Questions tagged [group-theory]
Groups are an abstract algebraic concept based on a set and a group law (a binary function which closes the set).
359 questions
0 votes
0 answers
21 views
Does wrap around matters in the class group accumulator
I would like to ask a question regarding class group accumulator. For the class group accumulator https://kodu.ut.ee/~lipmaa/papers/lip12b/cl-accum.pdf Which takes a set $\mathbf{X}=\{x_1,...,x_n\}$, ...
- 381
0 votes
1 answer
147 views
Efficiently Sample Non-Zero element in Constant Time
Say I have a field $\mathbb{F}_q$ for prime modulus $q$, and I have a function random() that yields a uniformly random element of $\mathbb{F}_q$ in constant time. ...
- 101
2 votes
1 answer
135 views
A cyclic group of prime order
Is a cyclic group of prime order always a multiplicative group? Can you give an example of a cyclic group with prime order?
- 21
1 vote
1 answer
89 views
Safe prime modulo groups Zp quadratic residues count in DH groups RFC3526?
Let's create an example with safe primes, suppose we have a group Zp* (operation is multiplication), and where p=23, q=11 and g=2. Then group elements are {1 2 4 8 16 9 18 13 3 6 12}, so there are ...
- 129
1 vote
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66 views
Are there real-world applications of point halving on an elliptic curve over a finite field of prime characteristic?
Let $E\!: y^2 = x^3 + ax + b$ be an elliptic curve over a finite field $\mathbb{F}_{\!q}$ of prime characteristic $p$ (mostly, $q = p$ in practice). It is well known that in the $\mathbb{F}_{\!q}$-...
- 495
2 votes
1 answer
176 views
Is it possible to use abstract groups to generalize DSA, ECDSA and EdDSA signature creation and verification?
It is known, that DSA algorithm is defined as: Bob Creates private $x$ and public $Y=G^x\bmod p$ keys, where $G$ - generator, $p$ - group prime order Selects random value $k$ from $1 \le k\le q-1$ $...
- 129
3 votes
2 answers
666 views
Is ElGamal homomorphic encryption using additive groups works only for Discrete Log ElGamal? What about EC ElGamal?
It is known that in Discrete Log ElGamal encryption, the ciphertext $E$ is encrypted as: $a\ =\ g^k$, where $k$ - random scalar from $[0,\ p)$, $g$ - group generator $b\ =\ (Y^k*m)\mod\ p$, where $Y$ -...
- 129
1 vote
0 answers
97 views
Is the following Inverse Computational co-Diffie-Hellman problem hard?
Let $\langle g \rangle \stackrel{\Delta}{=} \mathbb{G}$ and $\langle h \rangle \stackrel{\Delta}{=} \mathbb{H}$ be groups of prime order $p$. Given $( p, g, g^\delta, g^{\delta^{-1}}, h, h^\delta )$, ...
