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Questions concerning the mathematics of secure communication. Relevant topics include elliptic curve cryptography, secure key exchanges, and public-key cryptography (e.g. the RSA cryptosystem).

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Score of 2
0 answers
105 views

Setup. Fix an odd integer $n$ and a nonzero $b\in\mathbb Z_2^n$; all indices are mod $n$. For $a=(a_0,\dots,a_{n-1})\in\mathbb Z_2^n$ and each $k$, the two bits $g_k=a_{k-1}$ and $h_k=a_k+a_{k-2}+b_k$ ...
Score of 2
0 answers
122 views

We know integer factoring randomly reduces to Discrete Logarithm over multiplicative groups but is it known to be reducible to Elliptic Curve Discrete Logarithm Problem ($ECDLP$)? Is factoring ...
Score of 3
0 answers
101 views

https://cstheory.stackexchange.com/questions/48258/is-there-a-linear-time-algorithm-for-integer-multiplication-verification provides a trick to 'verify given three integers n,a,b if $n=ab$ holds?' in ...
Score of 2
0 answers
93 views

Let it be a finite field $\mathbb F_q$ consisting of a large characteristic power large enough to make solving the discrete logarithm intractable using current subbexponential methods. Let it be 2 ...
Score of 2
1 answer
86 views

I am implementing threshold Paillier encryption scheme. In the "regular" Paillier scheme, the decryption key is defined as $d = \phi(N)$ whereas in the instantiation of threshold Paillier I ...
Score of 4
1 answer
508 views

In cryptography, it seems to be a common choice to use the so-called Jacobian coordinates to represent a point of an elliptic curve (see e.g. Elliptic Curves: Number Theory and Cryptography, L. C. ...
Score of 2
1 answer
159 views

We define the successive minima in a lattice $L$ of rank $n$ as in Daniele Micciancio and Shafi Goldwasser, Complexity of lattice problems. A cryptographic perspective, The Kluwer International Series ...
Score of 2
0 answers
603 views

First, remember bn curves is a class of elliptic curves defined over curve $y^2=x^3+3$ with embedding degree 12 and $\mathbb G_2$ points lying over the curve twist $\frac {Y^2 = X^3 + 3}{i+9}$ defined ...
Score of 1
0 answers
114 views

The aim is for pairing inversion where miller inversion can only work if an equation is satisfied. So given a finite field modulus $q$ having degree $k$ ; and a finite field element $z$ having ...
Score of 2
0 answers
249 views

Let it be a finite field $FF$ with 2 finite field elements having their discrete logarithm in a large prime subgroup $s$ of $FF$… Will the only way to map the discrete logarithm of $FF$ always be to ...
Score of -3
2 answers
751 views

Background and Motivation The golden ratio, $$ \phi = \frac{1 + \sqrt{5}}{2}, $$ is a well-known irrational constant that appears frequently in geometry, algebra, and in the Fibonacci and Lucas ...
Score of 1
0 answers
267 views

There are many NP-complete problems, e.g. SAT, CVP, SIS, graph colouring, Minesweeper etc. By definition there are polynomial time reductions from one to another of these, at least in their decision ...
Score of 2
1 answer
245 views

There are several algorithms for lattice reductions in $n$-dimensions, LLL, etc. Here the lattice in question is in ${\mathbb R}^n$ and the basis vectors $b_1, \ldots, b_n$ are usually assumed to be ...
Score of 1
1 answer
119 views

In Theorem 8 of Micciancio’s lecture notes, a reduction from the Closest Vector Problem (CVP) to its optimization version (OptCVP) is given under the assumption that the lattice basis $B \in \mathbb{Z}...
Score of 1
1 answer
275 views

We got some unexpected to us results. Let $E$ be an elliptic curve over a finite field of large characteristic. For positive integer $k$, let $D=2^k$ and assume the order of $E$ is $\rho=D t$ with $t$ ...

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