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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Reuse of a DH / ECDH public key

I was wondering whether it is safe to use the same DH or ECDH key pair in more than one key agreement, particularly if these public keys are in a public registry. These public keys could be used by ...
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0answers
67 views

Elliptic curve point addition with $Z_1 = Z_2 = 1$

Elliptic curve point addition and point doubling operations using Projective and Jacobian coordinates require fewer field multiplication operations when considering $Z$ coordinates of input points ...
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1answer
206 views

Why a key pair is used in OpenSSL ECDSA_sign or ECDSA_do_sign instead of only private key ?

If the digital signature in ECC (ECDSA) is made using a private key, why is the OpenSSL library using ECKEY pair as an input parameter instead of the private key only ?
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1answer
378 views

Forward-secure static-ephemeral ECDH key agreement protocol

The question is whether the following simple key agreement protocol design has good security properties, and how it can or should be improved. Assumptions Alice is a persistent entity with a static ...
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0answers
34 views

Where can I find a versatile PKI and library leveraging curve25519?

I note that Things that use Curve25519 provides a long list of protocols, software, and libraries that leverage curve25519, but I'm wondering if there is any such software that more fully implements a ...
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1answer
648 views

How to calculate elliptic curve parameters?

I'm having a rough time understanding the math behind elliptic curves. I want to implement ECDH where user can define a, b, and p parameters of elliptic curve. How can I calculate generator base ...
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0answers
51 views

What is the hardness in Decisional Linear Assumption (DLIN)?

I had understood what does the DLIN assumption means and here is a related question. But I fail to understand the 'real hardness' in this problem. I would be grateful if someone can help me to ...
4
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1answer
148 views

ECDH and ECDSA in PGP with known public key

How are used ECDH and ECDSA in combination with public key ? Usually these methods are used for establish a secret themselves, ...
4
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1answer
116 views

OpenPGP Public-Key algorithm

What means when pgpdump shows this kind of algorithm in the Public-Key Encrypted Session Key Packet? ...
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2answers
358 views

How to derive a symmetric key from ECDH shared secret?

I am trying to implement the internal primitives of ECDH. Currently I'm able to multiply the receiver's public EC point with the sender's private key to arrive at the shared EC point. Next step is to ...
2
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1answer
205 views

OpenSSL ECDH key exchange mechanism

I am using FIPS based OpenSSL module for encryption of sensitive data for my desktop socket server and client applications. I am using ECDH for key agreement.The keys public and private pair is ...
2
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1answer
303 views

What are the differences between curve NIST P-521 and Edwards E-521 for signature?

I implemented and used the P-521 curve for ECDSA. Signatures are 132 bytes long. It seems that Edwards E-521 is safer but I did not investigated very deeper. What is its signature length ? How is it ...
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1answer
301 views

Why Curve25519 for encryption but Ed25519 for signatures?

NaCl and libsodium libraries use Curve25519 for authenticated encryption (actually for sharing a key which is used for encryption) and Ed25519 for signatures. What is the purpose of using different ...
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1answer
245 views

Edwards / Montgomery ECC with Weierstrass Implementation?

So let's assume I want to perform Ed448 or Ed25519 digital signatures or want to perform a DH key-exchange. Assume further that those curves (Curve448 or Curve25519) are required. But the problem is, ...
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2answers
451 views

Is Curve25519 vulnerable to private key exposure in the case of a bad RNG?

I'm really excited by what I've learned of advancements in elliptic-curve cryptography. Curve25519 seems to be a great choice at this point in time, but if I recall correctly, some elliptic curve ...
11
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1answer
559 views

Does Curve25519 only provide 112 bit security?

In a recent mail on the IETF CFRG mailing list it was claimed that: The (currently missing) security considerations (or somewhere) should describe why Curve25519 is ok when used in contexts where ...
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0answers
33 views

Safe generation of $k$ points on a curve such that the mutual discrete logs are hard?

