相关论文: Comparing the difficulty of factorization and disc…
Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the…
RSA is one of the most popular Public Key Cryptography based algorithm mainly used for digital signatures, encryption/decryption etc. It is based on the mathematical scheme of factorization of very large integers which is a…
We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our…
In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick Sort. In our first study in this paper, we reconfirm this through computer experiments…
There are several methods to measure computing power. On the other hand, Bit Length (BL) can be considered a metric to measure the strength of an asymmetric encryption method. We review here ways to determine the security, given an span of…
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
Being able to compute efficiently a low-weight multiple of a given binary polynomial is often a key ingredient of correlation attacks to LFSR-based stream ciphers. The best known general purpose algorithm is based on the generalized…
We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution…
Recently, Cai showed that Shor's quantum factoring algorithm fails to factor large integers when the algorithm's quantum Fourier transform (QFT) is corrupted by a vanishing level of random noise on the QFT's precise controlled rotation…
Quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of…
We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \log^{2 +…
Statistical computations are becoming increasingly important. These computations often need to be performed in log-space because probabilities become extremely small due to repeated multiplications. While using logarithms effectively…
Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…
We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices: one that performs block-column-wise QR, and another that is based on tiled QR. We show how the block-column-wise algorithm exploits BLR…
Sorting algorithms are the deciding factor for the performance of common operations such as removal of duplicates or database sort-merge joins. This work focuses on 32-bit integer keys, optionally paired with a 32-bit value. We present a…
Let $a,b\in \mathbb{N}$ be fixed and coprime such that $a>b$, and let $N$ be any number of the form $a^n\pm b^n$, $n\in\mathbb{N}$. We will generalize a result of Bostan, Gaudry and Schost and prove that we may compute the prime…
We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory qubits and the number of operations required to perform factorization, using the algorithm…
Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach…
As the dimensions and operating voltages of computer electronics shrink to cope with consumers' demand for higher performance and lower power consumption, circuit sensitivity to soft errors increases dramatically. Recently, a new data-type…
A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…