How does zk-DID (Zero-Knowledge Decentralized Identity) technically work?

Nguồn: LBankThời gian: 2025-03-19 01:48:00

How zk-DID (Zero-Knowledge Decentralized Identity) Technically Works

In an increasingly digital world, the need for secure and private identity management has never been more critical. Zero-Knowledge Decentralized Identity (zk-DID) emerges as a groundbreaking solution that allows individuals to prove their identity without disclosing sensitive information. This article delves into the technical workings of zk-DID, exploring its key components, protocol flow, security benefits, and potential applications.

1. Understanding Decentralized Identity (DID)

A Decentralized Identifier (DID) serves as a unique identifier for individuals or entities within a blockchain or decentralized network. Unlike traditional identifiers managed by centralized authorities, DIDs are controlled by the individual themselves. This self-sovereignty empowers users to manage their identities across various applications and services without relying on third-party intermediaries.

2. The Role of Zero-Knowledge Proofs

At the heart of zk-DID lies zero-knowledge proofs—mathematical constructs that enable one party to demonstrate the truth of a statement without revealing any underlying data. These proofs are essential for maintaining privacy while allowing verification processes to occur securely.

The two primary types of zero-knowledge proofs utilized in zk-DIDs are:

  • zk-SNARKs: Zero-Knowledge Succinct Non-Interactive Argument of Knowledge is known for its efficiency and compactness in proof generation.
  • zk-STARKs: Zero-Knowledge Scalable Transparent Argument of Knowledge offers scalability advantages and does not require a trusted setup phase.

3. Cryptographic Techniques Underpinning zk-DIDs

The effectiveness of zk-DIDs relies on several cryptographic techniques that ensure secure communication and data integrity:

  • Public-Key Cryptography: This technique facilitates secure communication between parties through asymmetric encryption methods where each user possesses both public and private keys.
  • Hash Functions: Hash functions create unique identifiers from input data while ensuring data integrity through irreversible transformations.
  • Homomorphic Encryption:This advanced form of encryption allows computations on encrypted data without needing decryption first, enhancing privacy during processing operations.

4. Protocol Flow: How zk-DID Operates

The operational flow of zk-DID can be broken down into several key steps that illustrate how users interact with this technology effectively:

  1. Initialization:
    The user generates their DID along with a corresponding private key stored securely on their device or wallet.
  2. Create Verification Proof:
    The user constructs a zero-knowledge proof demonstrating possession of their private key while keeping it confidential from external parties.
  3. User Interaction with Service Provider:
    The service provider requests verification from the user based on specific criteria related to access or authentication needs.
  4. Pseudonymous Verification Process:
    The service provider verifies the user's proof using cryptographic methods without gaining access to any personal information about them—ensuring anonymity throughout this process.

    5 . Security Benefits Offered by zk - DID < p > The implementation o f z k - D I D provides numerous security advantages : < ul > < li >< strong > Privacy : Users ' sensitive information remains confidential , protecting them against potential breaches . < li >< strong > Anonymity : Individuals can maintain anonymity while still proving necessary aspects o f their identity , fostering trust in digital interactions .   < li >< strong > Enhanced Security :  The use o f zero - knowledge proofs guarantees that verification processes are robust , minimizing risks associated with identity theft or fraud .    < / ul > 6 . Applications o f z k - D I D Technology                  < / h 2 > < p > The versatility o f z k - D I Ds opens doors t o various applications across industries :   
    • < strong > Identity Verification : Secure login mechanisms enabling seamless authentication across platforms .
    • < Strong > Compliance : Meeting regulatory requirements related t o privacy laws such as GDPR .
    • < Strong > Trustless Interactions : Facilitating decentralized systems like blockchain where trust is established through cryptographic means rather than centralized authorities .                                                                                        

