1
vote
2answers
144 views

Anomalous elliptic curves over finite rings

I was wondering if it is possible to solve the discrete logarithm on an Elliptic Curve E(Z/nZ) (defined over the ring of integers modulo a composite n) with #E(Z/nZ)=n by applying a method analogous ...
0
votes
1answer
680 views

Pairing on elliptic curve

Let $E(\mathbb{F_q})$ - elliptic curve. $G_1 = E(\mathbb{F_q})[r]$. $|G_1| = r$. $k$ is minimal such $r | q^k - 1$. $\pi_q$ - $q$-power Frobenius endomorphism. $G_2 = E(\mathbb{F_{q^k}})[r] \cap ...
2
votes
0answers
544 views

Elliptic Curves and cryptography. Recommended Reading [closed]

I have been studying RSA cryptography and want to extend this to ECC. I am interested in any books on the topic, that start off with basic principles of elliptic curves as I have almost zero knowledge ...
2
votes
2answers
855 views

Weil pairing and Miller's algorithm

I'm studying Weil pairing and its applications in cryptography. I already know that it can be defined like this: $$w(P, Q) = (-1)^n\frac{f_P(Q)}{f_Q(P)}\frac{f_Q}{f_P}(\mathcal{O})$$ where ...
0
votes
1answer
601 views

Elliptic curve over finite field: scalar multiplication

I'm implementing arithmetics for elliptic curves over secp256r1 as a homework assignment. For scalar multiplication, the assignment specifically specifies that $k$ is "any hexidecimal encoded ...
10
votes
5answers
1k views

Introducing Cryptology to Undergraduates

This summer I am going to give some lectures to some REU students. I am still tossing around ideas for what I am going to talk about, but one thing I would at least like to give one or two lectures ...