How does zk-DID (Zero-Knowledge Decentralized Identity) technically work?
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:
- Initialization:
The user generates their DID along with a corresponding private key stored securely on their device or wallet. - Create Verification Proof:
The user constructs a zero-knowledge proof demonstrating possession of their private key while keeping it confidential from external parties. - User Interaction with Service Provider:
The service provider requests verification from the user based on specific criteria related to access or authentication needs. - 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 .
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3.481 | -6.50% | |
0.00139 | -0.71% | |
0.03090 | 3.76% | |
1.483 | 12.18% | |
0.00450 | 0.00% | |
0.008063 | -0.47% | |
0.006333 | -0.25% | |
0.01485 | -6.78% | |
0.00000006379 | -6.01% | |
0.0093 | 6.90% | |
0.1837 | 0.22% | |
0.000119 | 0.00% | |
0.00338 | -15.50% | |
0.2657 | -2.96% | |
0.00279 | -2.11% | |
0.000855 | 1.18% | |
0.0000000001855 | -3.54% | |
0.1600 | -3.03% | |
0.0777 | -82.98% | |
0.004036 | -10.89% | |
0.001598 | 45.27% | |
3133.16 | 1.39% | |
2.552 | -11.05% | |
0.000000001275 | -14.83% | |
0.0000458 | -10.89% | |
0.001791 | 11.80% | |
8.410 | -9.89% | |
0.000287 | -4.97% | |
0.000270 | -21.74% | |
0.00695 | -4.66% | |
0.1500 | -6.07% | |
2.7062 | -0.95% | |
0.000000430 | -12.78% | |
0.8712 | -4.47% | |
0.000357 | -2.19% | |
0.1830 | -8.22% | |
0.004956 | 0.49% | |
1.7628 | -0.09% | |
0.03007 | -6.61% | |
0.6859 | 1.14% | |
0.9314 | -9.29% | |
0.0791 | -3.54% | |
0.1710 | -6.15% | |
0.0560 | -16.04% | |
0.1819 | -11.78% | |
0.000203037 | 2.02% | |
0.6068 | -6.80% | |
0.000385 | 0.26% | |
0.00006695 | -0.19% | |
0.002738 | 0.51% | |
1.045 | -16.60% | |
0.0657 | -7.07% | |
0.003953 | 1.26% | |
0.00320285 | -4.46% | |
18.2189 | -3.22% | |
0.0509 | -6.78% | |
0.002475 | -9.14% | |
0.01091 | -8.63% | |
0.0000016101 | -3.88% | |
0.007378 | -10.75% | |
0.05766 | -1.37% | |
0.0009700 | 6.63% | |
0.0875 | -0.34% | |
0.0029990 | -1.06% | |
0.01467 | -0.07% | |
0.00001131 | -5.51% | |
0.0000127 | -23.49% | |
0.760 | -8.76% | |
0.469 | -7.31% | |
0.001743 | -3.11% | |
0.00915 | 0.22% | |
0.000098 | 0.00% | |
0.002033 | 0.99% | |
12.60 | -5.12% | |
0.06484 | -5.40% | |
16.49 | -3.28% | |
0.8609 | -2.62% | |
0.005483 | -26.84% | |
2.357 | -10.79% | |
0.01999 | -9.26% | |
0.0121 | 2.54% | |
0.05575 | -3.95% | |
0.000801 | 13.46% | |
0.001496 | -2.48% | |
0.0041 | -2.38% | |
0.062949 | -1.99% | |
0.015358 | 2.73% | |
0.013417 | -5.17% | |
6.22 | -11.14% | |
0.005945 | -8.41% | |
0.00456 | 0.44% | |
0.002896 | -5.36% | |
0.006326 | -10.13% | |
0.003326 | -9.47% | |
0.06045 | -23.81% | |
0.21626 | -13.60% | |
0.740 | -8.98% | |
0.000873 | 4.05% | |
0.0023 | 0.00% | |