Technical Study
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0.03732
2.89%
0.01480
30.05%
0.00001277
-5.69%
0.0613
-1.76%
0.6371
1.58%
0.004446
-3.35%
6.18
-0.32%
25.32
14.00%
0.006192
0.88%
1.397
1.45%
0.1148
4.27%
0.2378
-5.26%
0.9899
1.58%
0.1996
0.05%
0.00000016147
0.20%
0.000851
0.35%
0.3112
2.71%
335.7
0.75%
0.357
-2.46%
0.000119
0.00%
0.00722
0.56%
0.003877
17.66%
0.01839
2.62%
0.001596
40.62%
1.6105
-33.78%
0.1819
-4.26%
10.739
33.54%
10.62
0.00%
0.001506
-7.32%
1.7629
-0.51%
0.00029882
5.37%
0.6953
-1.53%
0.00363
45.20%
0.00000000009555
3.25%
0.25620
-4.99%
2.949
0.41%
0.647
2.05%
0.4383
3.64%
0.0002401
-9.36%
0.004943
-0.82%
0.00364737
0.87%
0.000283
-8.41%
0.002047
23.16%
0.00483
2.99%
0.00875
-5.61%
0.002800
-8.62%
0.04858
0.14%
0.000369
-1.86%
0.000745
4.93%
0.001937
82.22%
0.02343
-2.62%
0.3178
-0.59%
0.1500
-0.40%
0.000376
-4.57%
0.00010365
9.89%
0.00833
-15.69%
0.06075
-3.22%
0.020532
5.13%
0.0590
22.66%
0.01067
-16.71%
1.023
-2.85%
0.6417
-21.72%
0.01464
-0.20%
0.7438
-7.06%
0.1098
0.92%
0.00004078
1.34%
6.120
-0.13%
0.0002868
-0.59%
0.000209802
-1.11%
0.000000001497
0.00%
0.001056
-9.43%
0.00000466
-6.80%
0.002486
-5.90%
0.000718
-9.46%
0.00806
-5.40%
0.000240
-2.44%
0.4348
8.95%
0.03949
-5.62%
0.000102
6.25%
44.48
0.16%
5.890
-2.13%
0.02590
-9.06%
0.01800
1.12%
17.348
-0.88%
2.207
0.27%
0.1523
1.20%
0.1421
-6.51%
0.63390
8.71%
0.00006644
1.05%
5.39
-1.82%
0.0686
-2.83%
0.5183
-3.28%
0.001025
-7.24%
0.0000214
0.00%
0.001417
-12.85%
0.1209
-4.28%
31.21
1.63%
0.00009726
15.79%
0.002070
-11.50%
0.0097
-20.49%
0.001614
1.57%
0.0937
0.11%
0.012983
-0.58%
0.00500
0.60%
0.000001648
-2.20%
0.00000003809
-2.08%
0.000629
-8.31%
0.891
-0.67%
0.005967
-22.60%
0.2511
-0.24%
0.05901
-6.39%
0.5829
1.50%
1.1796
-0.08%
0.04959
3.14%
3075.37
0.39%
0.000389
18.24%
0.2669
-15.91%
1.5027
-0.58%
0.07772
6.44%
0.0003198
-8.39%
0.0000046
17.95%
5.716
-2.44%
0.0058
-12.12%
0.00096
2.13%
0.009354
-2.81%
0.1795
-7.47%
0.3506
-2.20%
0.004642
-25.73%
0.000000000248
-2.36%
0.06315
-1.86%
0.01191
-0.08%
7.72
-3.14%
0.2148
-1.15%
7.6559
-5.24%
0.1388
0.87%
0.004817
12.84%
0.0479
-0.83%
0.00136
7.94%
1.2906
-4.53%
0.2580
-7.53%
0.721
0.14%
2.400
-0.33%
0.551
-1.96%
0.002039
-8.93%
0.02076
-4.86%
0.85436
0.00%
0.0042
0.00%
1.044
2.15%
0.0403
4.40%
0.3355
9.57%
0.002810
1.37%
0.02650
-5.63%
0.3988
-10.42%
166.78
0.22%
0.00262
2.34%
0.003881
6.97%
0.1207
4.41%
0.00618
-0.64%
1.986
1.27%
0.2083
-2.80%
0.01860
2.82%
0.03696
-8.17%
0.020541
-8.71%
0.05360
19.11%
0.002303
-11.80%
