QP-KEX: Classes of public-key cryptographic algorithms

CSEC has implemented two classes of this type of algorithms:

1) An already implemented in software, called QP-KEX, and inserted in the CSEC Software Libraries (see item (8) below).

2) One, more recently discovered, which has introduced in literature a new class of public-key algorithms called strongly asymmetric algorithms, and not yet implemented in software. A first work on this class was published in 2015. A second was submitted for publication on 19-2-2018.

Further innovative families of public key algorithms (PKA) are being studied.

Competitive advantages

1) The competitive advantage of the QP-KEX algorithm consists in the fact that it can produce keys of length between 256 and 300,000 bits without the need for libraries for the arithmetic of large numbers.

2) The strongly asymmetric algorithms have this feature, unique among the public-key algorithms: while for all the other public-key algorithms a breaking strategy is known, for the new algorithms it is not known and, judging by the time taken by the referee of the first work to give their (positive) response to the publication and the time taken by the referees of the second job for the same purpose, it is clear that some of the world’s best cryptanalysts (the branch of cryptography that studies the attacks on algorithms) they are committed and are trying to find such attacks. This inability to find attacks is the best proof of robustness to which a cryptographic algorithm can aspire.

Possible developments

For these reasons the strongly asymmetric algorithms have the qualities to act as candidates to be a new standard in the scenario of agreement of the public key algorithms. For them it is necessary:

1) Implement them in software.

2) Study their hardware version which, as in the flow case, will probably require radical changes in the mathematical structure.