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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156 views
How to properly add ECDSA private keys?
I'm currently working on an application that requires me to add two ECDSA private keys in order to make a new private key. The result has to have the property, that its corresponding public key is the ...
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2answers
91 views
While generating a random Elliptic curve what are the conditions i have to considerd?
I want to generate a random elliptic curve over a prime field. What are the conditions I should satisfy?
For the NIST recommended standard ECC-224 bit curve with prime $p=2^{224}-2^{96}+1$, a ...
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179 views
Storage of Private Keys
I'm building a bitcoin web application that will require all users to be assigned a wallet for adding funds to their account. I plan on exposing the public key to the user (the bitcoin address). Users ...
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69 views
Elliptic Curve is DH function or PKI?
can we reuse same ECC key on TLS for long terms or it must be used just once? (i mean can we use ECC like RSA?)
is there patent free ECC implementation ?
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Is there a method to break an EC curve for all key-pairs (Q,d) such that (Q=d*G) faster than breaking every single key-pair?
Related to this question: Is there any memory trade-off that helps such attack?
Obviously if the field size is very small (say 40 bits) it´s possible, but what if the field size is 160 bits long? or ...
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Are there reference implementations of ECQV implicit certificates?
I am interested in exploring ECC implicit certificates, specifically using the ECQV protocol. While the actual implementation would not difficult to perform using building blocks provided by most ECC ...
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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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111 views
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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401 views
How does one calculate the scalar multiplication on elliptic curves?
I found this example online:
In the elliptic curve group defined by
$$y^2 = x^3 + 9x + 17 \quad \text{over } \mathbb{F}_{23},$$
what is the discrete logarithm $k$ of $Q = (4,5)$ to the base ...
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54 views
Efficient algorithm for remainder calculation over prime field for ECC implementation?
I am working on 224-bit elliptic curve cryptography. In this 224-bit * 224-bit multiplication results 448-bit output. I am reducing 448-bit into prime field range( prime number $2^{224}-2^{96}+1$) ...
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131 views
File encryption with one keypair?
I'm working on a program that uses an ECC keypair in a (password protected) PKCS12 file (.pfx) to encrypt files. I like this method because I think it will be higher security (using ECDH to negotiate ...
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1answer
49 views
EC equivalent for RSA-OAEP
I have some questions regarding aforementioned subject:
Is there a EC equivalent of RSA-OAEP key transport/encryption algorithm ?
Is ECIES-KEM sufficient ?
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73 views
What are unified addition and differential addition in elliptic curve point arithmetic?
A lot of papers use these terms but I do not find a proper explanation of them. Can somebody tell the meaning / difference / intuition / application and if possible with an example.
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70 views
tower of extension field
while working on tate pairing, i have to implement towering technique. like i have point p on F(q) and point Q(F(q^k)) (here embedding degree k=12 for BN curve).
instead of taking a point Q on ...
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393 views
BouncyCastle Elliptic Curve implementation
I'm implementing ECDH key exchange in C# using the BouncyCastle library and I'm having a hard time understanding the elliptic curve side (FpCurve).
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118 views
ECDSA - point order criterion
i am creating some primitive demostration for ECDSA over small curve ( p < 229). But my implementation have some weird issues. Verify process return false even if the signature is correct. Because ...
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33 views
calculating beta for elgamal elliptic curves [duplicate]
Suppose we use elgamal elliptic curves for secure communication. Bob selects a prime $p$, an elliptic curve $E$, a point $\alpha$ on $E \pmod p$, and a secret integer $f$. Suppose that Bob has ...
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85 views
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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54 views
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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65 views
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 ...
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255 views
Diffie hellman key exchange on elliptic curve over an extension field [closed]
I am attempting to do a final semester project where I implement Diffie-Hellman key exchange on an elliptic curve over an extension field (2^256). Can anybody help me to generate the extension field ...
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46 views
Elliptic curve Cryptography [duplicate]
Possible Duplicate:
Can we use elliptic curve cryptography in wireless sensors?
How to map message character to point lies on Elliptic Curve? how to ecc used in wireless sensor networks? ...