0.3420
-3.99%
0.5426
-4.30%
0.0235
1.29%
1.5631
-4.01%
0.01045
-20.41%
0.1078
-2.71%
0.00000001315
-1.42%
0.0005509
-6.60%
6.4818
62.01%
0.0000003072
-4.00%
0.001282
-4.40%
0.03940
-3.24%
2.365
-2.07%
0.00003132
1.79%
0.280
-0.71%
0.03433
-3.05%
0.002927
-13.84%
0.003169
-0.63%
0.00002883
8.55%
0.6032
-5.28%
0.004717
-4.53%
0.0000000790
-3.19%
0.003915
-6.87%
9.786
0.16%
0.000870
1.99%
0.006889
44.48%
0.0006617
-0.62%
0.00016984
-15.08%
0.0274
-8.97%
0.00714
0.14%
0.777
1.17%
0.012978
0.67%
0.000002570
-10.45%
0.1445
0.00%
0.19680
-3.45%
0.0113
-4.24%
0.2120
-1.07%
0.006095
-8.70%
0.000642
9.74%
0.01450
-15.16%
0.674
-2.03%
0.008500
8.97%
6.5090
-3.22%
0.012770
-1.77%
0.6379
-2.48%
0.001151
1.77%
1.378
-1.78%
0.05451
4.97%
0.01484
3.63%
0.001839
0.99%
0.03135
0.06%
0.019094
7.42%
0.2827
-1.64%
0.1044
-0.38%
0.0030
-3.23%
0.01389
-17.12%
0.4712
-2.34%
0.002968
0.07%
0.00103
-13.45%
0.0005156
-8.84%
0.0000509
4.30%
0.002009
-13.14%
0.0809
-0.61%
0.1007
-0.79%
0.0108
1.89%
0.07669
-2.70%
0.003999
-0.50%
0.13434
-1.39%
0.02220
-21.42%
0.428
0.94%
0.0776
-3.48%
0.00005016
1.09%
3.0229
-2.14%
0.0007290
-4.69%
7.012
-1.17%
0.03024
-7.66%
0.001526
-7.46%
0.00000813
1.25%
0.011992
-4.22%
0.0000745
13.05%
0.1924
-0.82%
0.00000001565
3.23%
0.04439
-25.92%
0.0004481
6.03%
0.03457
-4.69%
0.0464
-0.43%
0.2219
-0.80%
0.2999
-0.27%
0.00000021520
-30.58%
0.00005507
-4.43%
0.003404
-1.62%
0.625
0.00%
2.322
-0.81%
0.00960
6.55%
0.0002839
-0.42%
2190.46
-0.36%
0.002220
8.56%
0.0000521
6.98%
1347
6.31%
0.01706
-14.44%
0.00421
0.24%
0.01811
-3.77%
0.000001664
-0.89%
0.1472
-0.88%
0.0007500
-20.06%
0.825
-0.12%
19.20
-1.54%
0.7622
-0.13%
0.004263
-0.35%
0.1588
-2.58%
0.1009
-2.51%
0.000349
-9.59%
0.000933
-11.90%
0.7620
-0.09%
0.930
1.64%
0.007188
-1.76%
23.594
-1.31%
0.000000513
-1.16%
0.02983
0.44%
0.2780
-1.21%
0.03000
0.00%
0.11723
5.21%
0.00002467
-4.64%
0.1034
-1.62%
0.004435
-12.20%
76.8
-2.04%
0.004399
-3.11%
0.0002212
-24.69%
0.0000000000000159
-11.17%
2.239
3.71%
0.002469
4.13%
0.01242
-5.91%
0.0098
-2.00%
0.0000086
-6.52%
3.484
-1.58%
0.002107
0.52%
0.2767
3.05%
0.01852
-6.13%
0.7419
-3.17%
0.2138
-0.74%
0.0051037
0.05%
25.0000
-0.44%
0.01556
-16.16%
0.1106
-1.43%
0.0360
-0.83%
0.000022
-8.33%
0.2226
-0.45%
0.0001532
-24.90%
0.0004851
21.88%
0.0099
2.06%
0.0000699
145.26%
0.0546
1.11%
0.0000002725
-31.24%
12.32
-0.32%
0.003922
-18.95%
0.489
1.03%
0.3339
0.15%
0.002920
-6.68%
1.4485
1.00%
0.000001970
-12.17%
0.00000000108
42.11%
0.003513
2.69%
0.00803
6.92%
0.0000266
-1.12%
0.2103