0.00852 | -5.44% | |
0.00000013792 | -7.38% | |
0.01139 | -4.77% | |
0.6388 | -6.73% | |
0.4679 | -5.95% | |
0.02686 | -4.62% | |
17.45 | 3.50% | |
0.0000240 | -1.64% | |
0.0000000394 | 3.41% | |
0.003980 | 11.77% | |
0.001413 | -21.89% | |
0.01712 | -0.98% | |
0.000222 | 18.72% | |
0.001627 | -10.11% | |
15.73 | -7.42% | |
0.3576 | -4.10% | |
0.01245 | -0.08% | |
1973.55 | -3.20% | |
0.00782 | -10.11% | |
0.0025 | -7.41% | |
0.003613 | 11.58% | |
10.74 | -7.09% | |
0.0002750 | -7.93% | |
0.02269 | -5.97% | |
0.549 | -5.67% | |
0.85394 | 0.08% | |
0.6580 | -5.45% | |
0.002650 | -6.79% | |
0.00003382 | -0.44% | |
0.003835 | -5.24% | |
0.000499 | 0.00% | |
6.92 | -12.18% | |
0.00005930 | -3.94% | |
0.469 | -5.63% | |
0.0005897 | -4.36% | |
0.03431 | -5.30% | |
0.000789 | -28.01% | |
0.3389 | -4.64% | |
0.01530 | -5.90% | |
0.00866 | -27.35% | |
0.01516 | -16.47% | |
0.002028 | -5.89% | |
0.1656 | -2.01% | |
0.0415 | -4.38% | |
0.00000003344 | -5.88% | |
0.7415 | -21.82% | |
26.45 | -5.54% | |
0.03341 | -8.52% | |
0.000527 | -22.73% | |
2.510 | -7.55% | |
0.0003044 | -23.75% | |
0.00101 | 0.00% | |
0.00206 | -9.25% | |
0.02632 | -4.84% | |
0.0309 | -8.85% | |
0.4088 | -3.58% | |
0.002428 | -7.29% | |
0.0000285 | -40.63% | |
0.000000001576 | -9.32% | |
1.6384 | 4.08% | |
0.00000001178 | -2.89% | |
8.16 | -5.99% | |
0.589 | -4.38% | |
5.166 | -6.07% | |
0.00233 | 0.00% | |
0.002298 | -7.53% | |
0.00068 | -8.11% | |
0.574 | 6.89% | |
0.2122 | -1.03% | |
0.001144 | -14.50% | |
0.3871 | -12.70% | |
0.001636 | -7.93% | |
0.0256 | -4.12% | |
0.002447 | -15.06% | |
4.691 | -6.96% | |
0.0602 | -7.38% | |
0.300 | -8.54% | |
0.0062 | -1.59% | |
0.0000544 | -2.68% | |
0.580 | -6.90% | |
0.03230 | -0.22% | |
0.4692 | -5.54% | |
0.031181 | 1.03% | |
1.926 | -6.00% | |
9.618 | -1.03% | |
0.0000002925 | 7.34% | |
1.716 | -6.99% | |
0.003441 | 7.70% | |
0.0852 | -5.65% | |
0.55461 | -4.29% | |
0.01805 | -2.96% | |
0.04258 | -0.09% | |
0.0004089 | 4.82% | |
0.03712 | -5.21% | |
0.011987 | 0.01% | |
0.004095 | -9.50% | |
0.01109 | -8.12% | |
0.0007191 | -2.03% | |
0.0151 | -4.43% | |
0.002877 | -15.75% | |
0.0205 | -11.26% | |
0.01312 | -11.53% | |
0.0001967 | -11.75% | |
0.1431 | -5.73% | |
2.176 | -0.50% | |
0.000001466 | -3.43% | |
0.0000002569 | -5.45% | |
0.2455 | -2.39% | |
0.1211 | -10.63% | |
0.0003999 | -4.74% | |
0.0002373 | -9.05% | |
0.0109 | 11.22% | |
0.0112 | -50.66% | |
0.0000000834 | -8.65% | |
0.00597 | -7.59% | |
0.2425 | -5.27% | |
0.005776 | -5.00% | |
0.001690 | -20.95% | |
0.000103 | 9.57% | |
1.0466 | -7.50% | |
0.000251 | 27.41% | |
0.1850 | -3.19% | |
0.001536 | -6.34% | |
0.001597 | -20.86% | |
0.01449 | -5.29% | |
0.02604 | -12.15% | |
6.37 | -5.77% | |
0.0471 | -4.66% | |
0.0110 | -1.79% | |
0.2653 | -4.67% | |
0.001106 | -6.19% | |
0.1836 | -7.04% | |
