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

ソース: LBank日時: 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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0.89%
0.002653
-12.04%
0.000000001497
0.00%
0.0002652
-8.68%
0.01563
3.37%
0.0000000533
2.70%
0.03627
-6.16%
0.001912
1.06%
0.00016951
8.78%
22.05
-4.26%
0.3071
2.23%
1.1780668
1.19%
0.1537
-1.16%
0.1888
5.18%
0.0000541
26.40%
0.003637
-5.51%
0.1041
2.56%
0.002133
-2.96%
0.004423
2.12%
0.004902
-2.74%
0.0934
2.19%
1.7666
0.27%
0.004979
-0.26%
0.066754
1.00%
0.00000477
5.07%
0.1271
-0.78%
0.0003060
49.93%
0.2362
11.52%
5.46
1.87%
0.00746
3.90%
0.001641
14.68%
0.0694
0.43%
0.00370985
11.61%
0.000371
-1.59%
0.0003306
-11.13%
0.0889
-0.11%
0.0480
0.42%
0.3574
1.48%
0.000398
6.42%
0.3731
5.13%
0.02746
-3.92%
0.11141
-0.01%
0.03551
3.89%
0.00101
8.60%
0.04623
-11.47%
7.7949
2.84%
0.01921
-6.43%
0.002087
0.43%
0.01467
-0.14%
0.06683
-2.92%
0.002225
-25.83%
0.000221
-7.14%
0.3463
11.39%
0.00000003863
-5.06%
0.002266
104.70%
0.695
0.87%
0.08557
-3.70%
0.001018
1.19%
0.0002139
1.52%
0.2975
-1.72%
0.01208
54.48%
19.9519
1.77%
0.5301
5.12%
0.1210
4.13%
0.06034
-9.33%
3057.41
0.78%
0.0025
0.00%
0.00240
-10.78%
0.0000087
-2.25%
0.000098
0.00%
0.02009
-2.76%
0.000002980
-7.54%
0.001584
3.73%
0.001021
-13.62%
0.0000225
-4.26%
0.280
-1.06%
0.0091
-9.90%
0.06165
1.72%
0.2016
7.06%
0.001114
3.34%
0.01149
-21.62%
1.1645
2.10%
0.27454
0.74%
0.014028
0.03%
0.01293
2.46%
0.0000050
-9.09%
0.005539
-0.27%
0.00496
0.40%
0.007353
6.95%
10.67
3.29%
0.000552
1.10%
0.001116
-10.43%
0.60730
5.25%
0.000827
6.03%
0.01019
6.48%
0.5787
0.70%
0.00000000009338
2.10%
0.006874
13.21%
0.000000583
7.76%
0.0002878
2.57%
0.001453
-10.97%
0.07612
-8.00%
0.2893
8.51%
1.5838
8.72%
0.1443
5.10%
0.1027
2.70%
0.2623
0.85%
0.1924
-0.41%
8.862
15.81%
0.00006568
1.31%
6.19
0.65%
0.0066
-1.49%
0.003711
5.79%
0.07287
-0.53%
0.000113
3.67%
3026
0.27%
0.002136
6.48%
0.00000008525
6.95%
0.116397
-9.11%
0.01194
0.25%
0.686
2.69%
1.3274
0.02%
0.01068
-1.93%
0.002589
1.21%
0.00925
8.95%
0.0877
2.10%
0.001219
1.84%
0.00235
-47.54%
0.002604
-12.09%
0.00001323
-2.07%
0.3075
-1.09%
0.1101
1.19%
0.0042
0.00%
170.81
2.84%
13.92
-3.93%
0.004427
1.40%
0.009757
-10.22%
0.00002566
7.77%
1.046
2.65%
0.1508
0.73%
0.0798
-1.60%
0.0006591
-3.34%
0.00694
-1.00%
7.053
-0.18%
0.0007646
-3.98%
2.202
-0.50%
1.6595
5.27%
0.06341
1.68%
0.05145
12.78%
0.00008400
4.70%
0.003157
-20.40%
0.6523
6.71%
0.01285
6.73%
0.00004050
-1.00%
0.0241
2.12%
0.003395
13.17%
0.00002678
16.64%
0.362
0.28%
0.00000001583
-8.66%
0.003043
-4.79%
3.522
1.18%
0.3557
2.24%
0.681
6.57%
0.9177
-0.09%
0.0276
-5.15%
0.0007889
-2.68%
0.001849
0.00%
0.560
0.90%
0.5547
-0.88%
0.0706
-2.49%
0.00285
14.00%
0.02585
-3.11%
2.385
-2.77%
0.2803
-0.39%
7.90
-2.35%
0.8031
1.86%
