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

Source: LBankDate/heure: 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
SpotFutures
USDTUSDCLTsBTCETHSTABLECOINS
PairesPrixVariations
86659.56
-1.29%
2010.70
-2.71%
620.4
-1.74%
138.47
-4.61%
0.00266
-0.37%
0.9999
0.00%
2.3884
-2.85%
3.610
-0.47%
2.5694
4.50%
0.3846
-1.81%
4.695
0.49%
11.51
-0.52%
0.6706
-1.02%
0.000701
-10.13%
0.000874
-18.32%
0.000001266
-0.86%
0.004793
-6.59%
0.001498
-11.88%
5.2956
-59.26%
1.3819
-21.47%
0.3287
-7.67%
0.04062
-5.00%
2.3203
-3.24%
0.001946
-71.79%
0.002234
-49.80%
0.000252
-53.25%
0.00519
-33.63%
0.000347
-38.48%
0.01988
18.76%
0.000584
5.99%
0.04836
-4.92%
0.0008043
51.10%
0.001715
-26.93%
0.002339
-9.17%
0.1464
3.76%
0.005725
-25.52%
0.05228
-6.71%
0.000007815
32.05%
0.01812
-1.63%
0.001518
-6.41%
0.002787
-5.01%
0.003316
-18.39%
0.0003131
-12.20%
0.003635
32.76%
0.004957
-15.75%
0.017130
-3.34%
0.000415
-15.65%
0.0004390
2.21%
0.003930
21.15%
0.13124
-8.11%
1.305
-4.74%
0.0010960
-17.81%
1457.3681
0.55%
74482.28843
23.77%
2005495.9434600
-1.36%
3.68055
-1.48%
3182.0000
0.00%
0.00083389
1.75%
3209.77707
-29.46%
0.00000011250
-1.06%
0.48649
-8.14%
22131.58301
-1.43%
151.09909
-2.64%
45.06755
-17.65%
0.0000439
-56.01%
0.004244
-47.72%
0.0000005622
-6.56%
14.7815
-1.85%
33.4469
6.87%
0.0000007612
-2.77%
6.4658
-1.03%
5.921828
4.78%
0.01904
-4.32%
0.1649
-3.06%
2.02873
0.69%
0.07288
-3.55%
0.654851
-2.64%
0.1986
-6.50%
0.000000000000059
-30.59%
8.1558
-1.16%
0.009748
0.00%
0.01447
-1.43%
0.006547
-1.07%
0.6125
-1.40%
0.00000000000018
-86.57%
1.5122
-3.79%
0.000027697
2.59%
1.1039
0.04%
0.01712
-7.56%
0.23291
0.00%
0.171433
-4.80%
4.1199
-0.72%
0.2666
1.72%
0.63572
-0.07%
0.060230
-0.63%
0.084360
11.68%
0.005520
-0.77%
0.2728
-0.37%
0.0030873
-0.88%
0.1544
4.25%
0.80
0.00%
0.4451
-4.63%
526.0000
0.00%
0.0012850
-0.84%
0.000659
-7.83%
1.2051
-1.02%
0.7126
0.39%
1.0523
0.08%
0.7021
-79.35%
1.3771
-0.47%
0.00006379
-18.25%
0.01508
-0.07%
0.2108
11.24%
0.106900
-0.09%
0.03714
1.06%
0.007893
-1.29%
0.00339270
-1.30%
97.0302
0.24%
0.023025
71.41%
0.16799
0.65%
0.19547
1.80%
0.00083396
8.48%
0.00546
-2.50%
225.32
5.61%
0.00001469
18.95%
8.5933
-0.18%
10.2645
-1.88%
0.8176
-7.79%
0.024492
-1.89%
0.0003203
2.04%
0.8533
-0.32%
0.04124
0.07%
0.0274
-0.36%
1.1645
0.03%
3.5273
13.15%
0.0908
-1.20%
0.006013
-7.46%
0.6136
-7.40%
0.00003440
-1.32%
4.5170
-0.64%
0.003135
-5.09%
0.0006022
-3.01%
0.000000770
14.93%
0.001424
-6.50%
0.00304
-2.56%
0.001511
-0.46%
0.1664
-2.29%
0.00005251
0.00%
1.2112
-2.60%
0.2304
1.10%
0.0030833
0.43%
0.000000001019
-12.31%
0.013625
-1.02%
0.00217
-0.46%