I have a multiplicative group $G$ of prime order $p$ implemented using a twisted Edwards curve (similar to Ed25519). I want to compute a set of $k$ distinct points $P_1,...,P_k$ that generate $G$, ...
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1answer
493 views

ECC considered secure in OpenSSL?

If I perform the following command: openssl ecparam -list_curves using my OpenSSL version (1.0.1f), it spits out the following supported curves: ...
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1answer
169 views

Modular reduction for NIST prime P256— understanding the data

I am working on a project where I need to implement elliptic curve cryptography, I am struggling from a long time in order to understand the working and the process. Modular finite field arithmetic, ...
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0answers
93 views

Why is there no 'ECDSA' version of 'DHE-RSA-CHACHA20-POLY1305'?

So I was just checking my TLS cipherlist and noticed that there was a 'DSS' / DSA / ECDSA version of every ...
3
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1answer
252 views

public key cryptography and authentication for cross-platform network application

I'm developing network based application for control and telemetry on Linux based embedded system. I'm using ZMQ network library and Google Protocol Buffers serialization library for communication ...
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0answers
45 views

Testing PRNG quality from ECC public keys?

Having a large set of ECC public keys $P_i = n_iB$ on a fixed curve $E$ over a prime field, is there a way to determine if coefficients $n_i$ were generated using a bad PRNG? In other words, can a ...
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3answers
5k views

Why is the P-521 elliptic curve not in Suite B if AES-256 is?

In the NSA's document, "The Case for Elliptic Curve Cryptography" (archived), we have ...
5
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1answer
127 views

EC: Why does $h>200$ need to hold?

From BSI-TR-03111 (PDF), on page 15: The class number of the principal order belonging to the endomorphism ring of E SHOULD be at least 200. This value commonly is referred to as $h$ in that ...
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1answer
246 views

Is SHA-1 safe for signing ECDHE parameters?

Is using the SHA-1 algorithm insecure for hashing the ephemeral ECDH public key in the signed_params structure? There are some worrying articles about using SHA-1: ...
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1answer
81 views

Parameter choice Supersingular Isogeny DH

In “Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies” by DeFeo, Jao and Plut (PDF), the public parameters are defined as: Supersingular curve $E$, and bases $P, Q$ ...
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141 views

Why develop Edward curve formulas that deviate from unification?

Edward curves were considered initially because they provide a unified formula for both doubling and addition, thus having inherent side-channel resistance. But a lot of work has been done recently ...
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1answer
175 views

Base point in Ed25519?

The paper "High-speed high-security signatures" by Bernstein et al. introduces the Edwards curve Ed25519. Concerning the base point $B$, it says that $B$ is the unique point $(x, 4/5)\in E$ for ...
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1answer
200 views

Point addition in NaCl/libsodium (Curve25519)

In NaCl and libsodium, the crypto_scalarmult function implements the operation $Q = kP$ (scalar/point multiplication). There doesn't seem to be a function for point ...
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1answer
213 views

How to generate own secure elliptic curves?

I know that the algorithm used to generate the Brainpool curves and the NIST curves is published. The algorithm should be this one (RFC5639 Appendix A). From what it looks like it's rather slow to ...
3
votes
1answer
50 views

Favor hash size or field size when systems are disparate?

I'm working on an implementation of Krawczyk's Hashed MQV (HMQV). I'm using Crypto++, which is a C++ library. C++ has some features where classes that represent the crypto objects can be combined ...
10
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2answers
863 views

Why Elliptic Curves?

What is the benefit of using elliptic curves over the standard finite field, when the cyclic subgroup we consider of the EC's solution group is just isomorphic to some integer residue class of prime ...
8
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1answer
196 views

Deterministic ECDSA signatures?

ECDSA signatures depend on parameter k that is chosen by the signer. As a result, there are many signatures for the same private key d and message m. What I want to achieve is a deterministic ...
6
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1answer
190 views

How to derive the curve Ed25519 from Curve25519?