0.04814 | -4.08% | |
0.01932 | -13.94% | |
0.1034 | -10.17% | |
0.002656 | -3.80% | |
0.00000000008180 | -13.07% | |
0.00885 | -13.41% | |
0.0051 | -85.91% | |
0.0140 | -5.41% | |
0.0598 | -6.85% | |
0.0001889 | 4.54% | |
53.67 | -18.99% | |
0.01895 | -11.78% | |
0.01336 | -2.20% | |
0.001691 | -6.47% | |
0.000000000235 | -2.49% | |
0.000651 | -12.50% | |
2.913 | -6.78% | |
0.03644 | -3.50% | |
2.158 | -2.53% | |
0.0003751 | -29.66% | |
0.00000407 | -4.24% | |
0.1028 | -7.14% | |
0.0928 | 7.28% | |
0.229 | -9.84% | |
0.529 | -8.00% | |
0.004798 | -8.38% | |
0.002241 | 10.94% | |
0.2668 | -5.19% | |
0.04932 | -8.68% | |
0.00002213 | -4.49% | |
0.0000021 | 5.00% | |
0.1025 | -11.94% | |
6.1844 | -2.31% | |
0.7614 | -0.07% | |
0.01122 | -9.44% | |
7.5096 | -10.42% | |
0.00000001372 | -12.72% | |
0.2841 | -12.12% | |
0.0884 | -7.05% | |
1.028 | -1.72% | |
0.000292 | -7.89% | |
0.2453 | -4.63% | |
0.0051019 | -0.19% | |
0.000792 | -1.61% | |
0.000657 | -12.52% | |
0.0000093 | 6.90% | |
0.0000000000000136 | -5.56% | |
0.7260 | 0.22% | |
0.01181 | -5.90% | |
0.01509 | -6.97% | |
0.00154 | -6.10% | |
0.1064 | -27.86% | |
0.000270 | 4.65% | |
0.0003434 | -14.04% | |
0.0104 | 8.33% | |
0.00966 | -7.82% | |
0.003180 | -6.83% | |
4.214 | -7.85% | |
0.09001 | -7.50% | |
0.1919 | -12.85% | |
0.1207 | -6.14% | |
0.012381 | 1.02% | |
0.00000001250 | -5.59% | |
0.000996 | -7.00% | |
0.004365 | -10.15% | |
0.00396 | -7.91% | |
0.003796 | -5.12% | |
0.10762 | -7.83% | |
15.62 | -5.62% | |
0.00622 | -49.59% | |
0.00002701 | -2.24% | |
0.772 | -6.88% | |
0.0002565 | -8.03% | |
0.0098 | -2.00% | |
0.1067 | -6.57% | |
0.377 | -3.83% | |
0.0000000737 | -1.34% | |
0.001312 | -6.69% | |
0.02840 | 373.33% | |
0.0000582 | -2.02% | |
38.60 | -4.76% | |
0.05856 | -17.87% | |
0.006500 | -2.99% | |
0.0470 | -10.13% | |
0.00001616 | 6.74% | |
0.005167 | -5.88% | |
0.0000000123 | -15.17% | |
0.00000633 | -11.47% | |
0.00090 | -6.25% | |
0.00927 | -5.79% | |
0.00728 | -8.31% | |
0.00000000000070 | 79.49% | |
0.0045 | -21.05% | |
0.002160 | -9.28% | |
0.0575 | -7.85% | |
0.0155 | -5.49% | |
0.0000032 | -8.57% | |
0.1271 | -5.22% | |
301.7 | -2.05% | |
0.0005440 | -11.67% | |
0.1465 | -7.04% | |
13.24 | -5.02% | |
0.3359 | -5.35% | |
0.0005460 | -2.66% | |
0.00013000 | 39.78% | |
0.1095 | -7.91% | |
0.0724 | -5.36% | |
0.2945 | -13.61% | |
0.0554 | -6.89% | |
0.0979 | -3.83% | |
0.000834 | -0.83% | |
0.0019573 | -5.59% | |
5.24 | -9.50% | |
0.0002897 | -5.60% | |
0.004539 | -3.57% | |
18.93 | -6.84% | |
0.02934 | -11.39% | |
0.0000000447 | -5.70% | |
0.0096 | 5.49% | |
0.018559 | 0.00% | |
0.441 | -4.13% | |
0.4216 | -3.28% | |
0.1712 | -6.96% | |
0.00001124 | 30.55% | |
0.2445 | -6.36% | |
0.0004239 | 8.22% | |
0.002810 | -5.07% | |
0.01156 | -6.47% | |
0.008749 | -2.79% | |
0.00000000001842 | -5.05% | |
