RSA System is generally slow (but why?)

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I wouldn't express it that way. Yes RSA is relatively slow in data encryption / decryption compared to symmetric ciphers such as AES. But on the other hand RSA is relatively fast in signature verification or encryption as compared to ECC with similar levels of security. In the end it really comes down to the operation you need to perform and if there are any alternatives you can compare the system to.

The fact that RSA in general is relatively slow is due to the mathematics behind it, namely modular arithmetics and number theory. Computers nowadays, especially their ALU (arithmetic logic unit), are just not designed for being highly efficient at these kinds of operations. Why? Because general CPUs do not need to be. As the name says they are general and modular arithmetics is specific to application areas such as cryptography or chemistry for example. This makes sense if you consider that integrating modular arithmetics operations into ALUs would drastically increase the size and at the same time reduce the maximum operating frequency.

There are applications where the relatively slow RSA operations really do introduce a bottleneck to the system. Examples might be high-end systems as used in banking or e-commerce, where inefficiencies in performance can have negative financial effects. For these use cases it might make sense to consider high-speed hardware solutions in form of cryptographic co-processors or hardware accelerators. The additional cost involved for a co-processor stands in no relation to the usefulness of employment in these areas. This however is not true for cost-sensitive embedded systems for which additional hardware often cannot be justified in terms of cost-performance ratio. In the end it's always a matter of your capabilities. With unlimited resources, not only in terms of money, but also in terms of area, bandwidth or required memory, RSA systems CAN be fast.

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