0.00263
2.33%
0.0119
-0.83%
0.03034
1.07%
3.7586
-1.40%
0.001629
-22.39%
1.0724
0.84%
0.002478
-1.74%
0.00007010
3.16%
0.00000004221
-8.30%
0.2599
62.44%
0.63900
-4.22%
0.4926
-2.94%
0.00000000003377
-1.97%
1.6732
3.00%
0.00002867
1.38%
0.02015
-2.28%
0.0003328
-2.92%
0.02640
1.93%
0.00215000
-2.41%
0.04448
9.34%
0.26604
-0.93%
0.00001459
6.65%
0.000000001419
-0.35%
2.7589
1.97%
0.00187
-8.78%
2.418
8.28%
238.1400
0.04%
0.0000140594
8.57%
0.7320
-2.47%
0.0254
0.00%
0.018518
0.00%
0.00004684
-0.85%
0.024613
-2.07%
0.54291
-3.08%
105.1355
0.07%
0.115794
0.01%
0.2080
-0.48%
3.3233
-5.64%
0.1479
-0.07%
0.000003894
0.41%
0.04804
-2.40%
37.35572
-11.48%
0.02254
-14.81%
7.3763
-4.56%
0.000809
-2.88%
0.0022955
-1.64%
0.01204
0.00%
91.786
-1.09%
0.227
0.00%
0.37424
-3.22%
0.00000001303
-1.51%
1.5857
-0.30%
48.7882
-1.47%
0.002146
3.87%
0.00000245
-6.13%
0.0003113
-5.26%
0.0433
3.59%
0.1007
8.40%
8.9445
0.01%
0.8391
1.88%
0.00000865
7.59%
0.01852
0.43%
1.46
0.00%
0.048160
4.74%
0.13099
-7.49%
0.3377
-0.62%
0.0007173
-0.01%
0.0004463
-14.91%
0.694
-1.56%
0.00000072
1.41%
0.057153
-1.83%
0.00000655
0.00%
0.024525
0.00%
0.04520
-3.42%
0.05246
-9.80%
0.03244
-1.10%
0.00001406
0.00%
0.0008753
3.98%
0.8410
14.52%
0.005549
2.27%
0.02151
0.28%
0.12110
-2.74%
0.04057
-4.77%
0.100230
-10.79%
3.0658
-0.02%
26.5136
0.63%
0.0321
3.22%
0.6003
0.08%
0.0024842
0.65%
2.310
-10.74%
0.1002
-1.57%
0.001820
-2.41%
0.1716
1.00%
0.07581
-2.37%
0.02252
1.53%
0.009320
-35.54%
0.01726
-1.26%
0.00519
3.59%
0.115940
-0.92%
0.00682
-12.11%
0.05382
0.26%
0.4542
8.22%
1.8276
-9.64%
0.00286
-0.69%
0.0016319
1.03%
0.0001704
-8.44%
0.00542
1.31%
0.00004382
0.02%
0.0010883
-3.70%
6.787
-3.22%
92.69
-0.99%
0.012875
53.07%
0.020269
-4.73%
0.0002759
-3.19%
0.023542
-5.28%
0.01889
-0.79%
0.0005806
0.66%
0.009335
0.18%
0.00009942
-1.48%
0.013284
-2.02%
0.0202
-71.39%
0.002762
-0.75%
0.002279
2.15%
179.12
-4.32%
1.7450
1.55%
0.0003635
-2.07%
0.02536
-9.04%
0.002693
5.65%
11.5601
-0.25%
0.00001918
-3.86%
0.004847
-1.76%
0.00224
-6.67%
0.002832
0.35%
0.0010008
-0.03%
0.05025
3.48%
0.13808
-10.08%
0.0006481
1.23%
0.1920
-12.49%
0.002024
-13.95%
0.0001298
-0.76%
0.0674
11.04%
0.008214
15.53%
0.0256
-2.66%
5.89
0.34%
0.6799
19.49%
0.00082109
-2.09%
0.00017844
0.58%
0.00048
0.00%
0.1283
0.39%
0.2589
0.19%
0.10356
-1.58%
0.000639
-0.16%
0.6024
-2.57%
0.00007711
2.92%
0.16182
-10.58%
4.1508
7.84%
0.00000487
-1.22%
0.000003545
16.15%
0.0338
9.39%
0.00000008162
-3.90%
0.00000011
-68.57%
0.000001411
-2.22%
11.38
0.18%
0.00503
9.83%
0.014751
3.95%
3.7999
4.09%
0.10593
0.18%
0.02249
12.00%
0.027683
7.72%
0.0000766
-27.26%
