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

Fonte: LBankTempo: 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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0.2517
-0.67%
0.1266
-3.65%
0.010618
4.61%
0.00000015883
6.06%
0.00056801
17.03%
1.7705
0.50%
0.000850
-0.82%
0.01223
-12.64%
0.0005710
-17.38%
0.005955
-3.72%
0.7046
-0.75%
1.524
-1.04%
0.005451
0.87%
0.02641
-0.64%
0.1260
4.39%
0.00065
0.00%
10.54
-0.38%
0.0000000513
21.85%
0.004184
20.75%
7.783
1.59%
0.0002695
-10.55%
0.1850
6.26%
0.5749
-0.64%
0.003065
1.39%
0.1135
4.32%
0.000378
1.07%
0.3609
12.85%
0.05295
-4.42%
0.00028349
-0.16%
0.007323
6.61%
0.004992
-0.36%
0.04097
5.62%
0.3038
-4.28%
0.000098
22.50%
0.0409
-21.65%
0.00003940
-0.28%
0.5172
-2.93%
0.000024
-7.69%
0.001444
12.29%
0.0309
-0.96%
0.0758
1.34%
0.00000452
2.49%
17.374
-0.33%
0.2793
-2.10%
0.3203
-5.63%
0.000387
0.78%
0.2148
0.61%
0.013968
7.43%
0.00094
-4.08%
7.9036
12.87%
0.1037
1.07%
17.91
0.28%
0.1501
1.76%
3.8796
4.29%
1.932
0.57%
0.01465
0.07%
0.02022
-7.88%
0.0025
4.17%
0.00191
0.53%
0.00852
0.95%
0.01833
-3.83%
0.000000001497
0.00%
0.066647
-0.04%
0.000806
11.33%
0.0540
1.31%
0.05886
0.02%
0.0120
-9.77%
0.000235
-12.96%
0.004020
1.31%
0.005739
2.79%
0.001941
1.30%
0.013138
-12.67%
0.03936
-2.96%
0.0100
-2.91%
0.00240
-10.78%
0.11778
12.14%
0.1945
-5.31%
0.00000000009290
-0.57%
0.00712
2.45%
10.10
-1.75%
0.0000090
0.00%
0.0000214
8.63%
0.3089
0.46%
0.000121
-1.63%
0.000000000254
-1.17%
0.08306
10.07%
0.00498
-0.20%
0.1014
-3.52%
0.910
0.89%
0.1535
-11.27%
0.1605
1.58%
0.01276
0.79%
0.000832
-1.54%
0.003361
-4.76%
0.000537
-2.89%
0.703
0.43%
0.0066
-2.94%
0.1945
-0.87%
0.001265
-33.03%
0.00008023
1.16%
0.01598
-10.12%
0.00004157
-1.89%
8.47
-4.29%
0.001073
-15.04%
0.002645
-16.59%
0.03494
-0.31%
0.0483
0.63%
0.000700
9.03%
0.004320
-5.14%
0.000715
0.00%
0.004218
38.25%
0.0000000356
-18.72%
0.003553
-1.33%
0.00131
-25.99%
0.0002818
0.18%
0.06895
1.59%
0.01190
0.08%
7.53
1.48%
0.004921
-7.33%
0.002570
1.78%
0.5686
0.00%
0.0231
-2.94%
0.0009273
16.66%
0.0946
1.72%
0.005496
3.91%
0.01320
0.00%
0.1432
1.27%
0.0004726
2.56%
0.0042
0.00%
0.2135
-0.09%
0.0000501
-4.02%
0.04771
-2.17%
0.0000846
7.77%
0.03036
-3.53%
0.0000003134
0.10%
0.004477
-7.31%
0.00002358
-4.50%
0.01638
-5.92%
1.047
-8.88%
0.908
-1.63%
0.2611
12.16%
0.0000000000000182
-12.92%
0.13682
-1.59%
0.003774
-8.46%
0.0023642
-0.63%
0.0935
1.74%
0.00000004017
-4.90%
7.096
-3.31%
0.284
0.00%
0.017569
-6.28%
0.9105