According to the paper "Faster addition and doubling on elliptic curves" by Bernstein and Lange, the Montgomery curve (Curve25519) $$v^{2}=u^{3}+486662\cdot u^{2}+u$$ is birationally equivalent to the ...
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2answers
72 views

How to compute two EC point multiplication?

I would like to know how to compute multiplication of two valid EC points over a curve E with generator G. i.e. Given only P and Q points then how to compute R = P * Q where $P = p G$, $Q = q G$ and ...
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0answers
72 views

Differential addition on Montgomery curve

Point multiplication using Montgomery ladder technique over Montgomery curves only require x coordinate, which in many situation leads to faster implementation as compared to point multiplication over ...
4
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1answer
123 views

Does exponentiation by squaring work on Montgomery curves?

Consider the point multiplication $Q=[d]P$, where $P$ a point on elliptic curve multiplied with an integer $d$ to get another point $Q$ on the same curve. This operation can be computed by a ...
3
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1answer
350 views

Which is better ECDHE with TLS 1.0

I have a webserver which only supports TLS 1.0 and I am not sure about something: Which is the better cipher in this group when aiming for the best security? ...
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1answer
1k views

Mapping points between elliptic curves and the integers

My primary question is: Is there an easy way to create a bijective mapping from points on an elliptic curve E (over a finite field) to the integers (desirably to $\mathbb{Z}^*_q$ where $q$ is the ...
6
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1answer
290 views

Difference between “ECDH with cofactor key” and “ECDH without cofactor key”?

I need to use “ECDH with a cofactor key” for generating symmetric key. I have a fair idea on how ECDH works, but I don’t understand the cofactor part. What is the difference between ”ECDH with a co-...
3
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1answer
215 views

Key exchange using ECDH vs ECIES

I'm a beginner to ECC crypto programming. Does any one explain to me the difference with using ECDH for shared key exchange and use of ECIES by encrypting shared key with the public key of the ...
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1answer
2k views

What are the advantages of a static ECDH key?

What are the advantages of using "static-ephemeral ECDH" over "ephemeral-ephemeral ECDH"?
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vote
1answer
99 views

Why we need ECDSA when we have ECDH?

ECDSA and ECDH give us the following methods: ...
2
votes
1answer
510 views

openSSL ECDH private key size

When you are using a named curve like P-256 in openSSL, is there any standard key size for ECDH private key keys? If you look at the ec_key.c file in the openSSL ...
2
votes
1answer
142 views

Can I use an ECDH Shared Secret from the same Private / Public Key Pair?

I'd like to know if using the ECDH shared secret of a static EC Private Key with it's own corresponding static EC Public Key causes a problem / weakness. (edit) not asking if it's ok to re-use the ...
2
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2answers
342 views

ECDH anonymous key exchange to avoid PKI

I want to use TLS to encrypt the communication between peers in a P2P network. Each peer has a well known 256bit peer identifier (the public key of a 256bit elliptic curve keypair). Both peers need ...
4
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1answer
414 views

EC ElGamal versus static+ephemeral ECDH

A client application needs to encrypt a UDP datagram for a server with known EC public key $P$. Performing a full ECDH key exchange would defeat the benefit of using UDP as a connectionless protocol. ...
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0answers
42 views

Clarify EC point addition and multiplication

Please clarify the below doubt regarding EC point addition and multiplication: $P$-Generator Point; $a$ and $b$ are integers; $X$ and $Y$ are EC points, defined as follows: $X = (a*P) + (b*P)$ $Y = ...
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1answer
216 views

How many bits of entropy does an elliptic curve key of length n provide?

A FAQ for an open source project makes the claim: Indeed, an elliptic curve key of length n provides $n/2$ bits of security. I have two questions: What is the practical difference between "...
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104 views

Is this a secure method of encrypting with authentication?

My goal is to allow two clients to send files securely over an untrusted network without the need for more than one block of information to be sent. Both clients have ECDSA keys of size 256 bits. I'd ...