0.001309
-2.17%
0.000442
7.02%
0.000002268
2.16%
0.0788
0.00%
0.000084
-67.57%
0.0001481
-11.85%
0.0000000360
-1.64%
216.000
1.50%
22.09
-4.00%
0.007117
-6.47%
0.19360
-1.53%
0.009009
8.06%
0.0000813
-8.14%
0.00760
-3.68%
0.1389
-13.73%
0.00053
0.00%
0.019733
5.63%
91.1358
1.25%
0.003007
-0.27%
0.01590
0.00%
0.0000000035
6.06%
0.68493
0.43%
0.1001
-23.53%
0.01713
-5.31%
0.002914
2.10%
0.1495
-1.52%
0.000006320
0.51%
0.48513
0.44%
0.4102
-3.00%
0.00018781
-0.08%
0.5482
0.90%
0.00332
2.15%
0.002524
-3.44%
0.05970
-0.67%
0.02131
10.07%
0.00017163
-0.13%
11.8232
-0.05%
0.00009731
-1.77%
0.07451
44.88%
0.5979
-0.83%
0.0110
4.76%
15.28
-1.10%
0.0909
-1.41%
0.002509
1.21%
0.00236
19.19%
0.0000565
-1.22%
6.4004
0.00%
0.03289
8.19%
0.035897
-1.75%
0.1376
0.07%
0.006759
-0.31%
0.04489
-4.93%
0.000472
-31.59%
0.00397
0.51%
0.0017
0.00%
13.96
-12.97%
15.48
4.31%
0.0059
-1.67%
0.0000215
1.42%
0.01122
20.13%
2.985
-1.62%
0.02614
-5.70%
1.984
1.07%
0.0021
5.00%
0.01032
-3.28%
34.0461
0.11%
0.8533
-9.00%
0.01666
0.12%
0.00001563
-0.45%
5.86
-13.95%
1.205
-0.66%
0.17264
-1.85%
9.67
-5.84%
0.00058415
0.21%
0.2329
3.37%
0.3719
2.31%
3.086
-1.56%
0.0000010
-33.33%
0.536
-2.19%
0.000995
-5.24%
0.26000
-45.34%
0.0000000045
-8.16%
0.3488
-0.26%
0.365
-1.62%
0.00460
0.22%
0.0000399
-1.48%
0.2849
1.10%
0.03908
4.94%
0.007608
-1.37%
0.002803
20.92%
0.0084180
-5.15%
0.00156
-2.50%
0.000130
0.00%
0.0000001110
-25.25%
0.0002305
0.52%
0.015000
77.10%
2.9997
-0.02%
4.3370
-2.16%
0.05206
-11.70%
0.002340
-5.26%
66.9999
-9.46%
0.00760
2.98%
0.001000
0.00%
0.02507
38.58%
0.2065
-2.96%
0.000000000344
-1.99%
0.001848
-0.05%
2.1111
0.00%
0.000600
-11.76%
0.1801
-0.94%
0.00728
4.45%
0.05042
-18.68%
0.00005993
-6.85%
0.012405
-0.10%
1.1587999
-2.80%
1.0000
0.03%
0.2142
-0.97%
0.014908
7.27%
0.000532
-8.75%
0.7943
-0.35%
0.00049
4.26%
0.00555000
-5.93%
0.08601
-1.70%
3025
-0.13%
1.5983
-0.46%
0.2163
1.45%
0.01255
-0.32%
0.6216
-1.25%
0.00000619
0.49%
0.0000854
-0.23%
0.005080
-8.05%
0.0242
-3.20%
0.9118
-1.14%
0.2401
-3.34%
0.4572
-1.32%
7.41
-2.76%
0.01799
-8.68%
1.001
1.73%
0.0036663
-0.36%
0.9511
3.66%
0.0000855
-2.06%
0.00000001395
-3.73%
0.00002471
2.32%
0.1404
-2.97%
0.006830
-11.40%
0.5131
-10.08%
0.03925
2.86%
0.0317
0.32%
0.10070
-3.23%
0.0360
2.86%
0.002842
-22.37%
0.01850
-0.27%
0.08942
-1.95%
0.000191
-5.45%
0.0000609
0.16%
0.1895
-9.20%
260.7
-3.23%
0.002865
5.33%
19.9812
0.36%
0.005386
-2.59%
0.01477
-3.84%
0.5393
7.22%
0.4473
-1.43%
0.1833
-2.03%
1.0859
-9.85%
2.868
-2.75%
0.2868
-2.48%
18.47
-4.94%
0.0122280
-0.13%
0.000509
0.20%
0.3997
10.75%
4.921
1.48%
0.0242
0.83%
0.0000000424
