Tagged Questions

Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also ...

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Are any of the major asymmetric ciphers distinguishable (EG, RSA, ECC)?

Related to "Is it possible to derive the encryption method from encrypted text?". Given ciphertexts generated by any of the major asymmetric ciphers (RSA, ElGamal, ECC, etc..) can these ciphertexts ...
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Are there security issues with discrete logarithm keys not being uniformly distributed?

Generally, algorithms based on discrete logarithm specify that private keys are chosen as scalars between 1 and the order of the group (denoted $q$ here). For instance IEEE P1363 and FIPS 186-3 both ...
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If I encrypt data with two different ECC Private keys, how secure is the result?

I'm wondering whether encrypting data with two different 256-bit ECC keys will result in a more secure encryption (minimum 384 bit equivalent) or will result in data that's effectively encrypted with ...
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Simple digital signature example that one could compute without a computer?

I am working on a document to explain Bitcoin to students. But I am having a hard time translating the principle described in §2 of the Bitcoin whitepaper in layman's terms. There is a great question ...
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What is proper size of window Using RSA Window method?

I want to Use Window method for RSA modular Exponentiation. because of SCA. But I don`t know what is proper window size.
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Scalar Multiplication for Elliptic Curve

Let $\mathbb{E}$ be the elliptic curve $y^2 = x^3 + 6x \text{ mod } 11$ and consider the point $P = (2, 3)$ on it. How do I compute $3P$? I have been able to figure out what $2P$ is, $2P = (5,10)$. ...
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Why can an elliptic curve private key be 1?

I often see in papers (e.g. this one) that for an elliptic curve with generator point $G$ and order $n$ the private key $d$ can take on any integer value in the range $[1, n)$. When $d = 1$ the ...
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How to convert roots of Weber polynomial to Hilbert class polynomial over modulo prime?

Using any non square root discriminant $D$, we should be able to find the Weber class polynomial. How can I convert the roots of a Weber polynomial to a Hilbert class polynomial over modulo prime?
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Is the Representation Problem hard on elliptic curves?

The RP in ECC would be to find $a_1,\ldots,a_n$ (integers) given $P$ and $Q_1,\ldots,Q_n$ (points in the EC) such that $P = a_1 \cdot Q_1 + \ldots + a_n \cdot Q_n$. Is it hard when DH-like ...
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Which elliptic curves are quantum resistant? [closed]

If I want to learn about quantum resistant crytography what are the best resources? Which type of elliptic curves should I be studying?
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Creating ECDH using OpenSSL

For academic reasons, I'm playing around with OpennSSL 1.0.2g. I tested RSA encryption/decryption. I created key exchange with DHKE. But I'm struggling to find a way, to create ECDH, using only ...
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Finding the subgroup in isogeny-based cryptography

Isogeny-based cryptography is one of the newest post-quantum cryptography. Hardness of this system is based on finding isogeny between two elliptic curves. Also this is theorem: Elliptic curves ...
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Single-scalar multiplication with sign bit

I want to know if there's an "easy" timing-free way to compute the sign of $y$-coordinate of $r G$, for a secret scalar $r$ and $G$ the generator of an elliptic curve. We have several choices for ...
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Quantum vs. regular computing time to break ECC?

How long exactly would it take for a regular computer to crack an elliptic curve public/private key via bruteforce, vs. a quantum computer using Shor's algorithm with a couple thousand qubits? Can ...
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Is a KDF needed when using X25519 for ECDH and XChaCha20-Poly1305 for AEAD?

Is a KDF needed when using X25519 for ECDH and XChaCha20-Poly1305 or XSalsa20-Poly1305 for authenticated encryption? My hypothesis is "no" because the key from X25519 is less than 256 bits long; ...
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Multiplying integers modulo $2^{255}-19$ using the Curve25519 polynomial reduction algorithm

I'm reading the Curve25519 paper and I see that in page 11, under the title "Multiplying integers modulo $2^{255}-19$", it says: The coefficients of $x^{10}$; $x^{11}$; ...; $x^{18}$ in $uv$ are ...
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Creating serial key generator using ECDSA, how to get signature short enough?

I've written some questions in this stackoverflow and got great responses but now I'm trying to wrap it all together. I have for the last couple of weeks been building a serial key generator project ...
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Has anybody implemented BGN cryptosystem to multiply two plain texts?

I have tried to use this code as follows, http://stackoverflow.com/questions/33581962/bgn-implementation-in-java but the issue is, when it generate the pairing, the output is in GTfiniteelement (for ...
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How to find HEXA value of String [closed]

This may be very easy thing, but i am just unable to understand this. I have a string "Hi", and in HEXA its written like this ...
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How many qubits are required to break RSA 2048 or 4096 with a universal quantum computer?

So in the news this week, IBM have created a universal quantum computer with 5 fully functional qubits. Logic and Moore's law dictates they will be able to scale this up to a lot more qubits within a ...
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Some confusions about Repeated Doubling Algorithm?

The following repeated point doubling algorithm is taken from the book Guide to Elliptic Curve Cryptography by D. Hankerson, A. Menezes, and S. Vanstone on page#93. Clearly, this algorithm is ...
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Could someone explain the given algorithm?

The following snapshot of the algorithm is taken from the book Guide to Elliptic Curve Cryptography published by Springer 2004. I don't understand that why at the statement 9.1 if both $T_1$ and ...
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Reuse of TLS client key/certificate in challenge-response protocol

The situation: We have a custom PKI with clients communicating with the server over standard SSL/TLS encrypted channel. PKI uses ECC, server certificate supports ECDHE_ECDSA key exchange mechanism and ...
15k views

Who uses Dual_EC_DRBG?

Recent news articles have suggested that the NSA may be involved in trying to influence the cryptography in public standards or commercially deployed software, to enable the NSA to decrypt the ...
6k views

ECDSA vs ECIES vs ECDH

Recently I started studying Elliptic Curve Cryptography and I just loved it. I want to transfer some big data (like 3KB), What is the best method, ECDSA, ECIES, or ECDH (and why)? I am confused, how ...
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elliptic curve point doubling in Jacobian coordinates

I am writing an application that uses Elliptic curve Diffie–Hellman for authentication. I found two formulas for point doubling in Jacobian coordinates. 1st) X_1 = (3x^2 + aZ^4)^2 ...