The **Asymmetric schemes** are based on a “** one-way function f()**”:

- Computing
is computationally easy.*y = f(x)* - Computing
is computationally infeasible.*x = f*^{-1}(y)

One way functions, in fact, are based on **mathematically hard problems** such as:

**Factoring Integers**(e.g. RSA): Given a composite integer*n*, find its prime factors.**Discrete Logarithm**(e.g. Diffie-Hellman, Elgamal & DSA): Given*a*,*y*and*m*, find*x*such that.**ax = y mod m****Elliptic Curves or EC**(e.g. ECDH & ECDSA): Generalization of discrete logarithm

**Remember:** The problems are considered mathematically hard, but no proof exists (so far).

**Note:** There are many other **public-key schemes** such as, NTRU or systems based on hidden field equations, which are not in wide spread use. Often, their security is not very well understood.

Facts about **Asymmetric Algorithms**:

**Public-key algorithms**have capabilities that symmetric ciphers do not have, in particularand__digital signature__.__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**.

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