17.45%
0.887
-3.90%
0.01295
-16.29%
0.01854
0.49%
0.0000018499
-8.82%
0.002178
2.78%
0.000000051506
-5.15%
0.001049
2.74%
0.00240
0.00%
0.000166
0.61%
3.968
-3.08%
0.00021272
31.24%
0.00002394
-5.15%
0.04624
-7.59%
0.000669
11.50%
0.2462
-0.49%
0.00030
42.86%
0.00064
-1.54%
0.02641
-0.83%
0.004803
4.62%
3.522
-3.74%
0.553
-2.12%
0.1160
0.52%
0.00000333
-2.06%
0.000287
2.14%
0.008099
-0.07%
0.0015
0.00%
0.1000
-0.10%
0.00481
-5.69%
0.00897
-14.33%
0.011253
-3.93%
0.000650
-9.09%
0.002763
-8.93%
0.006455
9.43%
0.586
-8.29%
0.00517
-0.96%
0.066331
-1.13%
0.05268
-21.15%
0.3157
0.29%
0.00412
-8.04%
7.78
-8.79%
0.03699
38.02%
0.7484
2.35%
0.01965
-2.48%
19.0120
2.91%
0.00772
-0.13%
0.08650
1.09%
0.02194
27.11%
0.000000560
-2.10%
0.003782
1.48%
0.1208
0.92%
0.001832
-5.47%
0.00139
0.00%
0.02163
12.42%
0.0093
-4.12%
0.13096
1.50%
0.005675
3.33%
18.09
-2.32%
0.0889
0.00%
0.5223
0.00%
0.00302
-1.31%
0.03984
58.35%
0.00003938
0.03%
0.0000618
-14.05%
0.03768
3.86%
0.01507
31.04%
0.00001266
-7.99%
0.0617
-1.44%
0.6388
1.41%
0.004485
-2.24%
6.21
-0.32%
25.20
12.80%
0.006226
0.84%
1.396
2.72%
0.1148
4.27%
0.2378
-5.26%
0.9899
1.58%
0.1999
0.35%
0.00000016302
0.12%
0.000856
0.94%
0.3110
1.83%
336.9
-0.21%
0.359
-2.71%
0.000119
0.00%
0.00723
0.70%
0.003902
18.93%
0.01856
2.83%
0.001604
41.20%
1.6300
-33.03%
0.1820
-0.82%
10.938
37.69%
10.65
-0.19%
0.001508
-7.48%
1.7632
-0.51%
0.00029883
5.38%
0.6962
-1.44%
0.00362
44.80%
0.00000000009559
2.86%
0.25648
-6.79%
2.952
1.44%
0.650
1.72%
0.4383
3.64%
0.0002438
-8.89%
0.004942
-0.84%
0.00364699
0.49%
0.000283
-8.41%
0.002131
28.22%
0.00486
3.40%
0.00875
-5.61%
0.002737
-10.26%
0.04879
0.58%
0.000365
-2.14%
0.000742
4.65%
0.001953
82.87%
0.02345
-2.45%
0.3188
-0.78%
0.1500
-1.06%
0.000375
-4.82%
0.00010295
10.76%
0.00849
-14.07%
0.06086
-3.76%
0.020532
5.13%
0.0590
22.66%
0.01083
-16.50%
1.027
-2.84%
0.6412
-22.02%
0.01466
-0.20%
0.7480
-6.95%
0.1097
0.55%
0.00004150
2.57%
6.118
-0.47%
0.0002887
-0.93%
0.000209802
-1.11%
0.000000001497
0.00%
0.001062
-9.08%
0.00000466
-6.80%
0.002507
-4.53%
0.000705
-10.65%
0.00814
-4.57%
0.000240
-2.44%
0.4289
6.64%
0.03917
-6.67%
0.000102
6.25%
44.71
0.22%
5.918
-2.25%
0.02599
-10.69%
0.01808
1.63%
17.412
-1.00%
2.209
-0.18%
0.1528
1.39%
0.1428
-6.61%
0.63451
8.83%
0.00006677
1.35%
5.41
-1.99%
0.0685
-4.60%
0.5210
-3.14%
0.001029
-6.79%
0.0000215
-2.27%
0.001426
-10.76%
0.1217
-4.25%
31.27
1.00%
0.00009726
15.79%
0.002082
-11.10%
0.0089
1.14%
0.001625
1.63%
0.0939
0.11%
0.013101
-1.25%
0.00496
-0.80%
0.000001656
-1.72%
0.00000003814
-1.55%
0.000623
-9.32%
0.893
-0.89%
0.006012
-22.08%
0.2516
-0.79%
