Topic
Least common multiple
About: Least common multiple is a research topic. Over the lifetime, 335 publications have been published within this topic receiving 2838 citations. The topic is also known as: L.C.M & LCM.
Papers published on a yearly basis
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Papers
TL;DR: It is proved that the expected number of operations which will be required is O(exp{ 83Qn n In In n)l/2) for some constant f > 0.
Abstract: The paper describes a "probabilistic algorithm" for finding a factor of any large composite integer n (the required input is the integer n together with an auxiliary sequence of random numbers). It is proved that the expected number of operations which will be required is O(exp{ 83Qn n In In n)l/2)) for some constant f > 0. Asymptotically, this algorithm is much faster than any previously analyzed algorithm for factoring integers; earlier algorithms have all required O(na) operations where a > 1/5.
130 citations
TL;DR: In this paper, the determinant of the GCD and LCM matrices on S was shown to be an integral matrix, and the inverses of the two matrices were calculated.
75 citations
Patent•
14 Mar 1991
TL;DR: In this paper, the authors proposed a cryptographic system consisting of at least one encryption station, one decryption station and a trapdoor generator, which is used for selecting r distinct prime numbers Pi, generating a modulus m that is a product of the prime numbers pi, selecting a pair of integers (a,b) satisfying 0 ≦ a < m and 0 ≖ b < m, computing for each pi a number N(pi) of distinct pairs of integers satisfying 0 x < pi and 0 ǫ y < Pi and = x 3 + a•x
Abstract: The cryptographic system comprises at least one encryption station, one decryption station and a trapdoor generator. The trapdoor generator comprises means for selecting r distinct prime numbers Pi, generating a modulus m that is a product of the prime numbers Pi, selecting a pair of integers (a,b) satisfying 0 ≦ a < m and 0 ≦ b < m, computing for each pi a number N(pi) of distinct pairs of integers (x,y) satisfying 0 x < pi and 0 ≦ y < Pi and = x 3 + a•x + b (mod Pi) and a sum N(pi) + 1 representative of an order of an elliptic curve defined as the set of pairs of integers (x,y), computing a least common multiple µ of the values N(Pi) + 1, selecting a public multiplier e relatively prime to µ, computing a secret multiplier d according to d≡ 1/e (mod µ), and transferring data comprising at least m, a, b and e to a storage means provided in the cryptographic system. Alternatively, the trapdoor generator comprises means for selecting r distinct prime numbers Pi each corresponding to a sum value (Pi + 1) that satisfies (Pi + 1) = 0 (mod j) wherein 1 ≦ i ≦ r and j is 3 or 4, generating a modulus m that is a product of the prime numbers Pi, computing the least common multiple µ of the numbers (Pi + 1), selecting a public multiplier e relatively prime to µ, computing a secret multiplier d according to d = 1/e (mod µ), and transferring data comprising at least m and e to a corresponding storage means provided in the cryptographic system.
71 citations
TL;DR: It is shown that certain problems involving sparse polynomials with integer coefficients are at least as hard as any problem in NP.
64 citations
TL;DR: Bourque and Ligh as discussed by the authors proved that the conjecture is true for n ≤ ≤ 7 and not true for N ≤ ≤ ≤ ≥ 8, and thus the conjecture can be solved completely.
62 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2023 | 3 |
| 2022 | 14 |
| 2021 | 19 |
| 2020 | 17 |
| 2019 | 14 |