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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