基本介紹
- 外文名:primality
- 詞性:名詞
- 英式音標:[praɪˈmælətɪ]
- 美式音標: [prɪ'mælɪtɪ]

Primality Testing in Polynomial Time多項式時間中的初級測試 《Primality Testing in Polynomial Time多項式時間中的初級測試》是2004年8月出版的圖書,作者是Dietzfelbinger, Martin。
Input #1: n > 3, an odd integer to be tested for primality;Input #2: k, a parameter that determines the accuracy of the test Output: composite if n is composite, otherwise probably prime write n − 1 as 2r·d with d odd by factoring powers of 2 from n − 1 WitnessLoop: ...
除標準算法操作外,BigInteger 還提供模 (modular) 算法、GCD 計算、基本 (primality) 測試、素數生成、位處理以及一些其他操作。 BigDecimal 提供適用於貨幣計算和類似計算的任意精度的有符號十進制數字。BigDecimal 允許用戶對捨入行為進行完全控制,並允許用戶選擇所有八個捨入模式。從以下版本開始:JDK1.1 pascal ...
另外,隨機性給予互動式證明系統的力量,以及對困難問題所能建立更簡單的算法的特質,例如多項式時間內的質數測試(primality testing)和對數空間的圖相連測試(graph connectedness testing),又隱含著隨機性是有可能增加計算能力的。量子計算機則是另一種先天就具有著機率性質的計算模式。
類似地,對於質數測試(primality test)有簡單的隨機化原地算法像是米勒-拉賓檢驗,也有簡單原地隨機化整數分解算法像是Pollard's rho 算法。參考RL和BPL有對這個現象更多的討論。在函式的程式設計 函式程式設計(functional programming)語言經常不鼓勵或不支援會覆蓋資料的原地算法,因為這是副作用的一種型態;反之,...
另外,隨機性給予互動式證明系統的力量,以及對困難問題所能建立更簡單的算法的特質,例如多項式時間內的質數測試(primality testing)和對數空間的圖相連測試(graph connectedness testing),又隱含著隨機性是有可能增加計算能力的。量子計算機則是另一種先天就具有著機率性質的計算模式。
機率素數檢測(probabilistic primality testing)是2018年全國科學技術名詞審定委員會公布的計算機科學技術名詞。定義 判定一個數是否素數的機率算法。其中由米勒(Miller)和拉賓(Rabin)在1980年完成的首個機率素數檢測算法稱為Miller-Rabin素數檢測。由阿格拉沃爾(Agrawal)、卡亞勒(Kayal)和薩克塞納(Saxena)在2002年...
[4]Michael O Rabin.Probabilistic algorithm for testing primality[J].Journal of Number Theory,1980.[5]Michael O. Rabin.Probabilistic Automata[J].Information and Computation,1963.[6]Silvio Micali,Michael O. Rabin,Salil P. Vadhan.Verifiable random functions[J].Foundations of Computer Science (...
Primality...399 Read-once branching programs...404 10.3 Alternation...408 Alternating time and space...410 The Polynomial time hierarchy...414 10.4 Interactive Proof Systems...415 Graph nonisomorphism...415 Defnition of the model...416 IP=PSPACE......
9.5 primality tests using orders of integers and primitive roots 378 9.6 universal exponents 385 10 applications of primitive roots and the order of an integer 393 10.1 pseudorandom numbers 393 10.2 the eigamal cryptosystem 402 10.3 an application to the splicing of telephone cables 408 11 ...
1.3 Primality testing(素性測試)1.4 Cryptography(密碼學)1.5 Universal hashing(全域散列)Exercises(習題)Randomized algorithms:a virtual chapter(虛擬章:隨機化算法)2 Divide-and-conquer algorithms(分而治之算法)2.1 Multiplication(乘法)2.2 Recurrence relations(遞歸關係)2.3 Mergesort(合併...
10.3.3 Optimal Binary Search Tree 447 10.3.4 All-Pairs Shortest Path 451 10.4 Randomized Algorithms 454 10.4.1 Random Number Generators 455 10.4.2 Skip Lists 459 10.4.3 Primality Testing 461 10.5 Backtracking Algorithms 464 10.5.1 The Turnpike Reconstruction Problem 465 10...
10.4 Randomized Algorithms / 隨機化算法494 10.4.1 Random-Number Generators / 隨機數發生器495 10.4.2 Skip Lists / 跳躍表500 10.4.3 Primality Testing / 素性測試503 10.5 Backtracking Algorithms / 回溯算法506 10.5.1 The Turnpike Reconstruction Problem / 收費公路重建問題506 10...
16.1. Primality testing using Jacobi sums 16.2. Sinnott's proof thatμ= 0 16.3. The non-p-part of the class number in a Zp-extension Appendix 1. Inverse limits 2. Infinite Galois theory and ramification theory 3. Class field theory Tables 1. Bernoulli numbers 2. Irregular primes 3. ...
Chapter Ⅴ.Primality and Factoring 1.Pseudoprimes 2.The rho method 3.Fermat factorization and factor hases 4.The continued fraction method 5.The quadratic sieve method Chapter Ⅵ.Elliptic Curves 1.Basic facts 2.Elliptic curve cryptosystems 3.Elliptic curve primality test 4.Elliptic curve factorization...
8.3 Testing for Primality 251 8.4 The Chinese tLemainderTheorem 254 8.5 Discrete Logarithms 257 8.6 Recommended Reading andWeb Sites 262 8.7 Key Terms, Review Questions, and Problems 263 Chapter 9 Public-Key Cryptography and RSA 266 9.1 Principles of Public-Key Cryptosystems 269 9.2 The...
19 Primality Testing and Carmichael Numbers... 129 20 Squares Modulo p ... 141 21 Is.1 a Square Modulo p?Is 2?... 148 22 Quadratic Reciprocity... 159 23 Proof of Quadratic Reciprocity...
10.4.3. Primality Testing 10.5. Backtracking Algorithms 10.5.1. The Turnpike Reconstruction Problem 10.5.2. Games Summary Exercises References Chapter 11 Amortized Analysis 11.1. An Unrelated Puzzle 11.2. Binomial Queues 11.3. Skew Heaps 11.4. Fibonacci Heaps 11.4.1. Cutting Nodes in ...
18 Primality testing 19 Factoring integers 20 Application:Public key cryptography Ⅴ Hibert 21 Grobner bases 22 Symbolic integration 23 Symbolic Summation 24 Applications Appendix 25 Fundamental concepts Sources of illustrations Sources of quotaions List of algorithms Lsit of figureds and tables References...
...2579.1.7生成素數(GeneratingPrimes)...2589.2素性測試(PRIMALITYTESTING)...
數學中,盧卡斯-萊默檢驗法(英語:Lucas–Lehmer primality test)是檢驗梅森數的素性檢驗,是由愛德華·盧卡斯於1878年完善,德里克·亨利·萊默(英語:Derrick Henry Lehmer)隨後於1930年代將其改進。方法 令梅森數Mₚ=2-1作為檢驗對象,定義數列{Lₙ}:L₀=4,,n>0.這個數列的開始幾項是4,14,194,37634...
