# Questions tagged [elliptic-curves]

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 consider more specific tags such as discrete-logarithm and ecdsa.

1,152 questions
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### What Set and MultiSet Hash allows Secure, Homomorphic, commutative comparison of key-value databases? (Orderless, Online alternative to Merkle trees)

I am interested in Merkle tree like hashes that do not require the data to be ordered, but will hash the data, not the byte by byte, page by page storage but rather hash UNORDERED data (presumably ...
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### What is the maximum message size when using ECDSA (specifically secp256k1?

I'm guessing that the message must conform to 256 bits but I was not able to find documentation of any message length limits.
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### Asymmetric encryption property required in an authentication protocol

We want to choose an asymmetric encryption scheme for use as follows: A device holds its private key, with the corresponding public key known and trusted by all. The device also holds a small $b$-bit ...
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### Cryptographically Secure Elliptic Curve

What are the properties a cryptographically secure Elliptic Curve must have? I have started to create a list and wanted to know if I forgot some important points, and if it is correct so far: A curve ...
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### Using the a multiple of the x coordinate as a private key

ECDSA specs require private key ($d$) to be a random integer ($r$) in the range $[1, N-1]$, where $N$ is the order of the base point ($G$). What if the private key instead is set to the x-coordinate ...
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### How Can I Know the Number of Points on an elliptic curve?

If I have the following Elliptic Curve: $$E: y^2 ≡ x^3 + 2x + 2 \mod 17$$ How Can I calculate the Number of Points on this elliptic curve $\#E$ ? and how can I invest the following law which ...
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### How do malware rely safely on ECDH algorithm to maintain secrecy of keys?

In traditional malware (especially ransomware) using RSA approach, the public key may be hard-coded in the malware binary and is used to encrypt a symmetric key generated on the system. The symmetric ...
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### multiplication of two points belong to elliptic curve

I have a question about multiplication of two points belong to elliptic curve. I know every think about adding and scalar multiplication but not about multiplication of two points. Is there any method ...
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### decoding a Ed25519 key per RFC8032

RFC8032 Edwards-Curve Digital Signature Algorithm (EdDSA) 5.1.3 Decoding states the following: Decoding a point, given as a 32-octet string, is a little more complicated. First, interpret ...
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### Crypto Vs crypto-less key establishment protocols for Internet of Things applications [closed]

With the advent of IoT, crypto-less key establishment protocols exploiting intrinsic channel randomness of physical layer are gaining great interest. These crypto-less protocols are computationally ...
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### Does secp256r1 or secp256k1 use a=-3?

I saw a post here which I think states that for P256, a is equal to -3. Why is elliptic curve parameter $a=-3$ somehow special I am not sure if this is correct, or maybe I am misunderstanding ...
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### What ECDSA key is used to sign the ECDHE key exchange?

I have a server using TLS1.2 with an ECDSA certificate using secp256r1. The algorithms being used to connect to my browser are TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384 as I expect from my server ...
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### Is it secure to encrypt with EC “for myself”? [duplicate]

I want to encrypt some small amount of data using ECDH for use by myself later, but I don't want to generate an ephemeral keypair like in ECIES, due to time and space constraints. Would it be safe to ...
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### How to deterministically generate a 256 bit ECC key from 128 bits of entropy without a CSPRNG

A safe way to generate a 256 bit ECC key from 128 bits of entropy is to use a CSPRNG, according to this answer: https://crypto.stackexchange.com/a/56551/43864 However, it's difficult to find a cross ...