0.00%
0.01290
0.16%
0.8081
6.12%
0.04532
3.14%
0.000853
-14.27%
0.03267
-2.65%
0.000298
7.97%
0.000385
-16.85%
0.9001
1.87%
0.0000001484
4.73%
1.533
0.46%
0.04988
1.49%
0.000216429
-15.44%
0.0986
7.52%
0.1710
1.42%
0.0002041
0.00%
14.28
7.05%
0.02906
-9.16%
1.1877668
0.28%
0.008969
-11.46%
0.0003981
0.66%
3051.75
0.37%
92.47
0.17%
0.0661
3.93%
0.0002165
-2.35%
1.4093
-1.24%
1.3303
0.65%
0.0104
-6.31%
0.002277
2.66%
0.0006926
0.67%
0.01746
18.69%
19.41
2.16%
0.0008111
-1.46%
0.01845
4.24%
0.11148
-0.02%
0.1083
-9.52%
0.1169
-1.85%
0.2596
1.41%
0.7537
-2.55%
0.03161
4.81%
0.003912
-10.87%
0.012517
0.01%
0.001186
-12.28%
0.1059
0.57%
0.6181
0.23%
0.0344
1.78%
0.0110
0.00%
0.001865
0.38%
0.003018
0.07%
1.4504
-2.84%
1.010
1.00%
0.003584
25.40%
0.781
-0.89%
0.00016500
46.68%
0.0031
0.00%
0.57981
-3.07%
0.4009
-2.53%
0.0000607
-0.65%
0.364
-3.19%
0.00000001287
-2.72%
0.06973
-10.19%
0.00000805
4.01%
0.0292
5.42%
0.3187
0.35%
0.03990
-0.67%
0.001260
-4.33%
0.000000495
-0.40%
0.0801
-2.55%
0.002713
-12.93%
0.1304
-1.66%
0.004213
-0.73%
0.0003932
-28.20%
0.00920
8.62%
0.0000000002074
-2.63%
0.01825
4.52%
1.6248
9.51%
0.0000000837
-0.24%
0.0000054
28.57%
0.002810
5.88%
0.2658
-3.90%
0.4778
-5.10%
0.0821
0.98%
0.01405
13.12%
0.007332
-2.32%
2198.42
-1.68%
0.0103
-4.63%
0.01868
-2.05%
22.58
-6.31%
0.2793
-3.12%
0.3017
-0.23%
0.561
0.90%
6.7065
3.05%
0.0007790
-13.44%
0.2608
-4.40%
0.001136
-0.87%
0.2820
0.93%
0.0000659
-6.66%
0.0470
-0.63%
0.005324
-2.42%
0.0699
-1.13%
0.000845
-6.11%
0.0890
-0.56%
0.1498
1.01%
0.1489
0.47%
0.01684
0.96%
0.00966
-2.62%
0.005900
16.19%
2.269
-8.88%
0.003486
-0.71%
0.3528
-1.31%
0.743
1.23%
0.9745
-0.01%
0.0005693
-3.56%
0.06250
-0.95%
7.97
-5.01%
0.0571
-5.46%
0.001020
-0.10%
0.001653
-8.12%
0.7630
-0.35%
0.0597
0.51%
0.1477
-3.02%
0.626
2.29%
0.0387
0.52%
0.00626
2.29%
0.01322
-0.08%
0.00270
-0.74%
0.00008997
-7.27%
1.234
4.14%
0.00010605
-28.74%
12.31
-2.30%
2.223
0.45%
0.000001660
1.90%
0.00000412
-1.67%
0.00230
0.88%
0.8911
-5.47%
18.40
0.49%
0.05737
-4.67%
0.0103
0.00%
0.00325
-27.78%
0.01825
-0.11%
0.003820
-13.71%
0.00001385
-3.21%
0.1989
0.20%
0.001210
-5.32%
0.1630
-6.21%
0.004276
1.11%
0.0000097
25.97%
0.000000109
-1.80%
0.638
1.11%
0.00005813
-7.44%
0.00000008476
8.75%
0.687
0.15%
0.001741
-11.22%
15.79
3.00%
0.00256
0.79%
3.516
0.00%
0.003497
4.17%
0.005647
7.21%
0.001045
-0.67%
0.01716
-6.13%
0.0051037
-0.19%
0.00000000001448
11.13%
18.28
-2.77%
0.001832
-9.49%
0.02494
-5.74%
0.2861