0.00000000000175 | -16.27% | |
0.8054 | -2.48% | |
0.000345 | -4.43% | |
0.1223 | -10.01% | |
0.000600 | -7.69% | |
0.2169 | -2.21% | |
0.0791 | 4.35% | |
0.3140 | -11.67% | |
0.0006751 | 0.69% | |
0.3251 | -5.88% | |
0.00000226 | -21.25% | |
0.640 | -12.57% | |
101.67 | 0.95% | |
0.01117 | -4.53% | |
0.0004936 | 0.88% | |
0.0000087 | -1.14% | |
0.0856 | -5.83% | |
0.00696 | -5.18% | |
2.723 | 2.60% | |
0.1159 | -7.13% | |
0.01431 | -9.83% | |
0.0000000615 | 7.33% | |
0.000002121 | -5.98% | |
1.179 | -5.68% | |
0.0000551 | 24.66% | |
0.0000008 | -38.46% | |
0.707 | -3.55% | |
0.02764 | 7.26% | |
0.000454 | -13.36% | |
0.2425 | -5.68% | |
0.00000722 | -0.28% | |
0.547 | -7.29% | |
0.2728 | -7.24% | |
0.001049 | -5.41% | |
0.1894 | -0.47% | |
0.00750 | -9.64% | |
0.2167 | 3.04% | |
0.04134 | -1.10% | |
15.05 | -7.04% | |
0.1937 | -4.39% | |
1299 | -9.16% | |
0.0000509 | -17.24% | |
0.04302 | -3.02% | |
0.0097 | -2.02% | |
1.320 | -4.28% | |
0.005534 | -5.40% | |
0.0221 | -5.96% | |
0.2575 | -6.43% | |
1.688 | -9.34% | |
0.00601 | 0.17% | |
0.01405 | -14.28% | |
16.09 | -5.52% | |
0.01107 | -4.32% | |
0.877 | -7.49% | |
0.0000560 | -6.82% | |
0.2444 | -12.05% | |
68.6 | -3.65% | |
0.0012 | 33.33% | |
0.8172 | -7.04% | |
0.01730 | -5.36% | |
0.0744 | -5.94% | |
0.0635 | -8.90% | |
0.01337 | -11.98% | |
0.656 | -5.75% | |
0.003948 | -7.74% | |
0.000000000000867 | 7.30% | |
0.002450 | 0.00% | |
0.00001982 | -2.70% | |
0.000412 | 0.49% | |
0.00003 | 0.00% | |
0.0841 | -7.28% | |
0.0234 | 0.86% | |
0.00003076 | 0.03% | |
0.652 | -3.69% | |
22.205 | -2.49% | |
0.000886 | -13.48% | |
0.1175 | -4.94% | |
5.530 | -5.81% | |
0.2457 | -6.26% | |
0.000008 | -27.27% | |
0.00681 | -2.30% | |
0.0301 | -4.44% | |
0.000024 | -4.00% | |
0.000661 | -4.76% | |
0.000910 | -4.51% | |
1.388 | -7.77% | |
0.1853 | -5.12% | |
0.5650 | 4.34% | |
0.00031 | -3.13% | |
0.000018 | -64.00% | |
0.00980 | -3.07% | |
0.00019 | -20.83% | |
141.98 | -5.84% | |
0.010884 | -2.31% | |
0.0783 | -8.31% | |
0.1891 | -4.30% | |
0.00008773 | -2.19% | |
0.00000000155 | -4.32% | |
12.15 | -8.23% | |
0.750 | 0.00% | |
0.1138 | -6.57% | |
0.001591 | -4.50% | |
0.00000000000011 | -21.43% | |
0.00000000001051 | -9.00% | |
0.2108 | -7.10% | |
0.03734 | -13.22% | |
0.002918 | -10.27% | |
0.00000018000 | -37.89% | |
0.00044 | 46.67% | |
0.00000000000020 | 0.00% | |
0.00000000001531 | 3.24% | |
0.4908 | -0.65% | |
0.5095 | -0.89% | |
0.00879 | -11.12% | |
0.002853 | 7.58% | |
2.809 | -4.91% | |
0.0070 | -12.50% | |
0.0649 | -0.15% | |
0.000079 | 33.90% | |
0.000600 | 0.00% | |
0.0000213 | -4.91% | |
0.002842 | 1.57% | |
0.00009002 | -2.29% | |
0.0417 | -6.71% | |
0.0413 | -7.19% | |
15.77 | -5.63% | |
0.00113 | 0.00% | |
0.0289 | -7.37% | |
0.000351 | 0.57% | |
0.2839 | -14.80% | |
0.0758 | -3.68% | |