0.05922
-6.00%
0.5838
1.16%
1.1824
-0.17%
0.05122
6.16%
3076.29
0.41%
0.000389
18.24%
0.2668
-17.55%
1.5011
-0.72%
0.07801
6.75%
0.0003200
-3.50%
0.0000046
17.95%
5.746
-2.53%
0.0058
-12.12%
0.00097
3.19%
0.009361
-2.78%
0.1795
-7.47%
0.3472
-3.18%
0.004740
-24.94%
0.000000000248
-2.36%
0.06319
-2.62%
0.01189
-0.17%
7.71
-3.75%
0.2152
-1.65%
7.6535
-5.55%
0.1389
0.58%
0.004626
7.73%
0.0480
-0.62%
0.00136
7.94%
1.2938
-4.85%
0.2641
-5.34%
0.725
0.42%
2.400
-0.70%
0.553
-1.95%
0.002045
-8.87%
0.02054
-7.48%
0.85380
-0.11%
0.0042
0.00%
1.044
1.36%
0.0404
3.59%
0.3359
8.92%
0.002820
1.66%
0.02636
-5.86%
0.4022
-11.60%
166.79
-0.01%
0.00262
1.16%
0.003890
6.93%
0.1211
4.31%
0.00621
-0.64%
1.995
1.22%
0.2083
-2.75%
0.01868
2.64%
0.03693
-9.57%
0.018130
-19.42%
0.05498
22.18%
0.002305
-10.55%
0.3453
-3.55%
0.5440
-4.49%
0.0235
-0.42%
1.5768
-2.59%
0.01111
-15.26%
0.1078
-2.80%
0.00000001316
-0.53%
0.0005514
-5.94%
6.4899
62.21%
0.0000003074
-3.94%
0.001283
-4.40%
0.03933
-3.58%
2.364
-1.70%
0.00003151
0.19%
0.281
-0.71%
0.03440
-3.32%
0.002928
-7.90%
0.003176
0.03%
0.00002645
3.24%
0.6038
-5.92%
0.004720
-4.24%
0.0000000796
-2.33%
0.003926
-6.52%
9.798
0.29%
0.000870
3.20%
0.006889
44.51%
0.0006624
-0.84%
0.00016984
-15.08%
0.0275
-9.24%
0.00667
-6.45%
0.778
1.04%
0.013053
1.16%
0.000002570
-10.45%
0.1456
-0.75%
0.19643
-4.78%
0.0120
-1.64%
0.2127
-1.21%
0.006109
-8.04%
0.000642
9.56%
0.01460
-17.28%
0.677
-2.03%
0.008000
2.56%
6.5338
-3.05%
0.012770
-1.77%
0.6413
-2.60%
0.001152
1.86%
1.378
-2.48%
0.05495
5.41%
0.01491
1.98%
0.001844
1.15%
0.03129
-0.06%
0.018901
5.05%
0.2830
-1.43%
0.1049
-0.29%
0.0030
-3.23%
0.01428
-14.95%
0.4728
-3.21%
0.002955
-0.81%
0.00152
27.73%
0.0005192
-7.17%
0.0000509
4.30%
0.002013
-14.67%
0.0813
-0.37%
0.1011
-1.37%
0.0110
5.77%
0.07707
1.16%
0.003999
-0.50%
0.13487
-2.22%
0.02239
-20.77%
0.427
0.00%
0.0782
-2.98%
0.00005016
1.09%
3.0365
-2.16%
0.0007266
-6.74%
7.069
-1.28%
0.03044
-8.12%
0.001530
-7.44%
0.00000817
1.87%
0.011992
-4.22%
0.0000745
13.05%
0.1927
-2.48%
0.00000001567
2.82%
0.04394
-27.12%
0.0004484
6.05%
0.03466
-4.49%
0.0464
-0.85%
0.2219
-0.98%
0.2999
-0.20%
0.00000021520
-30.58%
0.00005521
-3.78%
0.003402
-2.55%
0.626
-0.63%
2.300
-2.21%
0.00972
7.88%
0.0002829
-0.84%
2190.46
-0.36%
0.002220
-3.48%
0.0000521
4.62%
1355
6.27%
0.01703
-14.59%
0.00421
0.24%
0.01822
-4.16%
0.000001672
-0.06%
0.1475
-1.07%
0.0007500
-20.06%
0.826
0.00%
19.24
-1.43%
0.7654
0.17%
0.004268
-0.19%
0.1592
-2.39%
0.1012
-3.44%
0.000349
-9.82%
0.000934
-11.72%
0.7620
-0.09%
0.911
-0.55%
0.007259
-0.79%
23.586
-1.53%
0.000000518
0.39%
0.02985
0.47%
0.2784
-1.38%
0.03000
0.00%
0.11737
5.33%
0.00002478
-4.29%
0.1037
-1.80%
0.004433
-10.52%
77.1
-2.28%
0.004401
-3.19%
0.0002212
-24.69%
0.0000000000000159
-11.17%
2.255
3.35%
0.002384
-0.04%
0.01246
-5.39%
0.0098
-2.00%
0.0000086
-3.37%
3.484
-1.53%
0.002112
0.62%
0.2778
3.46%
0.01855
-5.89%
0.7419
-3.17%
0.2140
-1.15%
0.0051036
-0.06%
25.0000
-0.44%
0.01592
-14.59%
0.1108
-0.89%
0.0361
-1.10%
0.000022
-18.52%
0.2228
-1.33%
0.0001532
-24.90%
0.0004856
21.98%
0.0102
-0.97%
0.0000699
145.26%
0.0547
0.55%
0.0000002725
-31.24%
12.32
-0.56%
0.003927
-18.56%
0.491
2.29%
0.3333
-0.27%
0.002920
-6.68%
1.4478
0.58%
0.000001970
-12.33%
0.00000000110
44.74%
0.003495
1.69%
0.00805
7.33%
0.0000266
-1.12%
0.2112
-0.94%
0.03866
-13.45%
0.0000000002103
0.96%
0.001955
-0.05%
0.0000763
-9.81%
0.0008166
-7.59%
0.918
0.99%
0.0065104
-32.18%
0.003439
-0.86%
0.0569
-3.72%
0.03950
-8.48%
1.275
-0.31%
0.0771
0.13%
0.01478
2.00%
0.0001786
114.15%
0.02686
0.64%
0.05695
-0.54%
0.2861
-4.86%
0.05840
-2.75%
0.002473
3.34%
0.001302
-27.79%
3.40
-3.68%
0.001913
1.06%
0.000000000598
-3.55%
17.60
-1.51%
0.1762
-1.01%
0.0766
-1.03%
0.000000000000929
-2.42%
0.000000001818
-4.67%
0.1118
-6.37%
0.000000000658
-9.99%
0.0006363
-2.21%
0.0484
0.83%
0.001304
-4.40%
0.0000086
-3.37%
0.004983
-10.31%
0.3645
-3.11%
6.5085
-8.41%
0.005149
-3.50%
0.003912
0.00%
0.00120
-0.83%
0.1093
-1.89%
0.1703
-2.29%
0.0382
50.39%
0.001169
-4.02%
0.09000
-21.62%
0.00010610
-0.01%
0.00000000015505
-1.19%
0.0261
-2.61%
0.032810
-4.38%
0.00009300
-27.34%
0.02797
0.39%
0.00000000001749
3.43%
0.1541
-4.17%
0.0000000626
0.48%
0.0004089
5.69%
18.14
-0.60%
0.0168
-1.18%
0.00533
-1.30%
0.0000000508
-3.42%
0.00003
0.00%
0.000000002095
2.15%
0.0111
0.91%
0.02511
-0.79%
0.0004
-33.33%
15.13
-3.45%
0.001340
-2.76%
0.0022876
-5.27%
0.01290
-1.83%
0.961
-10.35%
0.000030
0.00%
0.013605
0.05%
0.0066
4.76%
0.0667
-4.44%
0.9168
-0.27%
0.00000724
1.54%
0.661
-3.50%
0.000106
-3.64%
0.000261
60.12%
0.006138
0.97%
0.000000000001766
-0.90%
0.0007592
-6.13%
0.00911
-1.09%
0.0196
2.62%
0.0000018
-10.00%
0.000504
44.00%
0.002701
0.04%
0.00000391
-6.01%
0.000283
-7.82%
0.0006855
-2.50%
0.0937
-3.60%
0.00725
-1.09%
0.0958
21.11%
0.0000000030204
-29.16%
0.0002383
-3.13%
0.000012
-60.00%
0.00306
0.00%
0.0000000173
15.33%
0.0925
-3.04%
0.00000000001278
14.01%
0.00006107
-37.58%
0.01685
-0.77%
0.008231
0.00%
0.001033
0.29%
0.804
-0.25%
0.04024
2.26%
0.0000235
0.00%
0.01116
-12.20%
0.000000000003
-25.00%
0.00000000000012
-53.85%
0.01303
-21.03%
0.1435
-5.59%
8.16
-1.21%
0.00000926
0.00%
0.0112
-2.61%
0.2597
-4.49%
1.530
-1.10%
0.00872
-5.93%
0.00685
-20.81%
0.00237
-15.96%
0.0437
-1.13%
0.3796
-1.99%
84.57
-8.55%
0.05024
-4.65%
2.51
97.64%
0.1281
-1.76%
0.000717
-13.51%
0.000786
-5.19%
0.002013
0.00%
0.0338
-2.31%
0.0000013
85.71%
0.01331
-0.67%
0.01084
-2.95%
0.0048
-26.15%
0.0000240
-4.38%
0.0987
0.61%
0.000835
-0.95%
0.0000651
0.93%
0.05877
-0.58%
0.169000
-26.52%
0.249
-17.00%
0.0570
-2.56%
0.004240
1.12%
0.1173
-1.10%
0.1351
-0.73%
0.1291
-1.90%
18.60
0.43%
0.3893
-1.74%
0.000852
-6.99%
0.000090
5.88%
0.00003
-50.00%
0.003591
-13.37%
450.00
80.00%
0.00647
-0.46%
0.0097
7.78%
0.05804
-0.14%
0.0000119
-15.00%
0.03325
3.52%
0.02945
-1.77%
0.00013
-7.14%
0.01050
0.00%
1.485
-2.50%
0.01674
-1.70%
0.0018
5.88%
0.000025
-3.85%
1.672
-3.13%
0.00027
0.00%
0.001439
-12.79%
0.0002201
-8.37%
0.00093
-27.91%
0.000189
-6.44%
0.02056
1.58%
0.002334
-3.99%
0.03745
-0.87%
0.00000000000098
-1.01%
0.000000000003846
-15.08%
0.00000000000212
19.77%
0.0515
-3.20%
0.00000000000012
0.00%
0.733
-2.01%
0.002244
-9.41%
0.0947
-2.87%
0.000037
-17.78%
0.0000061
0.00%
0.000001624
-3.22%
0.0867
-0.69%
0.1288
-13.85%
0.00000054
-1.82%
0.00002268
-0.18%
0.01286
-1.53%
0.00036
0.00%
0.0000000000000165
5.10%
0.000025
78.57%
0.0125
-6.02%
0.000076
-10.59%
0.0590
1.72%
0.0392
-2.00%
0.0809
-1.94%
3.026
-0.92%
0.0009040
-9.14%
0.0004418
-4.16%
0.02937
-6.82%
0.0696
-1.69%
0.0550
1.48%
0.0001
0.00%
0.0894
1.59%
0.1529
-0.78%
0.000017
21.43%
0.0000099
0.00%
0.537
-1.65%
0.000000000030
-57.14%
0.00000000000651
-0.15%
0.0353
-1.12%
0.000004
-55.56%
0.001100
-3.25%
0.750
0.00%
0.1345
-0.81%
0.003638
-9.91%
0.00004089
-1.64%
0.0119
-2.46%
0.001764
-5.01%
0.0000006650
0.76%
0.00000000000115
0.00%
0.0000138
39.39%
0.001025
-9.93%
0.1905
-2.11%
0.00040
11.11%
0.8437
0.14%
0.0007
-41.67%
0.00026
0.00%
0.1932
-1.58%
0.0822
-3.75%
0.00608
63.88%
0.001790
0.00%
0.00220
-8.33%
0.0371
-3.13%
0.2993
-0.03%
0.00000007
-41.67%
0.0001402
-0.07%
0.0005
0.00%
0.001047
-7.51%
0.00004
0.00%
0.489
-5.23%
0.0001553
1.84%
0.0000002164
-1.01%
0.00242
-7.98%
0.0000310
-0.64%
0.0004480
-15.26%
0.006303
-6.57%
0.1480
-1.33%
0.0006750
-6.13%
0.0066
3.13%
0.003526
-5.72%
0.00000000003011
79.65%
0.5375
1.66%
0.0014
55.56%
0.00000313
-5.15%
0.000062
40.91%
0.0000329
0.00%
0.0000077
30.51%
2.980
-2.23%
0.001233
-0.72%
0.000003220
101.25%
0.00000000058
5.45%
0.0000000186
0.54%
0.0182
0.00%
0.0009
0.00%
0.0700
39.44%
49.870
-1.46%
0.00011
-8.33%
0.0615
2.50%
0.3905
24.72%
0.00000042
-2.33%
0.000000110
8.91%
0.0108
10.20%
0.0005
25.00%
0.01299
-1.59%
0.7000
0.00%
0.00000000000288
-0.35%
11.5002
-4.96%
0.0026
0.00%
0.00009
-10.00%
0.000196
2.08%
0.000000000019
72.73%
0.3580