0.25%
0.2218
-1.68%
0.00770
-1.53%
0.0361
0.84%
0.0000000620
-2.67%
0.0568
-9.12%
0.01305
-0.31%
18.20
-1.30%
0.006940
-14.32%
166.70
-3.05%
0.00000712
-0.70%
0.002008
0.00%
0.00002417
-2.42%
0.000002024
3.64%
0.003456
4.44%
1.423
-0.91%
14.74
-0.74%
0.00004411
11.67%
0.00022505
0.02%
31.24
0.90%
0.0779
1.17%
0.01816
-1.89%
0.3711
6.85%
0.3978
3.38%
0.000001670
3.09%
0.7000
16.67%
0.002755
-7.11%
0.00776
-14.82%
0.00009381
-0.47%
0.002704
-0.44%
0.00648
0.15%
0.1524
0.79%
0.1157
-0.77%
0.00000000000026
-29.73%
0.002064
0.00%
0.001307
-0.15%
0.001106
-0.81%
0.0000645
7.14%
0.2159
0.09%
0.8439
-0.02%
0.0003889
-1.59%
0.0122
9.91%
0.0082
15.49%
0.3911
0.62%
0.1901
-1.30%
0.000159
1.92%
0.0027
-50.91%
0.550
-8.18%
0.0189
-1.56%
0.02112
7.59%
0.00003
50.00%
0.000085
3.66%
0.013000
4.52%
0.1941
-0.26%
0.724
0.98%
2.313
2.44%
0.0964
-1.03%
0.00000001651
-0.72%
0.0182
0.00%
0.006302
-7.69%
0.02763
-3.02%
0.00810
-9.40%
0.01290
-0.23%
0.0621
-5.77%
0.0366
1.95%
0.005432
2.03%
0.00000000001079
18.18%
0.425
-0.93%
0.20428
4.40%
0.01716
-7.69%
0.000000008400
140.00%
0.00000000015692
-0.26%
0.000000001895
-5.96%
0.1410
0.79%
0.0000490
-7.02%
0.808
-0.49%
0.2336
-2.83%
2.214
0.41%
0.001158
0.35%
1271
-0.16%
0.0872
0.00%
0.0786
-0.25%
0.0818
0.12%
0.00127
-0.78%
0.0468
-7.69%
0.01700
10.97%
0.1363
-1.87%
0.01470
0.00%
0.00129
-7.19%
0.0397
1.02%
0.0000002154
-2.45%
0.00895
-1.97%
0.000415
-16.50%
0.00000000000180
-26.23%
0.013600
0.44%
0.01750
4.17%
0.0003220
0.00%
0.5690
-26.44%
0.001902
-13.98%
0.6095
0.26%
3.48
-3.06%
2.217
-1.82%
0.020595
-1.96%
0.01044
-7.28%
500.00
19.05%
0.02772
-1.07%
0.4340
12.06%
0.0122
-3.17%
0.00000409
30.67%
0.000043
26.47%
0.01650
0.49%
0.1316
0.30%
0.0006849
-0.29%
0.2107
0.10%
0.0000000036990
23.26%
0.000118
-0.84%
0.05578
5.15%
0.033070
-4.15%
0.00000000001833
-44.29%
0.00462
-4.74%
0.000094
64.91%
0.230000
91.67%
0.0390
-1.52%
0.00549
-2.14%
78.8
-1.38%
0.0136
6.25%
0.3002
-2.44%
0.1179
-0.51%
0.01991
-0.50%
0.002323
3.94%
0.0674
1.97%
6.560
0.38%
0.000000000091
250.00%
0.0170
0.00%
0.00240
-8.40%
0.0002510
0.64%
0.00000000003782
4.16%
0.00876
-0.23%
2.117
-1.35%
0.06110
0.64%
0.0001
0.00%
0.000000000801
3.89%
0.023455
-8.26%
101.67
1.67%
0.00421
0.00%
0.0000019
11.76%
0.00000015700
43.87%
0.000000000004
-20.00%
0.2289
2.23%
6.9096
-7.81%
0.008231
-53.95%
0.000000000003830
0.26%
0.000400
-25.93%
0.5385
0.02%
9.770
0.00%
0.0000109
-6.03%
0.00000000000652
0.15%
0.000908
1.11%
0.000110
-4.35%
0.000389
