# Limitations of Modern Cryptosystems

Before exploring quantum key distribution, it is important to understand the state of modern cryptography and how quantum cryptography may address current digital cryptography limitations. Since public key cryptography involves complex calculations that are relatively slow, they are employed to exchange keys rather than for the encryption of voluminous amounts of date. For example, widely deployed solutions, such as the RSA and the Diffie-Hellman key negotiation schemes, are typically used to distribute symmetric keys among remote parties. However, because asymmetric encryption is significantly slower than symmetric encryption, a hybrid approach is preferred by many institutions to take advantage of the speed of a shared key system and the security of a public key system for the initial exchange of the symmetric key. Thus, this approach exploits the speed and performance of a symmetric key system while leveraging the scalability of a public key infrastructure.

However, public key cryptosystems such as RSA and Diffie-Hellman are not based on concrete mathematical proofs. Rather, these algorithms are considered to be reasonably secure based on years of public scrutiny over the fundamental process of factoring large integers into their primes, which is said to be “intractable”. In other words, by the time the encryption algorithm could be defeated, the information being protected would have already lost all of its value. Thus, the power of these algorithms is based on the fact that there is no known mathematical operation for quickly factoring very large numbers given today’s computer processing power.

Secondly, there is uncertainty whether a theorem may be developed in the future or perhaps already available that can factor large numbers into their primes in a timely manner. At present, there is no existing proof stating that it is impossible to develop such a factoring theorem. As a result, public key systems are thus vulnerable to the uncertainty regarding the future creation of such a theorem, which would have a significant affect on the algorithm being mathematical intractable. This uncertainty provides potential risk to areas of national security and intellectual property which require perfect security.

In sum, modern cryptography is vulnerable to both technological progress of computing power and evolution in mathematics to quickly reverse one way functions such as that of factoring large integers. If a factoring theorem were publicized or computing became powerful enough to defeat public cryptography, then business, governments, militaries and other affected institutions would have to spend significant resources to research the risk of damage and potentially deploy a new and costly cryptography system quickly.

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