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 ...

learn more… | top users | synonyms (2)

4
votes
3answers
383 views

What crypto system allows for 3 parties: Party 1 who makes an assertion, Party 2 mutates the assertion, Party 3 validates it

I'm looking for the cryptographic equivalent of a Drivers license where the issuer can be verified, the issuer doesn't need to know who you showed the drivers license to, but also allows ...
4
votes
1answer
297 views

Discrete logs on elliptic curve with embedding degree 3 with the 'MOV' attack

The curve $E(\mathbb{F}_{47}):y^2=x^3+x+38$ has order $61$ and $61|47^3-1$ so the embedding degree of $E$ is $3$ and therefore the MOV attack, presumably using some sort of distortion map and a ...
4
votes
2answers
1k views

ECC algorithm pollard's $\rho$ complexity

One of the methods to break a ECDLP is Pollard's rho algorithm. When ECDLP is defined over a finite field $F_p$, and given a relation $S=w.T$, where S and T are a member of $F_p$. Then ECDLP is to ...
4
votes
2answers
107 views

If we should not reuse primes in DH, shouldn't we not reuse ECDH elliptic curve properties?

An article How is NSA breaking so much crypto? describes NSA's methods for breaking encryption. If a client and server are speaking Diffie-Hellman, they first need to agree on a large prime number ...
4
votes
1answer
164 views

great discovery in the field of elliptic curves cryptography?

Prof. Adi Shamir says in The Cryptographers' Panel 2016: i think that NSA has made a great discovery in the field of elliptic curves cryptography and NSA wants to avoid the increased use and ...
4
votes
1answer
98 views

Are EC public/private keys significantly weakened by having a known byte?

I would like to use different EC keys for different purposes in an app, and I would like to easily see the purpose for which particular key (pair) was generated. With ~65K attempts, I can generate a ...
4
votes
3answers
148 views

Safe curves in Weierstrass form?

I would like to implement a protocol using elliptic curves. I'm thinking of using MIRACL so using curves in their Weierstrass form is preferable as it they are supported by this framework. I don't ...
4
votes
1answer
135 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
votes
3answers
140 views

Calculating $\mathbb F_{p^2}$-rational points of an elliptic curve defined over $\mathbb F_p$

How can I calculate points on an elliptic curve defined over $\mathbb F_p$, for example $y^2 \equiv x^3 + 1 \pmod p$, with coordinates in $\mathbb F_{p^2}$? (points might have complex number format in ...
4
votes
2answers
317 views

Using Lattice-based cryptography for TLS\SSL

Given the general benefits of Lattice-based cryptography, such as: Post quantum Security Security from worst case scenario Efficiency What could the outlook of shifting from RSA \ ECC-based ...
4
votes
1answer
233 views

Implementing CD serial key system

I am trying to create a system where to unlock the application one needs to enter a serial code. I have read many articles on the theme but there are two problems bugging me. One is, If I have a ...
4
votes
1answer
535 views

Blockwise Montgomery multiplication

I have to implement a 256*256 bit Montgomery multiplier for pairing computations. The straightforward approach is to use a bit-serial version, but I would like to utilize the built-in 64*64 bits ...
4
votes
2answers
362 views

Proof of elliptic curve difficulty

Are there any proofs that cryptographic functions on an elliptic curve are any more difficult than the analogues over modulo arithmetic? While at present, ECC appears to be more difficult, as it is ...
4
votes
1answer
422 views

How Were secp*k1 elliptic curve generators chosen?

The Koblitz elliptic curves specified in the SEC2 document https://docs.google.com/viewer?url=http%3A%2F%2Fwww.secg.org%2Fcollateral%2Fsec2_final.pdf all have the nice feature that the parameters are ...
4
votes
1answer
187 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 ?
4
votes
1answer
107 views

OpenPGP Public-Key algorithm

What means when pgpdump shows this kind of algorithm in the Public-Key Encrypted Session Key Packet? ...
4
votes
1answer
126 views

Is it ever unsafe to compress an EC point?

