## In this analysis, Michael A. Popov, Director Researcher at Prime States Quantum Lab looks at the future trends and applications of the CRISPR Cas9 tool

It could be difficult to explain simply why in the last 5 years mathematical cryptography community and community of researchers of CRISPR immunity have been working independently on a very similar ( If not the same ) problem. The problem of collision and pre – image resistance of the hash functions by CRISPR antiviral defence mechanism. Both mathematicians and CRISPR researchers describe intuitively the same attacks on hash functions which have been targeting the collision and preimage resistance properties.

The goal of my review, thus, hence, is to bridge the results obtained by the two communities and to define some future trends in this new and strangly “unconscious” area of genome editing having direct applications in personalized medicine.

*Hash functions : preimage and collision resistance.*

Hash functions are compressing functions, mapping messages of large size ( say, invading DNA type ) to hash values of small constant size ( for example, crRNA message in CRISP-cas systems ).

Mathematicians had found that hash functions must be collision – resistant ( I.e. it is hard ( but not impossible ) to find collision *produced self – targeting * when a couple of messages (crRNA and crRNA *) such that

* Hash(crRNA) = Hash (crRNA*) ).*

Following mathematicians, hash functions must be also preimage – resistant.This means for essentially all pre-specified outputs ( for example crRNA message in CRISP-cas systems ) it is computationally infeasible to find any input or unique conditions of crRNA biogenesis ( preimage )in the given cell at all such that.

*Hash(crRNA) = h*

When given any h for which a corresponding input is not known. It is very important because CRISPR immunity contains the challenge that the phage attacker is ” asked to solve” what should not be known in advance.

In some formal sense, usual definitions of preimage resistance include mathematical randomness. Theorists Rogaway and Shrimpton distinguish 3 cases of preimage resistance: *aPre* cases when the attacker challenge is random but Key is fixed, *ePre* case when Key is random but the attacker challenge is fixed and * Pre *cases when both attacker challenge and the Key of such coding “theory” are random.

In the CRISPR Cryptanalysis context the requirement of being random ( exactly speaking – pseudorandom ) seems much stronger than collision resistance. In both mathematical cryptography community and genome editing community preimage and collision resistance have became the most popular security notions for hash functions. Read more **here**.