92.09
6.11%
0.017926
2.31%
0.03133
51.13%
0.00909
1.68%
0.012516
-0.02%
0.01749
4.73%
0.04094
3.36%
0.020970
12.22%
0.04036
3.91%
6.6920
-0.82%
0.001606
-8.59%
0.004031
2.81%
0.000834
1.83%
25.1111
23.16%
0.00000001345
3.54%
0.2142
1.28%
0.0000488
-4.31%
0.00846
-6.42%
0.0111
0.91%
0.01431
14.48%
0.002721
4.17%
0.002481
-10.11%
0.0006995
3.51%
0.00003934
-0.18%
0.1922
1.16%
0.0031
3.33%
0.0115
7.48%
0.01448
-1.36%
0.004017
8.98%
0.01761
-3.98%
18.42
-0.05%
0.01154
0.70%
0.00000071500
336.80%
0.0361
1.40%
0.03888
-4.45%
2209.43
0.50%
0.0007793
-13.41%
0.012837
-6.71%
0.0004677
3.96%
0.000000000252
-1.18%
0.003157
-7.82%
0.4959
3.57%
0.0668
1.06%
0.0000000805
-4.05%
0.03197
-0.65%
0.004276
0.61%
0.1605
1.52%
0.003218
-7.61%
0.01857
0.38%
0.0191
1.06%
0.003978
-1.09%
0.05243
9.85%
0.0000724
5.54%
1.521
1.20%
0.000002244
13.33%
0.2114
0.76%
0.3972
-0.48%
0.001608
-3.48%
0.1154
1.14%
0.7628
-0.05%
2.400
7.29%
0.622
-0.80%
0.1086
-2.16%
0.03309
2.60%
0.2682
-3.39%
0.1481
0.47%
0.2554
1.51%
0.0598
1.01%
0.7937
6.74%
0.001646
6.95%
2.274
0.44%
0.000000559
16.22%
0.0002839
2.79%
0.000001681
0.96%
0.769
0.92%
0.897
0.45%
0.007265
0.82%
0.3922
1.82%
0.2227
-2.20%
0.424
-0.93%
0.0106
2.91%
0.05847
1.94%
0.0777
-0.13%
0.0005301
-2.66%
0.1939
-3.00%
0.0000003070
1.29%
0.0000092
-2.13%
0.00010600
-2.23%
0.003434
1.33%
2.219
0.23%
0.00005789
0.98%
0.0315
3.96%
0.001945
4.96%
0.0386
-0.52%
0.01931
6.10%
0.05533
-9.80%
0.0996
-0.70%
23.954
0.85%
0.013000
4.56%
0.001818
-0.60%
0.2158
0.56%
0.0051068
-0.06%
0.0099
0.00%
0.1635
2.51%
0.00009233
-1.41%
0.2265
-0.66%
0.02848
-0.77%
0.001627
-10.11%
0.0542
1.69%
0.0146000
-87.82%
12.37
0.81%
0.1724
4.23%
0.000211307
-4.68%
0.0006477
2.24%
0.004792
2.37%
0.0468
0.43%
0.000090
9.76%
0.0000002725
-31.24%
0.003840
3.20%
0.00257
1.18%
0.7400
1.96%
0.494
-0.40%
0.737
0.55%
0.04327
-2.02%
0.003550
0.82%
0.002850
-3.19%
2.242
5.70%
0.01605
-4.18%
0.831
-0.36%
0.2260
0.67%
0.01800
0.22%
0.0000269
-1.82%
0.005928
8.29%
0.000700
-2.10%
0.03489
11.79%
0.0004570
-9.43%
0.02027
9.92%
0.001182
2.16%
0.01714
2.82%
1294
1.89%
1.952
2.79%
0.0483
5.46%
0.00004914
2.74%
0.1493
0.61%
0.004424
20.28%
0.0000000000000168
-6.15%
0.00000398
-1.24%
0.0948
-0.84%
0.003440
-20.39%
0.00776
-14.82%
0.3208
2.92%
0.001381
4.07%
0.2801
8.19%
0.00022485
-0.14%
0.0000000002083
1.02%
0.0066
-2.94%
0.0567
-12.23%
0.02657
-2.28%
0.0580
3.39%
0.03073
23.46%
0.2155
0.23%
0.001806
-3.68%
0.0683
1.94%
0.723
0.84%
0.1044
0.77%
0.001124
-0.44%
0.810
1.50%
0.1920
0.05%
0.0122
22.00%
0.01290
0.00%
0.000001630
-3.55%
0.00000000001262
0.08%
0.1173
-3.54%
0.00000808
-0.25%
0.000329
-22.95%
0.0116
-6.45%
0.0004706
18.78%
0.00121
-7.63%
0.04317
-5.54%
1.404
1.08%
0.0382
50.39%
79.0
0.64%
0.005403
5.16%
0.8456
0.82%
0.00000000021945
39.85%
0.00000000001721
15.81%
17.424
-0.93%
0.000249
55.63%
0.0816
0.62%
17.82
1.31%
0.1286
-0.39%
0.005251
-0.83%
0.0000000623
0.48%
1.911
-0.16%
0.00000713
0.42%
0.20003
1.86%
0.1569
0.00%
0.1122
2.28%
0.0766
2.41%
0.0954
2.80%
0.03252
-7.77%
0.01203
-2.12%
0.0991
-1.20%
0.02535
1.04%
0.01650
0.49%
0.0000119
4.39%
0.01337
2.14%
0.0000000042630
42.05%
0.000843
96.05%
0.000001608
3.94%
0.01300
-1.44%
0.6494
1.79%
0.2650
-2.65%
0.00650
0.31%
0.001331
3.34%
0.00003
50.00%
0.000024
0.00%
0.00544
1.87%
0.002013
0.25%
0.1098
1.67%
0.00129
24.04%
0.0000002164
0.32%
0.00000000000012
-57.14%
1.238
0.73%
0.000504
44.00%
0.00306
-2.86%
0.1338
-0.59%
0.1183
-2.31%
2.641
-0.41%
0.0001884
55.57%
0.5287
0.09%
0.01686
-1.52%
0.001096
-0.36%
0.0000000159
3.25%
1.4259
3.27%
0.0135
-20.59%
0.0002441
-2.28%
0.1506
6.66%
19.35
-0.77%
0.00618
-0.64%
0.0805
-0.98%
0.0867
-0.46%
0.006046
7.14%
0.0000235
52.60%
0.4135
-4.72%
0.2815
0.72%
0.000000000001779
2.89%
0.0344
0.58%
0.00420
-0.24%
0.671
-0.59%
0.1530
-2.17%
0.0000485
-4.90%
18.06
-0.88%
0.0920
-0.76%
0.000000000710
-1.39%
0.000963
-5.59%
0.013598
-1.46%
0.02980
0.74%
0.0000019
0.00%
0.230000
91.67%
15.58
-0.13%
0.000757
-8.80%
0.000000001891
-0.37%
0.2239
0.95%
1.701
-0.70%
0.0108
8.00%
0.0935
-1.58%
6.509
1.45%
0.05938
3.16%
1.032
3.41%
0.022345
-9.00%
0.000000000409
-40.03%
0.0001
0.00%
0.0045
-10.00%
0.04024
2.26%
0.000000000003823
-12.42%
0.00000000000012
0.00%
498.90
-0.22%
0.0783
16.87%
0.004210
-0.28%
0.0393
1.55%
2.234
1.59%
0.002407
9.01%
0.0381
0.00%
0.00011
266.67%
0.000384
-1.29%
0.0057
-22.97%
3.52
1.73%
0.2120
2.91%
0.0023814
1.94%
0.000024
-4.00%
0.0015
-16.67%
0.00009784
-40.70%
0.02962
0.07%
0.000080
35.59%
0.01702
1.31%
0.0003
-80.00%
0.00000000000177
0.57%
0.05812
0.00%
0.000882
0.92%
0.0000251
-18.51%
0.000000000000957
3.13%
0.0092
16.46%
0.00008997
0.02%
0.000198
2.59%
0.00125
-1.57%
0.0523
6.95%
0.9990
99.88%
0.00805
-6.94%
0.00461
1.54%
0.000000008400
0.00%
0.0000061
0.00%
0.750
36.36%
0.0002402
-13.50%
0.00003069
1.89%
0.008233
0.04%
0.03749
-0.77%
0.0004337
7.86%
0.0006
20.00%
1.0100
2.02%
0.00040
-4.76%
0.00729
-5.32%
0.00014
0.00%
0.000270
-41.68%
0.000025
78.57%
7.1285
6.61%
0.000112
4.67%
0.00000000000038
-5.00%
3.018
-0.46%
9.770
0.00%
0.0009486
6.90%
0.3830
1.00%
0.00713
1.13%
0.00915
6.77%
0.1535
2.20%
0.0959
-0.93%
0.0000099
76.79%
0.000016
-11.11%
0.0000013
85.71%
0.00000000000651
-0.15%
0.0352
0.57%
0.00000926
-15.74%
0.02776
-0.50%
30.69
-0.78%
0.0488
-3.75%
0.002579
-0.15%
0.909
0.66%
0.1344
3.86%
0.00000000000115
-5.74%
0.0000067
-26.37%
1.2667
0.72%
0.001132
-8.71%
0.00000000109
43.42%
0.00041
28.13%
0.00011
10.00%
0.00024
-7.69%
0.0000000000000156
-1.27%
0.000061
84.85%
0.00000000003615
-0.22%
0.467
4.71%
0.000000002047
1.84%
0.00220
-8.33%
0.5292
-1.85%
0.000001600
228.54%
0.1937
0.68%
0.1300
-1.22%
0.477
1.71%
0.03455
-1.12%
0.00000326
-20.29%
3.58
-5.54%
0.0009
0.00%
0.003951
1.86%
0.004016
7.24%
0.002083
8.55%
0.0000000192
-2.54%
0.0010
11.11%
0.00000322
1.58%
1.097
0.64%
0.01306
1.24%
0.0000675
-0.74%
0.000062
40.91%
0.000055
-23.61%
0.0000310
-0.64%
0.000031
10.71%
0.0000082
-7.87%
0.000000000069
-30.30%
0.000000103
4.04%
0.00000000055
0.00%
0.0700
39.44%
0.001801
0.06%
0.0027
0.00%
0.00263
-2.59%
0.004106
-5.02%
0.0004904
-8.10%
0.0005
25.00%
0.00026
-3.70%
0.7000
0.00%
0.00002283
0.66%
0.0000700
-17.26%
0.2979
-0.07%
0.0437
-0.23%
0.00083
3.75%
0.000000000533
-0.37%
0.0795
1.27%
0.006407
1.06%
0.000000000019
72.73%
0.000423
-0.94%
0.3762
3.41%
0.001323
4.58%
0.000446
0.22%
0.0779
-0.51%
3.0640
-1.35%
0.008000
0.00%
0.00000007783
0.00%
0.000561
1.08%
0.3863
4.07%
0.000400
-42.86%
0.000000000747
-6.74%
0.000085
13.33%
50.0000
0.00%
0.000448
-0.88%
0.000000000120
15.38%
0.00000000000288
-0.69%
0.0005
25.00%
0.0012
9.09%
0.000000000782
0.51%
0.022500
0.45%
0.00000055
1.85%
0.0000647
0.31%
0.00000000000097
-3.96%
0.000000000375
0.27%
0.0000329
0.00%
0.00000000002900
73.03%
0.00000000000406
-0.25%
0.00000000003010
64.21%
0.000000000006
50.00%
0.00000091
3.41%
0.000000002344
-5.02%
0.000000039
-2.50%
0.00030000
-14.29%
0.0852
7.71%
0.0000006617
-0.41%
0.0005154
-6.32%
0.0064
3.23%
0.000194111
6.09%
0.000033
-13.16%
3.022
-0.59%
0.00231
-5.33%
0.000026
8.33%
0.0102
18.60%
0.0000017
-43.33%
0.00056
7.69%
0.001034
0.00%
0.00119
21.43%
0.0562
28.60%
0.00000012
0.00%
0.000307
27.39%
0.0013
116.67%
0.00023
9.52%
0.0609
-7.45%
0.0000010
42.86%
0.00000044
0.00%
0.0003220
0.00%
0.0568
8.40%
0.000817
-1.80%
0.01622
-0.25%
0.0003961
1.85%
0.4867
2.72%
0.10553
0.10%
0.0574
0.00%
0.1427
-2.26%
0.00742
-9.07%
0.01236
10.55%
0.2421
3.07%
58.5600
0.00%
0.0001549
6.68%
0.0004714
-3.91%
0.002862
8.12%
0.00371
0.00%
0.0009012
0.00%
0.13416
-0.10%
0.003456
0.82%
0.0004144
-4.21%
0.00600
0.00%
0.0007993
0.00%
6.309
2.90%
0.05253
-0.76%
0.033603
-2.99%
0.02050
4.81%
0.02364
-2.35%
0.0000397
0.00%
0.002935
0.41%
0.7869
0.94%
1899.00
0.00%
0.4419
-8.03%
1.27
-17.53%
0.6130
5.65%
0.0459
3.85%
0.03066
-0.65%
0.00407
5.17%
0.01157
-2.28%
0.2134
0.33%
2.5129
0.00%
1.000000
0.00%
0.3771
0.00%
0.5732
0.00%
50.556
1.07%
0.0578
-0.52%
0.000000100
0.00%
0.0001030
0.00%
0.00103
0.00%
0.6373
-0.34%
0.0700
0.00%
0.001171
0.60%
0.1535
3.79%
0.01943
1.57%
0.00004399
0.00%
0.000216
0.00%
0.544
1.49%
2.179
0.00%
1.5000
0.00%
3.9889
0.00%
1.1371
0.00%
0.000075
-5.06%
0.4424
0.00%
0.000394
-1.25%
0.06010
0.28%
0.9745
0.00%
0.0071
0.00%
0.000210
0.00%
0.1156
0.96%
0.01448
-0.07%
0.0265
-0.75%
0.1771
-0.06%
8.20
0.74%
0.004326
1.29%
0.3355
0.63%
0.000452
0.00%
0.0132
3.94%
0.0272
0.00%
0.1204
0.00%
0.006000
0.00%
0.000300
0.00%
0.00013
0.00%
0.00035
0.00%
0.0004
0.00%
0.00033
0.00%
0.011926
0.00%
0.000014
0.00%
0.001100
0.00%
0.000365
0.00%
0.001201
0.00%
0.0064
0.00%
0.0000002593
0.00%
0.000009
0.00%
0.00001584
0.00%
0.0000001013
0.00%
0.00005
0.00%
0.00006187
0.00%
0.000166
0.00%
0.001405
0.00%
0.2471
0.12%
0.000480
1.27%
0.000902
0.00%
0.0234
-7.87%
0.0001
0.00%
0.0009
0.00%
0.0560
0.00%
0.00012800
0.00%
0.004025
0.00%
0.0118
7.27%
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%
0.0065
0.00%
0.000310
0.00%
0.3284
0.00%
0.9500
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%
0.00000000002387
0.00%
0.00425
0.00%
0.00001
0.00%
0.00004
0.00%
0.000118
0.00%
0.0010
0.00%
0.0000241
-4.37%
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%
0.001210
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%
0.000086
0.00%
0.00007
0.00%
0.000033
0.00%
0.001234
0.00%
0.000449
0.00%
0.0066
0.00%
0.0012
0.00%
0.0004
0.00%
0.0007
0.00%
0.0240
0.00%
0.000522
0.00%
0.020562
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%
4.0009
0.00%
0.01595
0.00%
0.001000
0.00%
0.0786
0.00%
0.001563
0.00%
1.6349
0.00%
0.001790
0.00%
0.00000000000540
0.00%
0.000028
0.00%
0.000999
0.00%
0.0200
0.00%
0.0093
0.00%
0.0006
0.00%
65.1101
0.00%
1.432
3.39%
3.7189
0.00%
0.003015
0.00%
0.000082
0.00%
0.0070
-2.78%
0.016111
0.00%
4.1000
0.00%
0.0489
0.00%
0.0350
0.00%
0.0131
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%
0.020595
0.00%
0.0150
0.00%
0.002393
0.00%
0.0036
0.00%
0.001978
1.85%
0.1769
0.00%
2.2915
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%
12.1000
0.00%
1.76670591
0.00%
0.0024
0.00%
0.000399
0.00%
0.0001403
0.00%
0.0000000000270
0.00%
0.0000002850
0.00%
0.6700
0.00%
0.00007
0.00%
0.01989
0.00%
0.0026
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%
0.4900
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%
0.05578
0.00%
1.1760
0.00%
0.00689
0.00%
0.1725
0.00%
0.00010
0.00%
0.01463
0.00%
0.00614
0.00%
0.04851
0.00%
0.4606
0.00%
0.001800
0.00%
0.00006
0.00%
0.01200
0.00%
0.00010
0.00%
0.000001000
0.00%
0.0182
0.00%
101.67
0.00%
0.0000008
0.00%
1.3302
1.08%
0.01050
0.00%
0.00390
0.00%
0.0000325
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%
0.00146
0.00%
0.00036
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%
0.0032
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%
0.00070
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%
0.000000000128
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%
0.000510
0.00%
0.00218
0.00%
0.002100
0.00%
0.3101
0.00%
0.0000305
0.00%
0.00639
0.00%
0.4400
0.00%
1.4371
0.00%
0.000196
-0.51%
0.250
0.00%
0.4289
1.23%
0.3893
1.06%
0.001106
0.00%
0.0249
0.00%
0.6608
0.00%
0.0609
0.66%
0.00500
0.00%
0.0020
0.00%
0.00538
0.00%
0.4583
0.75%
0.000000001869
0.00%
5155.00
0.00%
1.519
-0.33%
0.0091
0.00%