0.52%
0.00681
1.79%
0.683
0.59%
1.400
0.29%
0.0057
-33.72%
0.005691
-4.74%
0.000000000000955
-0.21%
0.0065
-32.29%
0.004072
-10.94%
0.6549
2.50%
0.00004895
4.57%
0.4788
-1.48%
0.02998
-0.13%
1.921
0.21%
0.000025
-3.85%
0.00000000000385
-1.53%
0.0088
1.15%
0.0000000000000158
-2.47%
0.0000269
24.54%
0.001314
-3.31%
0.05812
-0.09%
0.000083
-18.63%
0.0002402
0.04%
0.4807
0.31%
0.022500
-3.92%
0.0985
0.41%
0.000072
30.91%
0.0000066
-27.47%
0.00146
-16.57%
0.00036
-10.00%
0.002895
-4.08%
0.1078
-1.73%
0.00002268
1.34%
0.00000000000014
16.67%
0.000000000713
-0.14%
0.000000000001711
-1.55%
0.00000000000285
-3.06%
0.00000000000122
16.19%
23.723
-0.25%
1.714
-0.46%
0.474
4.41%
0.000196
1.03%
0.00794
-6.70%
0.0000066
17.86%
0.00003
0.00%
0.000000100
0.00%
0.3803
1.14%
0.01652
-1.43%
0.00000926
-15.82%
0.0000252
1.61%
0.000000000756
0.27%
0.00007
-41.67%
0.000000000110
-4.35%
0.02523
0.32%
0.0752
12.24%
0.002579
-0.15%
0.0536
-0.37%
0.003479
-0.32%
5155.00
14.00%
0.03455
-3.71%
0.0001450
0.00%
0.2270
0.49%
0.00023846
-1.82%
0.00000060
-1.64%
0.02814
1.74%
0.0005121
7.63%
0.0445
-0.22%
0.002411
3.25%
0.003021
7.55%
0.000430
-0.46%
0.5278
0.23%
0.001790
-35.05%
0.0005
0.00%
0.000000002007
-0.89%
0.830
-0.36%
0.00027
0.00%
0.00011
10.00%
0.001801
-38.64%
0.0005307
-8.45%
0.0000003963
50.00%
0.000044
33.33%
0.1211
-0.41%
0.1346
-2.60%
0.00032
14.29%
0.0000000152
-1.30%
0.0000312
41.82%
0.01137
-0.70%
0.0826
8.68%
0.0963
-1.63%
0.000058
16.00%
0.05346
-0.71%
0.0015
7.14%
0.00171
2.40%
0.000310
0.32%
0.0000082
-18.81%
0.004001
-1.98%
1.105
1.84%
0.0064
8.47%
0.001210
-10.30%
0.0000680
-1.31%
0.0064
-1.54%
0.004328
0.42%
0.0012
20.00%
0.0006510
-3.13%
0.497
-2.93%
0.03778
-0.11%
0.4550
4.69%
0.0006754
3.10%
0.0004
0.00%
0.0009
0.00%
0.00390
34.02%
0.0504
-1.56%
0.0017
-5.56%
0.2196
-1.48%
0.00007
0.00%
0.1455
-1.02%
0.000423
-0.94%
0.000000750
54.00%
50.0000
0.00%
0.00000000000039
-2.50%
0.00000000055
-5.17%
0.1120
0.18%
0.0000061
1.67%
0.000000000535
0.00%
0.000446
0.22%
0.000000000682
-0.87%
0.00614
0.00%
0.000561
1.08%
0.03935
2.31%
0.01595
0.00%
0.00000323
0.62%
0.0012
9.09%
0.00004399
-0.02%
0.00103
17.05%
0.0000329
0.00%
0.0000000000270
0.00%
0.000009
0.00%
0.0007000
-3.31%
0.0005449
5.09%
0.0000397
11.83%
3.061
-0.94%
0.000190110
-2.46%
0.3341
1.15%
0.000685
-2.70%
0.0000821
-0.97%
0.1016
-0.49%
0.00000000072
-5.26%
0.0000029
-3.33%
0.00056
7.69%
0.00119
21.43%
0.000307
27.39%
0.00000000000102
-3.77%
0.0065
-4.41%
0.000018