0.0000010 | 150.00% | |
0.0000579 | -3.50% | |
0.0050 | -29.58% | |
0.0003604 | -5.48% | |
0.0777 | -11.80% | |
0.00000348 | -4.66% | |
1.248 | -5.60% | |
0.001013 | -5.68% | |
0.005978 | 55.64% | |
0.1444 | 0.77% | |
0.03362 | -5.48% | |
0.007999 | -19.60% | |
0.000000000001610 | 2.22% | |
0.0316 | -5.11% | |
1.257 | -1.80% | |
8.20 | -3.64% | |
0.17189 | -4.51% | |
0.2128 | -3.14% | |
0.1561 | -7.19% | |
0.0000000000000160 | -0.62% | |
0.04072 | -7.87% | |
0.0013 | 18.18% | |
0.02186 | -4.25% | |
0.01070 | 0.19% | |
0.01008 | -15.08% | |
0.00743 | -4.01% | |
0.00010000 | -21.26% | |
0.000000097 | -3.96% | |
0.5369 | -6.15% | |
0.0497 | 4.85% | |
6.066 | -4.53% | |
0.003505 | -3.63% | |
0.0006928 | -5.92% | |
0.0667 | -5.79% | |
0.05973 | -1.79% | |
0.1196 | -8.84% | |
0.000001606 | 1.01% | |
0.1071 | -6.38% | |
0.1128 | -1.23% | |
0.00225 | 0.00% | |
0.0110 | -5.98% | |
0.00002 | -60.00% | |
2.001 | -3.47% | |
0.002700 | 4.98% | |
0.000000000019 | 0.00% | |
0.001167 | -4.58% | |
0.0003489 | -4.12% | |
0.00000006 | 0.00% | |
0.0000032 | 10.34% | |
0.003939 | -0.08% | |
0.004203 | -0.80% | |
3.8900 | 0.00% | |
0.000820 | -6.07% | |
0.010200 | 0.99% | |
0.00173 | 13.82% | |
0.0002100 | -4.59% | |
0.000000000037 | -7.50% | |
0.00753 | -2.96% | |
0.1744 | -5.32% | |
0.00000000003658 | 2.75% | |
0.00000000000872 | 33.95% | |
0.00010999 | 80.10% | |
0.000057 | -3.39% | |
0.01215 | -11.64% | |
0.0000063 | -37.00% | |
0.05388 | -0.33% | |
0.000985 | -8.29% | |
0.000000000765 | 75.46% | |
0.4335 | -5.16% | |
0.0000061 | 281.25% | |
0.0001623 | 1.56% | |
0.03420 | -0.29% | |
0.001118 | -0.62% | |
0.0003495 | -12.63% | |
0.0422 | -3.21% | |
0.07887 | -2.49% | |
0.00063 | 800.00% | |
0.00002 | -75.00% | |
0.00004 | 0.00% | |
0.0030487 | -3.56% | |
0.001100 | -81.30% | |
50.0000 | 0.00% | |
0.02384 | -12.16% | |
0.0633 | -9.18% | |
0.0330 | -7.56% | |
0.00023 | -36.11% | |
0.02049 | 7.22% | |
0.000165 | -4.62% | |
0.02987 | -9.57% | |
0.0867 | -1.03% | |
0.3620 | -3.72% | |
4.56 | -7.13% | |
0.008231 | 0.00% | |
0.0000509 | 0.79% | |
0.00001 | 0.00% | |
0.0961 | -5.78% | |
0.0000082 | 70.83% | |
0.000000002031 | 26.07% | |
0.000914 | -3.99% | |
0.0528 | 1.93% | |
0.000001312 | -4.65% | |
0.000000000003920 | -16.40% | |
0.00404 | -7.34% | |
0.0008 | 60.00% | |
0.024504 | 0.00% | |
0.000000000572 | 36.84% | |
2.195 | -0.95% | |
0.02706 | -4.04% | |
0.0151 | 12.69% | |
0.0000194 | -37.42% | |
0.00238 | -4.03% | |
0.1627 | -9.36% | |
0.0084 | -1.18% | |
0.0007 | 0.00% | |
0.1003 | 0.30% | |
0.6998 | -0.01% | |
0.000019 | 0.00% | |
0.00008 | -38.46% | |
0.00004413 | -1.91% | |
0.00000103 | 3.00% | |
0.003352 | -8.54% | |
0.0001 | 0.00% | |
0.01713 | -4.46% | |
0.0009 | 0.00% | |
0.0773 | -4.09% | |
0.00000000015902 | 1.24% | |
0.00000000000098 | -2.00% | |
0.0271 | 0.00% | |
0.00000051 | 0.00% | |