-0.76%
0.03850
-13.42%
0.0000000002102
0.91%
0.001951
-1.51%
0.0000763
9.00%
0.0008144
-7.83%
0.915
1.33%
0.0065104
-32.18%
0.003438
-0.92%
0.0580
-0.51%
0.03918
-9.39%
1.269
0.32%
0.0770
0.65%
0.01477
2.07%
0.0001786
114.66%
0.02679
0.68%
0.05702
0.04%
0.2848
-4.62%
0.05821
-1.69%
0.002473
3.34%
0.001289
-27.83%
3.40
-3.13%
0.001904
0.79%
0.000000000598
-3.55%
17.57
-1.01%
0.1759
-0.73%
0.0765
0.00%
0.000000000000899
-4.56%
0.000000001819
-4.51%
0.1113
-5.68%
0.000000000685
-4.60%
0.0006347
-2.43%
0.0483
0.21%
0.001300
-4.69%
0.0000086
-3.37%
0.004971
-10.53%
0.3630
-2.97%
6.4965
-7.13%
0.005149
-6.59%
0.003912
0.00%
0.00120
-0.83%
0.1094
-1.80%
0.1705
-2.24%
0.0382
50.39%
0.001172
-2.66%
0.09000
-21.62%
0.00010610
-0.01%
0.00000000015505
-1.19%
0.0260
-2.26%
0.032747
-4.71%
0.00009300
-27.34%
0.02782
0.54%
0.00000000001518
-11.44%
0.1524
-3.97%
0.0000000626
0.48%
0.0004086
5.66%
18.12
-0.71%
0.0168
-1.18%
0.00533
-1.11%
0.0000000522
-0.76%
0.00003
0.00%
0.000000002050
2.81%
0.0111
0.91%
0.02508
-0.48%
0.0004
-33.33%
15.09
-2.83%
0.001336
-3.05%
0.0022773
-5.38%
0.01285
-1.83%
0.937
-12.67%
0.000030
3.45%
0.013605
0.05%
0.0063
0.00%
0.0667
-4.03%
0.9177
-0.26%
0.00000724
0.00%
0.659
-3.37%
0.000107
-1.83%
0.000261
61.11%
0.006146
1.65%
0.000000000001765
-0.84%
0.0007593
-6.05%
0.00910
-0.55%
0.0195
2.09%
0.0000018
-10.00%
0.000504
44.00%
0.002701
0.04%
0.00000394
-2.96%
0.000261
-14.98%
0.0006795
-2.82%
0.0934
-3.51%
0.00725
-1.09%
0.0967
22.25%
0.0000000030204
-29.16%
0.0002382
-3.17%
0.000012
-60.00%
0.00306
0.00%
0.0000000171
14.77%
0.0919
-3.67%
0.00000000001162
-5.22%
0.00006107
-37.58%
0.01684
-0.82%
0.008231
0.00%
0.001032
-0.77%
0.803
-0.12%
0.04024
2.26%
0.0000235
0.00%
0.01114
-12.35%
0.000000000003
-25.00%
0.00000000000018
-30.77%
0.01303
9.22%
0.1432
-5.67%
8.12
-1.34%
0.00000926
0.00%
0.0114
-0.87%
0.2591
-3.25%
1.527
-1.10%
0.00869
-6.16%
0.00685
-20.81%
0.00237
-15.96%
0.0436
-0.91%
0.3759
-2.57%
83.62
-9.05%
0.05024
-4.09%
2.51
97.64%
0.1278
-1.39%
0.000716
-13.73%
0.000786
-5.19%
0.002013
0.00%
0.0338
-2.03%
0.0000013
85.71%
0.01323
-0.82%
0.01081
-2.70%
0.0048
-26.15%
0.0000243
-0.82%
0.0987
0.92%
0.000835
-0.95%
0.0000651
0.15%
0.05851
-0.37%
0.169000
-26.52%
0.249
-17.00%
0.0569
-2.23%
0.004220
0.57%
0.1168
-0.93%
0.1336
-1.26%
0.1286
-1.91%
18.58
0.87%
0.3886
-1.47%
0.000850
-8.01%
0.000090
5.88%
0.00003
-50.00%
0.003590
-12.91%
450.00
80.00%
0.00648
0.15%
0.0099
11.24%
0.05804
-0.14%
0.0000119
-15.00%
0.03326
4.04%
0.02940
-1.44%
0.00014
0.00%