0.00%
0.0645
-4.30%
0.0000007
40.00%
0.00006
0.00%
0.0789
-0.88%
1.2684
4.06%
0.01685
-0.71%
0.10399
-2.88%
0.3811
-1.45%
0.00015
0.00%
0.7418
-2.29%
0.001123
-3.27%
0.001007
3.92%
58.5600
0.00%
0.0004062
-6.69%
0.02947
-2.38%
0.0254
0.00%
0.003906
5.57%
0.00371
0.00%
0.0009012
0.00%
0.0004398
-4.60%
0.00600
0.00%
0.002171
10.09%
0.0007993
0.00%
6.093
-0.44%
0.2240
2.24%
0.000029
3.57%
0.03507
-10.88%
0.001776
9.16%
0.000014
0.00%
3.0849
-5.14%
0.02372
0.38%
0.003847
-5.94%
0.7855
-1.62%
1899.00
0.00%
1.54
0.00%
0.01274
-5.77%
0.1530
-11.15%
0.0450
1.12%
0.001356
3.27%
0.03125
-0.70%
0.00405
2.02%
0.01187
-0.34%
0.2148
6.02%
2.5129
0.00%
0.453
0.67%
1.000000
0.00%
0.3771
0.00%
0.5732
0.00%
50.157
-1.42%
3.038
-0.23%
0.0585
-1.85%
0.0001030
0.00%
0.6385
0.41%
0.0871
0.00%
0.0700
0.00%
0.001157
1.40%
0.00000091
7.06%
0.01936
-1.78%
0.1957
1.66%
0.000216
0.00%
0.548
1.11%
2.179
0.00%
1.5000
0.00%
3.9889
0.00%
1.1371
0.00%
0.000079
0.00%
0.4424
0.00%
0.0071
0.00%
0.000210
0.00%
0.0268
0.75%
0.1786
-2.56%
8.23
-1.44%
0.000452
0.00%
0.0272
0.00%
0.000000002356
-2.77%
0.00000042
-8.70%
0.1204
0.00%
2.644
0.27%
0.006000
0.00%
0.000300
0.00%
0.00013
0.00%
0.00035
0.00%
0.000000040
11.11%
0.0004
0.00%
0.00033
0.00%
0.011926
0.00%
0.0000154
0.00%
0.000014
0.00%
0.001100
0.00%
0.000365
0.00%
0.001201
0.00%
0.0000002593
0.00%
0.00001584
0.00%
0.0000001013
0.00%
0.00035000
0.00%
0.000024
-11.11%
0.00005
0.00%
0.00006187
0.00%
0.000166
0.00%
0.000000000011
0.00%
0.001405
0.00%
0.2462
-0.04%
0.000452
0.00%
0.000902
0.00%
0.0234
-10.00%
0.0001
0.00%
0.0009
0.00%
0.0560
0.00%
0.00012800
0.00%
0.000450
-0.66%
0.004025
0.00%
0.0110
-5.98%
0.00000100
0.00%
0.0000000104
0.00%
0.00000006
0.00%
0.00000000001676
0.00%
0.001000
0.00%
0.0000000053
0.00%
0.0000000039
0.00%
0.00001626
0.00%
0.000000000374
0.00%
0.00024
-4.00%
0.000310
0.00%
0.3284
0.00%
0.9500
0.00%
0.0020
0.00%
0.000405
0.00%
----
0.001290
0.00%
0.00000011
0.00%
0.0000006633
-0.33%
0.000758
0.00%
0.001000
0.00%
1.6799
0.00%
0.0927
0.00%
0.00000000002387
0.00%
0.00425
0.00%
0.00001
0.00%
0.00004
0.00%
0.0010
0.00%
0.00037
0.00%
0.001963
0.00%
0.00000055
0.00%
0.2994
0.00%
0.00006767
0.00%
0.00005458
0.00%
0.001263
0.00%
0.0072
0.00%
0.0001000
0.00%
0.05056
0.00%
1.3575
0.00%
0.00136
0.00%
0.000086
0.00%
0.000033
0.00%
0.000038
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%
0.4998
0.00%
0.0000111
0.00%
0.00000145
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%
1.1071