I am working with a library that outputs EC points in uncompressed form. To save space, I'm considering modifying said library to use compressed EC points. Assuming that I keep track of the sign bit ...
4
votes
1answer
313 views

Elliptic Curve Crypto, is a distributed signing method possible using Shamir's Secret Sharing?

Note: A distributed signature scheme exists for RSA: Practical Threshold Signatures, Victor Shoup. Is it possible to adapt such scheme for ECC? A centralized signing machine is vulnerable to ...
4
votes
1answer
231 views

How can I tell which curve a given ECDSA implementation uses? (P-521 or something else)

I'd like to test and see if certain software uses P-521 ECC curves, or if it uses another variant. Without having access to the sourcecode, or the specification, is there any way for me to test which ...
4
votes
2answers
666 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.
4
votes
1answer
64 views

Optimal same-base exponentiation?

I've (finally) implemented the answer to this question in our library, which stated how to transform montgomery curves (and points) to weierstrass curves (and points). Now, for scalar multiplication, ...
4
votes
1answer
92 views

Is there any reason not to use EdDSA with Weierstrass curves?

I'm volunterely working for a crypto library and we're planning on adding Curve25519 support (finally). At the same point I had the idea of adding support for EdDSA in the same run. Our library is ...
4
votes
2answers
245 views

Which multiplicatively homomorphic encryption scheme supports encryption of 0?

I want a multiplicatively homomorphic encryption scheme that supports encryption of 0 (e.g. Elgamal doesn't support). I also want the multiplication to be operated on the ciphertext of 0, i.e., if ...
4
votes
0answers
39 views

EC Schnorr signature: multiple standard?

I 'm working on some EC-Schnorr signature code. Reading various papers on that, it's seems EC-Schnorr is not standardized as well as ECDSA. For example, I found two main differences in two main ...
4
votes
0answers
244 views

Is there a flaw in this ECC blind signature scheme?

Recently I've found the following work on the internet: An ECC-Based Blind Signature Scheme The paper claims to be an ECDSA blind signature however it seems that their scheme has a flaw in it. The ...
4
votes
0answers
214 views

Using the same private key for two ECC key pairs

Let $(d_1,Q_1)$ and $(d_2,Q_2)$ be ECC key pairs over two different elliptic curves (say NIST P-224 and NIST P-256). According to the Elliptic Curve Discrete Logarithm Problem (ECDLP), if the private ...
4
votes
0answers
1k views

Reasons for Chinese SM2 Digital Signature Algorithm

In the IETF RFC draft named "SM2 Digital Signature Algorithm" a signature algorithm is specified. The RFC does however not mention why this signature algorithm has been defined. Nor does it specify ...
3
votes
2answers
262 views

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?
3
votes
2answers
277 views

Is there any reason to use RSA or DSA when we have ECC?

I am having trouble coming up with a use case for RSA or DSA. It appears that ECC is better in every way. Is this true? I am looking for cases where RSA/DSA is superior to ECC, not where it is used ...
3
votes
2answers
196 views

Is it possible to choose which point will have the public key of a given Elliptic Curve?

I am wondering if there is a feasible way that, given a specific elliptic curve (such as secp256r1), I could create a keypair where the public key has a given $x$-coordinate. If it is not possible, is ...
3
votes
2answers
529 views

Finite fields and ECC

I understand modular arithmetic(or at least I think I do!) and I've tried to read and learn about how the Math in RSA works(and I think it went pretty well). I've been reading up on ECC and it looks ...
3
votes
2answers
397 views

Are all possible EC private keys valid?

I usually generate a key pair using openssl or Bouncy Castle. I'm using curve secp256k1. The 256bit private keys look fairly random. Do all values of "private ...
3
votes
2answers
2k views

What curve and key length to use in ECDSA with BouncyCastle

I'm developing a client/server system in Java which is not interacting with third party software, so I don't have to worry about compatibility. At a certain point, I need the client and server to ...
3
votes
2answers
394 views

Elliptic Curve Cryptography Encryption Results

I'm playing around with a package that does Elliptic Curve Cryptography from http://jecc.sourceforge.net/ Every time I encrypt a value it produced a different result (same private key). However I'm ...
3
votes
1answer
87 views

Why do the subexponential algoriths for the DLP not work for the ECDLP?