0.01050
0.00%
1.485
-2.11%
0.01670
-1.71%
0.0018
5.88%
0.000025
-3.85%
1.670
-2.85%
0.00027
0.00%
0.001420
-13.99%
0.0002201
-8.37%
0.00093
-27.91%
0.000190
-5.94%
0.02048
1.69%
0.002335
-4.93%
0.03745
-0.87%
0.00000000000103
7.29%
0.000000000003846
-15.08%
0.00000000000212
19.77%
0.0515
-3.20%
0.00000000000012
0.00%
0.731
-1.22%
0.002234
-9.77%
0.0942
-2.48%
0.000037
-17.78%
0.0000061
0.00%
0.000001624
-3.22%
0.0866
-0.12%
0.1288
-13.85%
0.00000054
-3.57%
0.00002265
0.31%
0.01286
-1.08%
0.00036
0.00%
0.0000000000000159
-1.85%
0.000025
78.57%
0.0122
-3.94%
0.000076
-10.59%
0.0591
1.90%
0.0390
-1.52%
0.0810
-1.34%
3.020
-0.56%
0.0009049
-9.32%
0.0004421
-4.10%
0.02948
-6.50%
0.0694
-1.00%
0.0548
1.48%
0.0001
0.00%
0.0897
2.99%
0.1531
-0.20%
0.000017
21.43%
0.0000099
0.00%
0.532
-1.85%
0.000000000030
-57.14%
0.00000000000651
-0.15%
0.0351
-1.13%
0.000004
-55.56%
0.001100
-3.25%
0.750
0.00%
0.1352
-0.66%
0.003639
-9.68%
0.00004089
-1.64%
0.0119
-2.46%
0.001761
-5.02%
0.0000006650
0.51%
0.00000000000115
0.00%
0.0000138
39.39%
0.001025
-9.77%
0.1902
-1.50%
0.00040
11.11%
0.8430
0.19%
0.0007
-41.67%
0.00024
-4.00%
0.1922
-0.98%
0.0816
-4.00%
0.00608
63.88%
0.001790
0.00%
0.00220
-8.33%
0.0370
-2.89%
0.2993
-0.03%
0.00000007
-41.67%
0.0001402
-0.07%
0.0005
0.00%
0.001044
-7.86%
0.00004
0.00%
0.490
-3.54%
0.0001551
1.70%
0.0000002169
0.14%
0.00242
-7.98%
0.0000310
-0.64%
0.0004474
-14.98%
0.006314
-6.47%
0.1475
-0.87%
0.0006708
-6.61%
0.0066
3.13%
0.003327
-11.02%
0.00000000003011
79.65%
0.5396
0.86%
0.0014
55.56%
0.00000314
-4.56%
0.000062
40.91%
0.0000329
0.00%
0.0000091
15.19%
2.979
-1.55%
0.001233
-0.72%
0.000003220
101.25%
0.00000000056
-1.75%
0.0000000192
4.35%
0.0182
0.00%
0.0009
0.00%
0.0700
39.44%
49.879
-1.37%
0.00011
-8.33%
0.0618
0.16%
0.3905
24.72%
0.00000042
0.00%
0.000000108
2.86%
0.0108
10.20%
0.0005
25.00%
0.01299
-1.59%
0.7000
0.00%
0.00000000000288
-0.69%
11.5002
-4.96%
0.0026
0.00%
0.00009
-10.00%
0.000194
1.04%
0.000000000019
72.73%
0.3564
-8.90%
100.71
-0.94%
0.01200
0.00%
0.00011
-15.38%
0.003229
-10.53%
0.0027
0.00%
0.3061
0.26%
0.00004399
0.00%
0.000000000120
10.09%
0.00000007783
0.00%
0.000400
-20.00%
0.00000000003580
-1.70%
0.000000000769
-4.00%
0.000056
-27.27%
0.00077
-8.33%
0.000453
-0.44%
0.000092
6.98%
0.000000001868
-0.05%
0.00011
0.00%
0.000000000750
-7.75%
0.0475
-4.62%
0.00006
-40.00%
0.00774
12.34%
0.000000000375
0.27%
0.000190693
-0.96%
0.000028
-15.15%
0.00000000000039
-4.88%
0.00000000000400
2.83%
0.000000008400
0.00%
0.000000000533
0.00%