0.00%
0.000383
0.00%
4.0009
0.00%
0.001000
0.00%
0.0437
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%
0.000350
0.00%
0.0200
0.00%
0.0093
0.00%
0.0006
0.00%
65.1101
0.00%
3.7189
0.00%
0.003015
0.00%
0.00000012
0.00%
0.000082
0.00%
0.0072
0.00%
0.016111
0.00%
4.1000
0.00%
0.0489
0.00%
0.0131
0.00%
0.0006
0.00%
4.4022
0.00%
0.0745
0.00%
0.002461
0.00%
0.001160
0.00%
0.001100
0.00%
0.3882
0.00%
0.001000
0.00%
0.076250
0.00%
0.0150
0.00%
0.002393
0.00%
0.0036
0.00%
0.001942
0.00%
0.1769
0.00%
2.2915
0.00%
0.0000000196
-0.51%
0.0004
0.00%
0.000257
0.00%
0.000620
0.00%
0.03000
0.00%
0.000946
0.00%
0.4820
0.00%
0.0490
0.00%
0.0096
0.00%
0.0060
0.00%
0.04500
0.00%
0.000259
0.00%
0.0502
0.00%
0.004163
-1.93%
12.1000
0.00%
1.76670591
0.00%
0.0024
0.00%
0.000399
0.00%
0.0001403
0.00%
0.0000002850
0.00%
0.6700
0.00%
0.0086
0.00%
0.01989
0.00%
0.00047
0.00%
0.0026
0.00%
0.0009
0.00%
0.2888
0.00%
0.00501
0.00%
0.02700
0.00%
0.00315
0.00%
0.0650
0.00%
0.3515
0.00%
0.00125
0.00%
0.4900
0.00%
0.9900
0.00%
0.5000
0.00%
0.010100
0.00%
0.0069
0.00%
0.88686
0.00%
0.00084
0.00%
0.0000285
0.00%
1.1760
0.00%
0.00689
0.00%
0.1725
0.00%
0.00010
0.00%
0.01463
0.00%
0.04851
0.00%
0.4606
0.00%
0.00021
0.00%
0.001800
0.00%
0.0000007
0.00%
0.000001547
0.00%
0.01200
0.00%
0.00010
0.00%
0.000001000
0.00%
0.00250
0.00%
0.0000008
0.00%
1.3089
-0.80%
0.01050
0.00%
0.0000325
0.00%
0.018686
0.00%
1.0000
0.00%
0.34211
0.00%
0.00132
0.00%
0.0000077
0.00%
0.0005
0.00%
0.1495
0.00%
0.00036
0.00%
0.001277
0.00%
0.03520
0.00%
3.3999
0.00%
0.0000023
0.00%
0.000000005
0.00%
0.000514
0.00%
0.001987
0.00%
0.00080
0.00%
0.000313
0.00%
0.0000029
0.00%
0.00200
0.00%
0.00000007783
0.00%
0.0032
0.00%
0.3131
0.00%
0.000495
0.00%
0.00049
0.00%
0.300
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%
0.000506
0.00%
0.01030
0.00%
0.0489
0.00%
0.00070
0.00%
0.003000
0.00%
0.0000269
0.00%
0.0000000500
0.00%
0.0000001300
0.00%
0.7997
0.00%
0.0001543
0.00%
0.000000000128
0.00%
0.000426832
0.00%
0.00002805
0.00%
0.1600
0.00%
0.0000245
0.00%
0.000056
0.00%
0.1197
0.00%
20.3888
0.00%
0.000510
0.00%
0.00218
0.00%
0.002100
0.00%
0.00240
0.00%
0.3101
0.00%
0.0000305
0.00%
0.00639
0.00%
0.4400
0.00%
1.4371
0.00%
0.000195
-1.52%
0.0000274
0.00%
0.00865
0.00%
0.3668
0.00%
0.250
0.00%
0.4289
0.21%
0.3915
0.08%
0.001106
0.00%
0.0249
0.00%
0.6608
0.00%
0.0607
-0.82%
0.00500
0.00%
3.79
0.00%
0.01168
0.78%
0.0020
0.00%
0.00538
0.00%
0.000000001869
0.00%
1.536
-0.78%
0.0091
0.00%