrational cases. Does anyone know of any publications in this area?

No, XOR and multiplication are not the same in encryption.

XOR (exclusive or) is a binary operation that takes two input values and returns a single output value. It produces a 1 in each bit position where the corresponding bits of either but not both operands are 1. XOR is commonly used in encryption algorithms, such as the one-time pad.

On the other hand, multiplication is a mathematical operation that takes two input values and returns a single output value. In encryption, multiplication is used in some algorithms, such as the RSA algorithm.

In the context of fractional and irrational cases, XOR and multiplication are not directly applicable. Both XOR and multiplication are binary operations that operate on integers or binary data. In order to use these operations with fractional or irrational values, we would need to convert them into an appropriate format, such as fixed-point or floating-point representation.

The IEEE Standard 754 Floating Point Numbers is a widely used standard for representing floating-point numbers in computers. It specifies how floating-point numbers are encoded in binary format and how arithmetic operations are performed on them.

In the context of IEEE Standard 754 Floating Point Numbers, XOR and multiplication can be applied to the binary representations of floating-point numbers. However, the results may not always be meaningful, especially for irrational values.

For example, consider the multiplication of two irrational values, such as pi and e, represented in IEEE Standard 754 Floating Point format. The result of this multiplication would also be an irrational value, but its representation in binary format would be an approximation, subject to rounding errors. Similarly, XOR may be used to manipulate the binary representation of floating-point numbers, but its effect on the actual value represented by the binary format may not be straightforward.

XOR and multiplication have different properties, which make them suitable for different purposes in encryption. XOR is a reversible operation, meaning that applying it twice to the same value will result in the original value. Multiplication, on the other hand, is not reversible in the same sense.