0.000000002387
-0.83%
0.000000040
2.56%
0.000000000129
0.78%
0.00030000
-14.29%
8.94
-2.19%
0.00000152
4.83%
0.0249
9.69%
0.0000296
-12.43%
0.000033
-13.16%
0.001500
0.00%
0.2237
-0.53%
0.0562
28.60%
0.01075
-9.13%
0.001650
50.00%
0.00021
0.00%
0.00083
0.00%
0.0085
41.67%
0.000700
38.34%
0.0000017
-41.38%
0.0000010
42.86%
0.0822
-0.60%
0.005123
-3.97%
0.02311
-14.91%
1.2799
0.38%
0.01475
-7.06%
0.1167
-1.77%
0.0003842
-5.79%
0.4896
0.62%
0.10555
1.39%
0.1369
-4.13%
0.3718
-2.24%
0.003258
-18.10%
0.2565
0.23%
58.5600
0.00%
0.0592
0.85%
0.0004530
-13.43%
0.0907
-4.53%
0.0004917
-6.84%
0.0003220
0.00%
0.002600
-7.04%
0.0009012
0.00%
0.0004036
-4.06%
0.00600
0.00%
0.0007993
0.00%
6.159
-0.77%
0.2216
1.00%
0.0000675
-0.74%
0.0000397
0.00%
0.002785
-5.66%
0.0012
0.00%
0.7732
-2.80%
1899.00
0.00%
0.4397
-3.28%
0.5933
-3.12%
0.0480
2.13%
0.00426
4.93%
0.00221
-5.56%
0.2083
-1.84%
2.5129
0.00%
0.468
2.86%
1.000000
0.00%
0.3771
0.00%
0.5732
0.00%
1.871
-0.95%
0.0569
-1.22%
0.000000100
0.00%
0.0001030
0.00%
0.00103
0.00%
0.6826
6.13%
0.0700
0.00%
0.00000000003010
63.06%
0.001126
-2.26%
0.00000088
3.53%
0.1526
-0.33%
0.01891
-0.84%
0.1908
-2.15%
0.000216
0.00%
2.179
0.00%
1.5000
0.00%
3.9889
0.00%
1.1371
0.00%
6.444
-0.89%
0.000079
0.00%
0.4424
0.00%
0.000398
2.58%
0.0071
0.00%
0.000210
0.00%
14.15
0.21%
0.0761
-3.55%
0.1140
-0.96%
0.1771
0.00%
0.004281
-1.11%
0.000452
0.00%
0.0272
0.00%
0.1204
0.00%
2.707
2.04%
1.116
1.92%
0.006000
0.00%
0.000300
0.00%
0.0025
0.00%
0.00035
0.00%
0.0004
0.00%
0.00033
0.00%
0.011926
0.00%
0.001100
0.00%
0.000365
0.00%
0.001201
0.00%
0.0064
0.00%
0.0000002593
0.00%
0.00001584
0.00%
0.0000001013
0.00%
0.000024
-4.00%
0.00005
0.00%
0.00006187
0.00%
0.000166
0.00%
0.001405
0.00%
0.2467
0.33%
0.000496
6.21%
0.000902
0.00%
0.0001
0.00%
0.0009
0.00%
0.0560
0.00%
0.004025
0.00%
0.00000100
0.00%
0.0000000104
0.00%
0.000685
0.00%
0.00000006
0.00%
0.001000
0.00%
0.0000000053
0.00%
0.0000000039
0.00%
0.00001626
0.00%
0.000423
0.00%
0.0065
0.00%
0.000310
0.00%
0.3284
0.00%
0.9500
0.00%
0.0057
0.00%
0.000405
0.00%
----
0.001290
0.00%
0.00000011
0.00%
0.00023846
0.00%
0.000758
0.00%
0.001000
0.00%
0.000058
0.00%
1.6799
0.00%
0.0920
0.00%
0.000098
0.00%
0.00000000002387
0.00%
0.00425
0.00%
0.00001
0.00%
0.000118
0.00%
0.0010
0.00%
0.00037
0.00%
0.001963
0.00%
0.00000055
0.00%
0.00006767
0.00%
0.00005458
0.00%
0.001263
0.00%
0.001210
0.00%
0.00171
0.00%
0.0072
0.00%
0.0001000
0.00%
0.05056
0.00%
1.3575
0.00%
0.00136
0.00%
0.00007
0.00%
0.001234
0.00%
0.000449
0.00%
