• Honam Mathematical Journal
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• v.34 no.1
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• pp.93-101
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• 2012

Let $E_A^B$ denote the elliptic curve $E_A^B:y^2=x^3+Ax+B$. In this paper, we calculate the number of points on elliptic curves $E_A^0:y^2=x^3+Ax$ over $\mathbb{F}_p$ mod 24. For example, if $p{\equiv}1$ (mod 24) is a prime, $3t^2{\equiv}1$ (mod p) and A(-1 + 2t) is a quartic residue modulo p, then the number of points in $E_A^0:y^2=x^3+Ax$ is congruent to 0 modulo 24.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.591-611
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• 2001

In this paper, we classify elliptic curve by isomorphism classes over some finite fields. We consider finite field as a quotient ring, saying $\mathbb{Z}[i]/{\pi}\mathbb{Z}[i]$ where $\pi$ is a prime element in $\mathbb{Z}[i]$. Here $\mathbb{Z}[i]$ is the ring of Gaussian integers.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.485-489
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• 2006

In this paper, we slightly improve the Baby-step Giant-step for certain elliptic curves. This method gives the running time improvement of $200\%$ in precomputation (Baby-step) and requires half as much storage as the original Baby-step Giant-step method.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.433-447
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• 2013

In this paper, we calculate the number of points on elliptic curves $y^2=x^3+Ax$ over $F_{p^r}$ modulo 24. This is a generalization of [8], [9] and [16].

• ETRI Journal
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• v.32 no.3
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• pp.362-369
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• 2010

While the elliptic curve cryptosystem (ECC) is getting more popular in securing numerous systems, implementations without consideration for side-channel attacks are susceptible to critical information leakage. This paper proposes new power attack countermeasures for ECC over Koblitz curves. Based on some special properties of Koblitz curves, the proposed methods randomize the involved elliptic curve points in a highly regular manner so the resulting scalar multiplication algorithms can defeat the simple power analysis attack and the differential power analysis attack simultaneously. Compared with the previous countermeasures, the new methods are also noticeable in terms of computational cost.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.155-163
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• 2012

Let E be an elliptic curve over $\mathbb{Q}$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the $\mathbb{Z}_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.437-449
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• 2009

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.207-208
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• 2007

In this work, authors considered a result concerning elliptic curves $y^2=x^3+cx$ over $\mathbb{F}_p$ mod 8, given at [1]. They noticed that there should be a slight change at this result. They give counterexamples and the correct version of the result.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.771-780
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• 2012

We study biminimal curves in 2-dimensional Riemannian manifolds of constant curvature.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.745-757
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• 2020

A set {a₁, a₂, …, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves E_k constructed by a Diophantine triple {F_2k, F_2k+2, 4F_2k+1F_2k+2F_2k+3}, and find all integer points on the elliptic curve under assumption that rank(E_k(ℚ)) = 2.