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The First Rule of Cryptography … You Don’t Talk About Zero Or The Identity Element
Okay, sorry for misquoting Fight Club! Overall, the title is a little bit tongue-in-cheek, as the zero value is often a major problem in cryptography, and where we often just don’t want it to happen. It can, too, be a blind spot for security architects and developers and who implement calculations without checking for the zero value.
Why is zero such a problem? Well, to perform our cryptographic processing, we use mathematical operations, such as multiplication and division. As you should remember, when we multiply by zero, we get zero, and when we divide by it, we get infinity. These operations will reset the calculation, and no matter what we do, we can never recover any previous information from our value. We might also use exponents, and where g⁰ gives us unity.
Within our secure computations, we typically need to reverse an operation back to the original value. This often involves encrypting — performing a certain mathematical operation — and then decrypting — reversing the same mathematical operation.
For example, if we multiply a value of seven by four and add three, we can compute:
Val = 7 * 4 + 3 = 31
and, to reverse, we just subtract 3 and divide by 4:
