# Tag Info

### Why do we use groups, rings and fields in cryptography?

Kindly, let me know what was the actual problem which leads us to use groups in cyptogrpahy? Well, we use groups and other similar mathematical constructs because: We found there are problems that ...
Accepted

### Why "pairings on elliptic curve" are used?

Although the question is a bit broad, I think it's an interesting one. Giving a bit of context helps with the explanations. In the 80's, many cryptographic primitives have been design, based on group ...
Accepted

### Pairing on FourQ

The facts you mention regarding the embedding degree show that FourQ is not a pairing-friendly curve, and hence you cannot compute a pairing on it efficiently. Indeed, the representation of group ...
Accepted

### Are pairings still the most efficient implementation for identity and attribute-based encryption?

I am just going to answer regarding identity-based encryption (IBE): I don't know much about the situation for attribute-based encryption. Also, I am just answering based on today's situation: recent ...

### Do I need to prove this?

I purposefully did not look at the details of the change you are proposing because whatever the change is, the answer is a resounding YES. If you make any change to a cryptographic construction, then ...

### Why do we use groups, rings and fields in cryptography?

Groups have properties which are useful for many cryptographic operations When you multiply 2 numbers in a cryptographic operation you want the result of the multiplication also to be in the same set....
Accepted

### Multilinear Pairing in Cryptography

Pairings, or bilinear maps, have indeed found a great deal of applications in crypto; hence, researchers have soon pointed out that further "degrees" of linearity (trilinear maps, etc.) would provide ...
Accepted

### How is it decided if $G_1$ and $G_2$ are two “additive” or “multiplicative” cyclic groups?

Notation is basically a free choice of the author, as they describe functionally the same. And there is no fixed definition for this. However, common practice in mathematical publications is: ...
Accepted

### BN-Curves for 256-bit symmetric security

A BN-curve over a 256-bit prime field $\mathbb{F}_p$ has, being an elliptic curve, a 256-bit group attached to it, say of order $N$. As the best known attacks take $\approx\sqrt{N}$ times, this gives ...
Accepted

### Division of two Elliptic curve points in KZG polynomial commitment scheme!

In this lecture, they use multiplicative notation for the pairing groups instead of additive notation. Thus, division is well-defined. Division is just the inverse of the group operation. The choice ...