Elliptic curve cryptography is much more secure for the same parameters because attacks that work on the DLP do not work on the ECDLP. Why do the attacks fail in the latter case?
3
votes
1answer
184 views

Difference between Pseudo Mersenne primes and Generalized Mersenne primes

The field prime numbers $p$ proposed by the NIST standards are referred to as Generalized Mersenne prime numbers [1] and as Pseudo Mersenne prime numbers [2]. Is there a difference between Pseudo ...
3
votes
1answer
400 views

ECC keys vulnerable to brute force attack?

I have started learning about Elliptic curve cryptography. Since the key size required in ECC is relatively lesser than the key size in RSA to provide the same amount of strong encryptions, I wonder ...
3
votes
1answer
138 views

What does signed fixed window method mean in ECC?

I am studying (sliding) window method in Elliptic Curve Cryptography (ECC) but I am confused by the term, signed fixed window method. By the way term is used in a research paper and not in the book ...
3
votes
1answer
264 views

counting points on elliptic curve

Given an elliptic curve with equation $y^2=x^3+ax+b$, and i want to find the number of points $(a,b)\in E(\mathbb{F}_p)$ where the polynomial has repeated roots, how do i do it? I have an intuition it ...
3
votes
1answer
118 views

Counting points on elliptic curve over binary field

How to count number of rational points on elliptic curve over binary field?
3
votes
2answers
81 views

Is there a way to do single key-pair asymmetric encryption?

All of the information on asymmetric encryption I can find uses key-exchanging to get a mutual symmetric key. What I am trying to do is encrypt a message with a public key and have it only readable ...
3
votes
1answer
325 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, ...
3
votes
1answer
171 views

What are the differences between the elliptic curve equations?

I think we're all aware of the "classical" Weierstrass (short?) elliptic curve equation: $y^2\equiv x^3 + ax +b \pmod p$. Well known examples of these curves include the NIST's and Brainpool ones. ...
3
votes
1answer
98 views

what is the public information in Elliptic curve cryptosystems [closed]

Currently my knowledge about Elliptic curve is quite limited to the textbook and I don't know how a practical Elliptic curve cryptosystem works. I read an example about key exchange using Elliptic ...
3
votes
2answers
225 views

In ECC, how do I prove that point addition is commutative?

I am studying elliptic curve cryptography and this question is related to the commutative property of point addition operation. Point addition $P_3(x_3,y_3)$ of two points $P_1(x_1, y_1)$ and ...
3
votes
1answer
976 views

Montgomery Ladder vs Double-and-Add

I would like to know what (if any) are the advantages of using Montgomery Power ladder over the Double-and-Add-Always algorithm. I think that firstly, Monty would be slightly faster than DoubleAndAdd. ...
3
votes
1answer
412 views

How are Elliptic Curve Cryptography and Pairing Based Cryptography related?

I have been doing a project that uses the PBC library developed by Ben Lynn. But I am still not clear on how PBC is related to ECC. I know that this is a site for complex crypto QA, but I did not know ...
3
votes
1answer
208 views

Impact of algorithms for factoring using elliptic curves over $\mathbb{Q}$

Recently a few papers have appeared that describe a new approach to factoring, using elliptic curves over $\mathbb{Q}$. See, e.g., Factoring integers and computing elliptic curve rational points, ...
3
votes
1answer
49 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 ...
3
votes
1answer
126 views

Doubling a point on an elliptic curve

I'm working with the elliptic curve $\mathcal{E} : y^2 = x^3 + 11x^2 + 17x + 25$ over $(\mathbb{Z}_{31},+,\cdot)$ and am trying to double $P=[2,7]$. Following the instructions here, I'm doing the ...