0.0066
0.00%
0.0004
0.00%
0.0007
0.00%
0.0240
0.00%
0.000522
0.00%
0.020562
0.00%
0.9990
0.00%
0.0000111
0.00%
0.007000
0.00%
0.000363
0.00%
0.0012
0.00%
0.000792
0.00%
0.001200
0.00%
0.000331
0.00%
0.001050
0.00%
0.000383
0.00%
0.01595
0.00%
0.001000
0.00%
50.0000
0.00%
0.0006
0.00%
0.0786
0.00%
0.001563
0.00%
1.6349
0.00%
0.00000000000540
0.00%
0.000028
0.00%
0.000999
0.00%
0.001801
0.00%
0.0200
0.00%
0.0093
0.00%
0.0006
0.00%
65.1101
0.00%
1.444
1.98%
3.7189
0.00%
0.000082
0.00%
0.0072
1.41%
0.016111
0.00%
4.1000
0.00%
0.0489
0.00%
0.00008997
0.00%
0.0131
0.00%
0.0013
0.00%
0.1078
0.00%
4.4022
0.00%
0.0745
0.00%
0.002461
0.00%
0.001160
0.00%
0.3882
0.00%
0.001000
0.00%
0.076250
0.00%
0.020595
0.00%
0.0150
0.00%
0.0036
0.00%
0.1769
0.00%
2.2915
0.00%
0.000257
0.00%
0.000620
0.00%
0.000946
0.00%
0.022345
0.00%
0.4820
0.00%
0.0490
0.00%
0.0096
0.00%
1.76670591
0.00%
0.0024
0.00%
0.000399
0.00%
0.0000000000270
0.00%
0.0000002850
0.00%
0.6700
0.00%
0.0102
0.00%
0.00007
0.00%
0.01989
0.00%
0.2888
0.00%
0.00501
0.00%
0.02700
0.00%
0.0650
0.00%
0.3515
0.00%
0.00125
0.00%
0.000446
0.00%
0.4900
0.00%
1.0100
0.00%
0.5000
0.00%
0.010100
0.00%
0.0069
0.00%
0.88686
0.00%
0.05578
0.00%
1.1760
0.00%
0.000561
0.00%
0.1725
0.00%
0.01463
0.00%
0.01451
1.11%
0.00614
0.00%
0.4606
0.00%
0.001800
0.00%
0.000001000
0.00%
0.0000008
0.00%
1.3475
2.49%
0.00390
0.00%
0.0000325
0.00%
0.00000326
0.00%
1.0000
0.00%
0.00455
0.00%
0.34211
0.00%
0.00132
0.00%
0.0000077
0.00%
0.0005
0.00%
0.00146
0.00%
0.001277
0.00%
0.03520
0.00%
0.0000023
0.00%
0.000000005
0.00%
0.000514
0.00%
0.001987
0.00%
0.000313
0.00%
0.0000029
0.00%
0.0007000
0.00%
0.00200
0.00%
0.03455
0.00%
0.0032
0.00%
0.000495
0.00%
0.00049
0.00%
0.00041
0.00%
0.00017800
0.00%
0.007210
0.00%
0.00635
0.00%
0.0900
0.00%
0.00006
0.00%
0.000000000009
0.00%
0.01030
0.00%
0.00240
0.00%
0.00070
0.00%
0.003000
0.00%
0.000310
0.00%
0.0000269
0.00%
0.0000000500
0.00%
0.0000001300
0.00%
0.000996
0.00%
0.7997
0.00%
0.0001543
0.00%
0.000426832
0.00%
0.00002805
0.00%
0.00776
0.00%
0.1600
0.00%
0.0000245
0.00%
0.000057
1.79%
0.1197
0.00%
0.00056
0.00%
0.000510
0.00%
0.00218
0.00%
0.002100
0.00%
0.000270
0.00%
0.0668
0.00%
0.000055
0.00%
0.3101
0.00%
0.0000301
-1.31%
0.00639
0.00%
0.4400
0.00%
1.4371
0.00%
0.002579
0.00%
0.250
0.00%
0.4432
3.41%
0.3844
-1.84%
0.001106
0.00%
0.0249
0.00%
0.6608
0.00%
0.0627
2.96%
0.5300
0.57%
0.00500
0.00%
3.58
0.00%
0.01168
1.21%
0.0020
0.00%
0.00538
0.00%
0.4487
1.13%
5155.00
0.00%
2.217
-0.45%
1.497
-2.35%
0.0091
0.00%