0.000018 | 0.00% | |
1.72 | -28.33% | |
0.00010 | 42.86% | |
0.1201 | -8.74% | |
0.0000289 | -9.40% | |
0.00000011220 | -28.39% | |
0.00484 | -3.39% | |
0.0005665 | -6.05% | |
0.0002 | 0.00% | |
47.975 | -1.96% | |
0.3000 | -15.73% | |
1.035 | -6.67% | |
0.00000000000291 | 2.83% | |
0.00046 | -6.12% | |
0.004522 | -4.17% | |
0.0755 | -7.70% | |
0.000001955 | -0.76% | |
0.0000021 | -84.78% | |
0.000022 | -4.35% | |
0.00083 | -19.42% | |
0.0192 | 3.78% | |
0.00995 | -0.50% | |
0.001035 | 47.65% | |
0.000064 | 72.97% | |
0.000042 | 2.44% | |
0.0712 | -7.53% | |
0.6707 | -7.41% | |
0.2087 | -1.93% | |
0.000000000526 | 17.15% | |
0.000005 | -28.57% | |
0.0000001300 | 0.00% | |
0.001263 | 0.00% | |
0.0000119 | 0.00% | |
0.000190118 | -0.22% | |
0.0055 | -3.51% | |
0.000011 | 0.00% | |
0.0000000109 | 105.66% | |
0.000079 | 2.60% | |
0.00000011 | 37.50% | |
0.00004398 | 0.00% | |
0.0658 | -1.50% | |
1.0497 | -7.95% | |
0.01224 | -4.38% | |
0.5316 | -2.64% | |
0.0938 | -10.84% | |
0.01499 | -3.60% | |
0.09394 | -6.31% | |
0.2616 | -9.14% | |
0.410 | -2.61% | |
0.00012 | 0.00% | |
0.1020 | -2.86% | |
0.002130 | -0.98% | |
0.001253 | -4.93% | |
1.4113 | -7.81% | |
58.5600 | 0.00% | |
1.2918 | -7.33% | |
0.0001450 | 0.00% | |
0.0443 | -20.18% | |
0.02886 | -0.59% | |
17.720 | -3.19% | |
0.001773 | -9.40% | |
0.003238 | -9.33% | |
0.0006617 | -0.21% | |
0.003135 | -8.81% | |
0.00385 | 0.00% | |
0.0009012 | 0.00% | |
0.0003822 | -3.36% | |
0.001618 | -12.63% | |
0.0007993 | 0.00% | |
5.932 | 0.66% | |
0.0000329 | 0.00% | |
0.000027 | -6.90% | |
0.001189 | -15.25% | |
0.010569 | -4.96% | |
0.002586 | -10.27% | |
0.002229 | -7.01% | |
1899.00 | 0.00% | |
0.4167 | 0.31% | |
0.0970 | -0.72% | |
0.1049 | -18.11% | |
0.04211 | -9.13% | |
0.000114 | -6.56% | |
0.4825 | -10.43% | |
0.000743 | -2.49% | |
0.1252 | -4.72% | |
1.267 | 2.34% | |
0.0394 | 0.25% | |
0.00204 | -1.92% | |
0.000119 | 0.00% | |
0.0846 | 8.74% | |
0.00000282 | -4.08% | |
0.00975 | -0.31% | |
2.73 | -7.77% | |
0.539 | -7.86% | |
1.000000 | 0.00% | |
0.1695 | -2.25% | |
0.3771 | 0.00% | |
0.5732 | 0.00% | |
1.788 | -1.32% | |
2.626 | -3.92% | |
0.0513 | -3.93% | |
0.000000049 | -51.00% | |
0.0001320 | 0.00% | |
0.1289 | -5.77% | |
0.06843 | -3.25% | |
0.615 | -6.53% | |
0.6479 | -5.22% | |
0.0700 | 0.00% | |
0.000000000003 | 0.00% | |
0.001097 | -3.01% | |
0.00000080 | 0.00% | |
0.1602 | -5.54% | |
0.000216 | 0.00% | |
0.0000000030210 | 0.00% | |
1.5000 | 0.00% | |
3.9889 | 0.00% | |
1.1371 | 0.00% | |
0.4424 | 0.00% | |
0.0372 | -5.82% | |
0.000370 | -2.37% | |
0.0071 | 0.00% | |
0.01532 | -5.14% | |
0.000210 | 0.00% | |
1.364 | -1.87% | |
0.00777 | -2.39% | |
0.1487 | -3.06% | |
6.60 | -5.71% | |
0.0403 | -5.84% | |
0.000452 | 0.00% | |
0.230000 | 0.00% | |
0.000000002389 | -1.20% | |
0.00000041 | -4.65% | |