-8.51%
100.71
-0.94%
0.01200
0.00%
0.00011
-15.38%
0.003215
-11.87%
0.0027
0.00%
0.3065
-0.07%
0.00004399
0.00%
0.000000000117
8.33%
0.00000007783
0.00%
0.000400
-20.00%
0.00000000003610
4.82%
0.000000000782
-2.37%
0.000056
-27.27%
0.00077
-8.33%
0.000452
-0.22%
0.000092
6.98%
0.000000001868
-0.05%
0.00011
0.00%
0.000000000747
-0.66%
0.0480
-2.83%
0.00006
-40.00%
0.00774
12.34%
0.000000000375
0.27%
0.000190140
4.73%
0.000028
-15.15%
0.00000000000040
0.00%
0.00000000000403
1.26%
0.000000008400
0.00%
0.000000000533
0.00%
0.000000002300
-4.41%
0.000000041
7.89%
0.000000000129
0.78%
0.00030000
-14.29%
8.98
-2.29%
0.00000152
4.83%
0.0246
-3.15%
0.0000282
-9.90%
0.000033
-13.16%
0.001500
0.00%
0.2241
-0.93%
0.0562
28.60%
0.01107
-5.87%
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%
0.0815
-1.69%
0.005136
-3.89%
0.02318
-14.75%
1.2801
-0.12%
0.01479
-7.39%
0.1176
-1.75%
0.0003844
-5.95%
0.4917
0.57%
0.10563
0.78%
0.1381
-3.90%
0.3725
-2.64%
0.003198
-15.46%
0.2574
0.70%
58.5600
0.00%
0.0596
0.68%
0.0004536
-13.32%
0.0910
-4.61%
0.0005077
-3.83%
0.0003220
0.00%
0.002606
-6.83%
0.0009012
0.00%
0.0004038
-4.38%
0.00600
0.00%
0.0007993
0.00%
6.197
-0.29%
0.2233
1.18%
0.0000675
-0.74%
0.0000397
0.00%
0.002786
-5.30%
0.0012
0.00%
0.7731
-3.12%
1899.00
0.00%
0.4410
-1.61%
0.6000
-2.55%
0.0480
5.73%
0.00426
4.67%
0.00220
-5.98%
0.2091
-2.38%
2.5129
0.00%
0.470
2.84%
1.000000
0.00%
0.3771
0.00%
0.5732
0.00%
1.877
-1.16%
0.0569
-2.90%
0.000000100
0.00%
0.0001030
0.00%
0.00103
0.00%
0.6814
5.91%
0.0700
0.00%
0.00000000003010
63.06%
0.001127
-3.26%
0.00000089
-5.32%
0.1534
-0.39%
0.01932
-1.02%
0.1907
-2.75%
0.000216
0.00%
2.179
0.00%
1.5000
0.00%
3.9889
0.00%
1.1371
0.00%
6.463
-0.98%
0.000080
2.56%
0.4424
0.00%
0.000393
1.03%
0.0071
0.00%
0.000210
0.00%
14.20
0.21%
0.0763
-3.78%
0.1142
-1.13%
0.1769
-0.34%
0.004293
-0.88%
0.000452
0.00%
0.0272
0.00%
0.1204
0.00%
2.701
1.12%
1.119
2.10%
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%
0.000025
4.17%
0.00005
0.00%
0.00006187
0.00%
0.000166
0.00%
0.001405
0.00%
0.2461
-0.16%
0.000483
2.11%
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%
1.448
1.69%
3.7189
0.00%
0.000082
0.00%
0.0071
0.00%
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
0.83%
0.00614
0.00%
0.4606
0.00%
0.001800
0.00%
0.000001000
0.00%
0.0000008
0.00%
1.3373
-0.25%
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%
0.4445
3.30%
0.3853
-1.73%
0.001106
0.00%
0.0249
0.00%
0.6608
0.00%
0.0633
3.26%
0.5300
0.26%
0.00500
0.00%
3.58
0.00%
0.01172
1.12%
0.0020
0.00%
0.00538
0.00%
0.4505
1.49%
5155.00
0.00%
2.222
-0.67%
1.501
-2.91%
0.0091
0.00%