Elliptic curves are a mathematical structure. In cryptography, it is common to use the structure $y^2 = x^3 + ax^2 + b$ over a finite field. Questions relating to elliptic curves and derived algorithms should use this tag and might also consider specific tags such as discrete-logarithm and ecdsa.
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How to calculate y value from ((y*y) mod prime) efficiently
i am working ECC-224 bit. can any one tell me, how to calculate y value from ((y*y) mod prime) efficiently for large bit numbers.
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Elliptic curve cryptography related key attacks
This question is an extension of Families of public/private keys in elliptic curve cryptography
As described above, bitcoin "type 2" deterministic wallets use a root private/public key pair, where ...
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What is the fastest elliptic curve operation f(P) in affine coordinates such that f^n(P)=P only if n is large?
I'm working with the affine representations of points of a Koblitz curve.
I've read many papers that show that computing some functions, like $f(P)=3P$ can be computed faster than the standard way. ...
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How to represent point-at-infinity in affine coordinate
In projective coordinates point-at-infinity can be identified with z=0. How to identify the point-at-infinity in affine coordinate.
Whether x=0 and y=0 can be considered as point-at-infinity in ...
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Generating non-supersingular elliptic curves for symmetric pairings
I am looking into the application of pairings in CPABE in particular. I've notice that the scheme uses a supersingular curve as the basis of the pairing. Looking through Ben Lynn's thesis for the ...
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Complex Numbers on Elliptic Curves & Usage in Tate Pairing
I'm working with understanding the internals of the Tate Pairing. I was going through an example of the curve $E: y^2 = x^3 + 3x$ over $\mathbb{F_{11}}$. The author is showing the computation of ...
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Hardware implementation of pairing
I would like to design a hardware-based accelerator for a pairing algorithm to make it faster. I know that I need to do arithmetic over a base and an extension field.
Could anyone would suggest which ...
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Adding and multiplication in jacobian coordinates
How can I derive formulas for adding and multiplication of 2 points in Jacobian coordinates $(x,y) = (\frac{X}{Z^2},\frac{Y}{Z^3})$ over an elliptic curve?
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How fast can a wrong decryption key be detected using ECC?
When can a decryption function detect that the ECC key I use for decryption is incorrect? Is it possible to do that during initialization, or does the complete message have to be decrypted to do that?
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Use curve25519 for ElGamal crypto
DJB described curve25519 in his paper which can be found here: http://cr.yp.to/ecdh/curve25519-20060209.pdf. It seems that the main purpose was for Diffie-Hellman key exchange. I think this means that ...
