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3 | 3 | import java.math.BigInteger; |
4 | 4 | import java.util.Random; |
5 | 5 |
|
6 | | -//The algorithm is referred from |
7 | | -//https://www.geeksforgeeks.org/shors-factorization-algorithm/ |
| 6 | +// The algorithm is referred from |
| 7 | +// https://www.geeksforgeeks.org/shors-factorization-algorithm/ |
8 | 8 | public class ShorAlgorithm { |
9 | | - //trying to find the order of exponent given the base and the number |
10 | | - private int exponent(BigInteger base, BigInteger number) { |
11 | | - BigInteger result = BigInteger.ONE; |
12 | | - int increment = 0; |
13 | | - while (!result.equals(BigInteger.ONE) || increment == 0) { |
14 | | - result = result.multiply(base).mod(number); |
15 | | - increment++; |
16 | | - } |
17 | | - return increment; |
| 9 | + // trying to find the order of exponent given the base and the number |
| 10 | + private int exponent(BigInteger base, BigInteger number) { |
| 11 | + BigInteger result = BigInteger.ONE; |
| 12 | + int increment = 0; |
| 13 | + while (!result.equals(BigInteger.ONE) || increment == 0) { |
| 14 | + result = result.multiply(base).mod(number); |
| 15 | + increment++; |
18 | 16 | } |
| 17 | + return increment; |
| 18 | + } |
| 19 | + |
| 20 | + // implementing the shor algorithm |
| 21 | + public BigInteger[] shorAlgorithm(BigInteger number) { |
| 22 | + if (number.mod(new BigInteger("2")).equals(BigInteger.ZERO)) { |
| 23 | + BigInteger p = number.divide(new BigInteger("2")); |
| 24 | + BigInteger q = new BigInteger("2"); |
| 25 | + return new BigInteger[] {p, q}; |
| 26 | + } |
| 27 | + |
| 28 | + Random random = new Random(); |
| 29 | + BigInteger base = BigInteger.ZERO; |
| 30 | + do { |
| 31 | + base = new BigInteger(number.bitLength(), random); |
| 32 | + } while (base.compareTo(BigInteger.ZERO) <= 0 || |
| 33 | + base.compareTo(number) >= 0); |
19 | 34 |
|
20 | | - //implementing the shor algorithm |
21 | | - public BigInteger[] shorAlgorithm(BigInteger number) { |
22 | | - if(number.mod(new BigInteger("2")).equals(BigInteger.ZERO)) { |
23 | | - BigInteger p = number.divide(new BigInteger("2")); |
24 | | - BigInteger q = new BigInteger("2"); |
25 | | - return new BigInteger[]{p, q}; |
26 | | - } |
27 | | - |
28 | | - Random random = new Random(); |
29 | | - BigInteger base = BigInteger.ZERO; |
30 | | - do { |
31 | | - base = new BigInteger(number.bitLength(), random); |
32 | | - } while (base.compareTo(BigInteger.ZERO) <= 0 || base.compareTo(number) >= 0); |
33 | | - |
34 | | - BigInteger hcf = base.gcd(number); |
35 | | - if(hcf.compareTo(BigInteger.ONE) > 0) { |
36 | | - return new BigInteger[]{hcf, number.divide(hcf)}; |
37 | | - } |
38 | | - |
39 | | - int result = exponent(base, number); |
40 | | - if(result % 2 != 0) return null; |
41 | | - |
42 | | - BigInteger congruentResult = base.modPow(BigInteger.valueOf(result/2), number); |
43 | | - if(congruentResult.equals(number.subtract(BigInteger.ONE))) return null; |
44 | | - |
45 | | - BigInteger p = congruentResult.add(BigInteger.ONE).gcd(number); |
46 | | - BigInteger q = congruentResult.subtract(BigInteger.ONE).gcd(number); |
47 | | - |
48 | | - if(!p.equals(BigInteger.ONE) && !q.equals(BigInteger.ONE)) |
49 | | - return new BigInteger[]{p, q}; |
50 | | - return null; |
| 35 | + BigInteger hcf = base.gcd(number); |
| 36 | + if (hcf.compareTo(BigInteger.ONE) > 0) { |
| 37 | + return new BigInteger[] {hcf, number.divide(hcf)}; |
51 | 38 | } |
| 39 | + |
| 40 | + int result = exponent(base, number); |
| 41 | + if (result % 2 != 0) |
| 42 | + return null; |
| 43 | + |
| 44 | + BigInteger congruentResult = |
| 45 | + base.modPow(BigInteger.valueOf(result / 2), number); |
| 46 | + if (congruentResult.equals(number.subtract(BigInteger.ONE))) |
| 47 | + return null; |
| 48 | + |
| 49 | + BigInteger p = congruentResult.add(BigInteger.ONE).gcd(number); |
| 50 | + BigInteger q = congruentResult.subtract(BigInteger.ONE).gcd(number); |
| 51 | + |
| 52 | + if (!p.equals(BigInteger.ONE) && !q.equals(BigInteger.ONE)) |
| 53 | + return new BigInteger[] {p, q}; |
| 54 | + return null; |
| 55 | + } |
52 | 56 | } |
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