0.1204 | 0.00% | |
0.004000 | 0.00% | |
0.000300 | 0.00% | |
0.00035 | 0.00% | |
0.000000039 | 0.00% | |
0.0005 | 0.00% | |
0.00033 | 0.00% | |
0.011926 | 0.00% | |
0.0000192 | 0.00% | |
0.001100 | 0.00% | |
0.000365 | 0.00% | |
0.001201 | 0.00% | |
0.0063 | 0.00% | |
0.0000002593 | 0.00% | |
0.00001584 | 0.00% | |
0.000091 | 0.00% | |
0.0000001013 | 0.00% | |
0.00030000 | 0.00% | |
0.00005 | 0.00% | |
0.00006187 | 0.00% | |
0.000077 | 0.00% | |
0.001405 | 0.00% | |
0.2459 | -0.12% | |
0.000902 | 0.00% | |
0.0228 | 3.64% | |
0.000000000776 | 2.65% | |
0.0001 | 0.00% | |
0.0009 | 0.00% | |
0.0560 | 0.00% | |
0.000451 | 0.89% | |
0.004025 | 0.00% | |
0.00000000053 | -1.85% | |
0.0120 | 1.69% | |
0.0000000104 | 0.00% | |
0.00000000001605 | 0.00% | |
0.001000 | 0.00% | |
0.0000000045 | 0.00% | |
0.00001626 | 0.00% | |
0.000000000375 | 0.00% | |
0.00024 | -4.00% | |
0.000000008400 | 0.00% | |
0.0000002144 | 0.19% | |
0.000427 | 0.00% | |
0.0063 | 0.00% | |
0.000310 | 0.00% | |
0.3284 | 0.00% | |
0.9900 | 0.00% | |
0.000405 | 0.00% | |
-- | -- | |
0.00000000000101 | 0.00% | |
0.001290 | 0.00% | |
0.00000000000426 | -1.16% | |
0.00000011 | 0.00% | |
0.0000006650 | 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% | |
0.00000000002387 | 0.00% | |
0.00425 | 0.00% | |
0.000118 | 0.00% | |
0.0010 | 0.00% | |
0.00037 | 0.00% | |
0.001963 | 0.00% | |
0.00000055 | 0.00% | |
0.2993 | 0.00% | |
0.00006767 | 0.00% | |
0.0027 | 0.00% | |
0.00005458 | 0.00% | |
0.00280 | 0.00% | |
0.001210 | 0.00% | |
0.00171 | 0.00% | |
0.0195 | 0.00% | |
0.0001000 | 0.00% | |
0.000000000101 | -12.17% | |
0.05056 | 0.00% | |
1.3575 | 0.00% | |
0.00136 | 0.00% | |
0.000092 | 0.00% | |
0.000033 | 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% | |
0.9990 | 0.00% | |
0.0000111 | 0.00% | |
0.000363 | 0.00% | |
0.0012 | 0.00% | |
0.000808 | 0.00% | |
0.001200 | 0.00% | |
0.000100 | 0.00% | |
0.001050 | 0.00% | |
0.000383 | 0.00% | |
0.01590 | 0.00% | |
0.001000 | 0.00% | |
0.0006 | 0.00% | |
0.0786 | 0.00% | |
0.001563 | 0.00% | |
1.6349 | 0.00% | |
0.001791 | 0.00% | |
0.00000000000540 | 0.00% | |
0.000028 | 0.00% | |
0.000999 | 0.00% | |
0.001801 | 0.00% | |
0.000365 | 0.00% | |
0.0200 | 0.00% | |
0.0093 | 0.00% | |
0.0006 | 0.00% | |
65.1101 | 0.00% | |
3.7189 | 0.00% | |
0.000082 | 0.00% | |
0.016111 | 0.00% | |
4.1000 | 0.00% | |
0.0489 | 0.00% | |
0.0131 | 0.00% | |
0.0013 | 0.00% | |
4.4022 | 0.00% | |
0.0745 | 0.00% | |
0.001120 | 0.00% | |
0.3882 | 0.00% | |
0.001000 | 0.00% | |
0.076250 | 0.00% | |
0.0150 | 0.00% | |
0.002500 | 0.00% | |
0.0036 | 0.00% | |
0.001969 | 0.77% | |
0.1769 | 0.00% | |
2.2915 | 0.00% | |
0.0000000200 | -0.50% | |
0.0005 | 0.00% | |
0.000258 | 0.00% | |
0.000632 | 0.00% | |
0.03000 | 0.00% | |
0.000946 | 0.00% | |
0.0002031 | 0.00% | |
0.4820 | 0.00% | |
