Dear Salah,

Where is your question?

Did you mean:

Can we apply elliptic curve cryptography over special algebras?

In fact, elliptic curves are useful for their algebraic advantages where solutions have a nice algebraic structure as a group.

So to keep such properties, you need to use the algebra that preserves the basic structure of the elliptic curve, for example, Elliptic curves over finite fields: E(Fq ).

Concerning B-algebra, in general, are not groups so it is not applicable in this domain unless you should study the connections between B-algebra and groups.

Wish you good luck to find a way.

Best regards

Thank you Kaddoura,

yes, I Know that EC work on the properties of group, but B-algbra not group , but I will propose may develop the properties of EC ( or similar) over special algebra ( like B-algebra), to reduce the condition and properties.

I think there exist, but it is now secrete.

thankk

Dear Salah,

The elliptic curve definition requires a group structure.

It is a must.

Best regards

Dear Kaddoura ,

yes, must now EC define on Group, but, this structure it's old, and the conditions of group are difficult on the system, but the new algebra like B, BCI, BH, BCH, BCK, and BF algebras, easy on the system satisfy the condition of one of previous algebras. when representation of group, or ring we need special operation isomorphic, may there exist difficult to representation group, or ring, for non-commutative cryptography, and this problem from the definition of group or ring.

thank you.

Dear Salah,

Could you please support your claim by a reference ?

Best regards