Score:0

Crypto

An elliptical curve over GF(2^3) is defined as y^2+xy=x^3+ax^2+b with the given value of a= g^3 and b=1.R = P + Q, where P = (0, 1) and Q = (g^2, 1)

mazino

10/8/22, 8:53 AM

An elliptical curve over $GF(2^3)$ is defined as $y^2+xy=x^3+ax^2+b$ with the given value of $a= g^3$ and $b=1$. $R = P + Q$, where $P = (0, 1)$ and $Q = (g^2, 1)$

Can someone solve this question using an elliptical curve cryptosystem? I have tried solving it but could not do it. I need to find R.

1 + 6

elliptic-curves

kelalaka

10/8/22, 8:59 AM

Welcome to Cryptography.SE. What did you try? Hint: how many values $a$ and $b$ can take?

mazino

10/8/22, 9:07 AM

I have the answer but i am unable to understand how it came. Saw it in a textbook. Answer: We have λ = 0 and R = (g^5, g^4).

kelalaka

10/8/22, 9:12 AM

this is just a calculation of the point addition with symbolic computation. Show your steps in your question so that we can help you. Answer is not work!

fgrieu

10/8/22, 9:22 AM

@mazino: this exercise starts with a [finite field](https://en.wikipedia.org/wiki/Finite_field) with $2^3$ elements and some generator $g$. It's then defined an Elliptic Curve group formed by the $(x,y)$ with $x$ and $y$ in the field and matching the equation, plus another element for the neutral. You are asked to apply [that group's addition](https://en.wikipedia.org/wiki/Elliptic_curve#The_group_law). There's nothing elliptical involved. One difficulty is that the equation is not in the most usual form, hence you need to change that form, or use an appropriate addition formula.

mazino

10/8/22, 12:07 PM

I got my answer. I used the formulas above. Thanks for commenting.

kelalaka

10/8/22, 7:05 PM

could you write your answer and close this question?

Score:-1

Crypto

mazino

10/8/22, 7:21 PM

I used these calculated values to solve the above question

0 + 1

kelalaka

10/8/22, 8:50 PM

We have $\LaTeX$/MathJax enabled on our site. And the answer should include the steps.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: An elliptical curve over GF(2^3) is defined as y^2+xy=x^3+ax^2+b with the given value of a= g^3 and b=1.R = P + Q, where P = (0, 1) and Q = (g^2, 1)

TH: เส้นโค้งวงรีเหนือ GF(2^3) ถูกกำหนดเป็น y^2+xy=x^3+ax^2+b โดยมีค่า a= g^3 และ b=1.R = P + Q โดยที่ P = (0, 1) และ Q = (g^2, 1)

RO: O curbă eliptică peste GF(2^3) este definită ca y^2+xy=x^3+ax^2+b cu valoarea dată a= g^3 și b=1.R = P + Q, unde P = (0, 1) și Q = (g^2, 1)

RU: Эллиптическая кривая над полем GF(2^3) определяется как y^2+xy=x^3+ax^2+b с заданным значением a= g^3 и b=1.R = P + Q, где P = (0, 1) и Q = (g ^ 2, 1)

VI: Một đường cong elip trên GF(2^3) được định nghĩa là y^2+xy=x^3+ax^2+b với giá trị đã cho là a= g^3 và b=1.R = P + Q, trong đó P = (0, 1) và Q = (g^2, 1)

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