Privacy is a really hard topic nowadays in different branches; scientific or humanistic. In the political/society there are basically two models.
The first is a liberal scheme where the personal information (first entity) are encrypted and stored by a second entity, but a third entity can ask the second the plain information to execute statistics or retrieve new information (maybe with a machine learning algorithm). The first, usually, doesn't know what will happen to its data!
The second model is a closing scheme in which the first entity can decide if and which information can be used by third entities.

Privacy is the property of not identify someone from the information we have.

But we need data to achieve important scientific research.

So... what can we do?

For this reason, Cryptography create models and schemes to achieve privacy.

...and the differential?

Differential privacy is a privacy definition where we try to protect a single entity privacy with respect groups informations, in which the entity is in or not.
Knowing that someone is in a group, can disclosure some information on the first entity.
If you think about it, it should be easy to understand why is hard to be anonymous.

Homomorphic Encryption

Homomorphic encryption is a cryptographic scheme theoretically defined in 1978 by RSA's peoples and then get (almost) practical usable by Craig Gentry in 2009.

What is homomorphic encryption?

HE wants to achieve the idea of algebraic homomorphism: have the possibility to do operation on encrypted data.

The idea is brilliant: you encrypt information and then can compute things without never knowing what you are working with!
This permits to build scheme where the computation is done by a third entity (yeah, let's call it the cloud).

but

homomorphic scheme are usually not that practical IRL 😢.

DP + HE + Machine Learning

Machine learning is the millennium tool for info/pattern finding

ML is an amazing tool in which you insert a lot of data and then you ask questions and it (mathe)magically gives you patterns, informations and previsions.
But at some point, the algorithm has to work on real data and here starts all the privacy problem:

will my personal informations, used in the ML phase, hurt me and disclosure my identity?

It is, but it gets hard sometimes.
If we even want to add the differential privacy properties, all became even harder!

Block Cipher : Boolean Function

Block ciphers are fundamental primitives to build security and they have to be as secure as possible.

The security that a BC (alone) has to achieve is directly connected on how a BC is defined in the mathematical terms.

A lot of insecurity and attack that can be found are connected more on bad practices and/or computational security that it is now not more secure.

The intrinsic algebraic security is based on algebraic properties that a BC has or not. They can define mathematical attacks that can broke a cipher or not: maybe the attack is the best known but it is, still, computable infeasible.