0.0490 | 0.00% | |
0.0096 | 0.00% | |
2.1111 | 0.00% | |
0.0060 | 0.00% | |
0.04306 | -0.28% | |
0.0550 | 0.00% | |
0.004258 | 2.18% | |
8.4900 | 0.00% | |
1.76670591 | 0.00% | |
0.0024 | 0.00% | |
0.0048 | 0.00% | |
0.000399 | 0.00% | |
0.0001702 | 0.00% | |
0.0000000000270 | 0.00% | |
0.0000002850 | 0.00% | |
0.6700 | 0.00% | |
0.00011 | 0.00% | |
0.0864 | 0.00% | |
0.000835 | 0.00% | |
0.0102 | 0.00% | |
0.00006 | 0.00% | |
0.01989 | 0.00% | |
0.0017 | 0.00% | |
0.0014 | 0.00% | |
0.2888 | 0.00% | |
0.00501 | 0.00% | |
0.02700 | 0.00% | |
0.00294 | 0.00% | |
0.0650 | 0.00% | |
0.3515 | 0.00% | |
0.00125 | 0.00% | |
0.000446 | 0.00% | |
0.4900 | 0.00% | |
0.000062 | 0.00% | |
1.0100 | 0.00% | |
0.5000 | 0.00% | |
0.0069 | 0.00% | |
0.88686 | 0.00% | |
0.00077 | 0.00% | |
0.05578 | 0.00% | |
1.1760 | 0.00% | |
0.000561 | 0.00% | |
0.1725 | 0.00% | |
0.03786 | 0.00% | |
0.01463 | 0.00% | |
0.01324 | -3.85% | |
0.0000076 | -13.64% | |
0.00614 | 0.00% | |
0.4606 | 0.00% | |
0.00021 | 0.00% | |
0.001800 | 0.00% | |
0.00126 | 0.00% | |
0.01200 | 0.00% | |
0.000001000 | 0.00% | |
0.0000008 | 0.00% | |
1.3374 | 2.10% | |
0.00390 | 0.00% | |
0.0000325 | 0.00% | |
0.017744 | 0.00% | |
1.0000 | 0.00% | |
0.34211 | 0.00% | |
0.00130 | 0.00% | |
0.0000077 | 0.00% | |
0.1195 | 0.00% | |
0.00146 | 0.00% | |
0.001277 | 0.00% | |
0.03520 | 0.00% | |
0.0000023 | 0.00% | |
0.000000005 | 0.00% | |
0.001518 | 0.00% | |
0.00083 | 0.00% | |
0.000313 | 0.00% | |
0.0007000 | 0.00% | |
0.00011 | 0.00% | |
0.00200 | 0.00% | |
0.0032 | 0.00% | |
0.3905 | 0.00% | |
0.000495 | 0.00% | |
0.249 | 0.00% | |
0.00041 | 0.00% | |
0.00013699 | 0.00% | |
0.002563 | 0.00% | |
0.00625 | 0.00% | |
0.0900 | 0.00% | |
0.00006 | 0.00% | |
0.000000000009 | 0.00% | |
0.000700 | 0.00% | |
0.01030 | 0.00% | |
3.7449 | 0.00% | |
0.00070 | 0.00% | |
0.003000 | 0.00% | |
0.000310 | 0.00% | |
450.00 | 0.00% | |
0.0000269 | 0.00% | |
0.0000000500 | 0.00% | |
0.000602 | 0.00% | |
0.000000000129 | 0.00% | |
0.000426832 | 0.00% | |
0.000002400 | 0.00% | |
0.00002801 | 0.00% | |
0.00776 | 0.00% | |
0.0810 | 0.00% | |
0.0000245 | 0.00% | |
0.1197 | 0.00% | |
0.00056 | 0.00% | |
0.000510 | 0.00% | |
0.00218 | 0.00% | |
0.002100 | 0.00% | |
0.00170 | 0.00% | |
0.0620 | 0.00% | |
0.000055 | 0.00% | |
0.3101 | 0.00% | |
0.0000211 | 0.00% | |
0.00755 | -0.13% | |
0.4400 | 0.00% | |
1.4371 | 0.00% | |
0.0000259 | 0.00% | |
0.00625 | 0.00% | |
0.6000 | 0.00% | |
0.250 | 0.00% | |
0.001106 | 0.00% | |
0.0249 | 0.00% | |
0.6608 | 0.00% | |
0.0503 | -6.33% | |
0.000000000800 | -4.19% | |
0.00500 | 0.00% | |
3.58 | 0.00% | |
0.0020 | 0.00% | |
0.00538 | 0.00% | |
0.02592 | -4.28% | |
0.4259 | 0.07% | |
0.304 | -4.10% | |
0.000000001868 | 0.00% | |
0.0018 | 0.00% | |
5155.00 | 0.00% | |
0.0091 | 0.00% | |
0.0299 | -3.86% |