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### Is there a feasible method by which NIST ECC curves over prime fields could be intentionally rigged?

The NIST elliptic curves P-192, P-224, P-256, P-384, and P-521, prescribed in FIPS 186-4 appendix D.1.2, are generated according to a well defined process, but using an arbitrary random-looking seed ...
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### How do I get the equivalent strength of an ECC key?

I know how to calculate the comparable symmetric strength of an RSA modulus: calculate the running time for a field sieve. This is how NIST gives approximate symmetric sizes for asymmetric algos in ...
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### Curve25519 vs "Million Dollar Curve"

Quoting from the Million Dollar Curve website: By using publicly verifiable randomness produced in February 2016 by many national lotteries from all around the world, we propose to generate a ...
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853 views

### Rely on NSA Suite B Cryptography?

NSA's Suite B Cryptography suggests some cryptographic algorithms for encryption, digital signatures, message digests and key agreements. The selected algorithms and their key size are suggested by ...
5k views

### Do Weak Elliptic Curves Exist?

I'm running into very contradictory opinions when try to understand if weak elliptic curves exist. I'm not interested in the case when a curve's weakness is attributed to properties of an EC's prime, ...
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### What EC curve is used by Apple iOS platform?

I can't find information about EC curve used by Apple's iOS platform. The algorithm name that I could see in their docs is: ...
• 366
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### Why is the strength of an Elliptic Curve Cryptography (ECC) half the size of the prime field size?

I've looked around and couldn't find a direct answer. As a general rule, I've read from various sources (here here, and here) that the strength of an elliptical curve key is half of the size of the ...
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296 views

### Elliptic curves with field sizes that not byte-aligned

Why there are abnormal field size like 521, 571, 233, 283 bits in prime and binary fields that are defined by NIST?
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### Proving Non-Existence of ECC Backdoors

In light of the NIST Dual EC DRBG scandal, I was intrigued by a NIST slide (slide 9) that said the two points P and Q can be chosen so that the chooser can prove they don't have a backdoor. This ...
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### How to interpret the article claiming NIST P-256 curve to be unsafe?

Here: http://safecurves.cr.yp.to/ , I read that the NIST P-256 elliptic-curve is not safe. The article lists several aspects (off-curve point, side-channel, etc.) where implementing P256 can fail the ...
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### Why do we use $a=1$ in elliptic curves?

$y^2 + xy = x^3 + ax^2 + b$ is the elliptic curve over $\mathbb F_{2^m}$. In the elliptic curve standard, most of the curves use $a=1$ a lot. Is there any mapping for this such that \$y^2 + xy = x^3 +...
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### Limitations of Elliptic Curve Cryptography?

Simple question, what are the limitations of ECC, both in terms of application and how secure it is? I heard that the NSA were able to read emails a few years back due to a backdoor they had ...
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397 views

### Kleptographic attack of ECDSA key generation?

Kleptographic attacks can be designed for RSA key generation, Diffie–Hellman key exchange, DSA/ECDSA signing, etc. Is it also possible for ECDSA key generation? More detailed: Is it possible for an ...
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1 vote
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### Severity of Cooking NIST P Curve Constants

Bruce Schneier and Gregory Maxwell have both stated that they believe the constants chosen for NIST's P curves (i.e. P-256r) are cooked. DJB has put together a detailed list of red flags but, outside ...
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1 vote