Cryptography Reference
In-Depth Information
In most cases, they have either practical drawbacks, such as very long keys (some-
times in the range of several megabytes), or the cryptographic strength is not well
understood. Since about 2005, there has been growing interest in the cryptographic
community in such asymmetric schemes. This is in part motivated by the fact that
no quantum computing attacks are currently known against these four families of
alternative asymmetric schemes. This is in contrast to RSA, discrete logarithm, and
elliptic curve schemes and their variants, which are all vulnerable to attacks using
quantum computers [153]. Even though it is not clear whether quantum computers
will ever exist (the most optimistic estimates state that they are still several decades
away), the alternative public-key algorithms are at times collectively referred to as
post-quantum cryptography
. A recent topic [18] and a new workshop series [36, 35]
provide more information about this area of active research.
6.5 Lessons Learned
Public-key algorithms have capabilities that symmetric ciphers don't have, in
particular digital signature and key establishment functions.
Public-key algorithms are computationally intensive (a nice way of saying that
they are
slow
), and hence are poorly suited for bulk data encryption.
Only three families of public-key schemes are widely used. This is considerably
fewer than in the case of symmetric algorithms.
The extended Euclidean algorithm allows us to compute modular inverses quickly,
which is important for almost all public-key schemes.
Euler's phi function gives us the number of elements smaller than an integer
n
that are relatively prime to
n
. This is an important function for the RSA crypto
scheme.
