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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0.0085 | -4.49% | |
0.00450 | 0.00% | |
0.0008830 | -3.81% | |
0.00152 | 0.00% | |
1.416 | 5.12% | |
0.0598 | -4.01% | |
0.02197 | 15.51% | |
0.509 | -7.45% | |
0.000119 | 0.00% | |
0.00280 | -5.08% | |
0.008089 | 0.16% | |
0.476 | -5.93% | |
0.2663 | -2.74% | |
0.00039099 | 0.00% | |
0.000853 | 1.07% | |
0.01513 | -7.52% | |
6.29 | -12.40% | |
0.1610 | -11.59% | |
0.02045 | -6.79% | |
0.1894 | -5.82% | |
0.1600 | -3.03% | |
0.1134 | 0.27% | |
0.5800 | 28.43% | |
1.7628 | 0.00% | |
0.01040 | -7.31% | |
0.002705 | -9.50% | |
0.00724 | -0.69% | |
2.7269 | 1.61% | |
0.013814 | -0.83% | |
3114.46 | 0.38% | |
0.0000430 | -16.99% | |
0.00579 | -10.65% | |
0.002510 | -10.99% | |
0.00219 | 0.00% | |
18.2327 | -2.71% | |
0.9245 | -10.29% | |
0.0000000001863 | -3.97% | |
0.004099 | -8.42% | |
0.01596 | -8.43% | |
0.00006723 | -0.36% | |
0.000000437 | -13.98% | |
0.000360 | -2.44% | |
0.00005956 | -4.11% | |
0.005008 | 0.60% | |
0.1840 | -8.32% | |
0.6862 | 1.00% | |
0.008000 | 12.76% | |
7.8237 | -6.80% | |
0.013642 | -0.12% | |
0.1723 | -6.10% | |
0.00001149 | -4.96% | |
0.01096 | -4.70% | |
0.5823 | -4.59% | |
0.05846 | 3.30% | |
0.000203037 | 1.61% | |
0.00914 | -1.51% | |
0.4613 | -8.44% | |
0.000387 | 0.78% | |
0.00175 | -9.79% | |
2.624 | -8.32% | |
0.002738 | 5.63% | |
0.004044 | 3.85% | |
0.0004373 | 8.19% | |
0.0001965 | -10.27% | |
1.033 | -17.09% | |
0.0516 | -5.84% | |
0.005515 | -33.62% | |
0.00319329 | -6.34% | |
0.018552 | 23.68% | |
0.063025 | -1.97% | |
0.007774 | 1.21% | |
0.000841 | 6.59% | |
0.01469 | 0.27% | |
0.06705 | 6.33% | |
0.1727 | -5.73% | |
0.0029970 | -0.70% | |
0.0000135 | -18.18% | |
2.392 | -13.83% | |
0.002228 | 90.26% | |
0.8599 | -3.26% | |
0.002447 | 32.84% | |
0.000742 | 5.70% | |
0.752 | -8.96% | |
0.002048 | 2.40% | |
0.001501 | -4.64% | |
0.0112 | 2.75% | |
0.05575 | -3.95% | |
14.62 | -18.10% | |
1.0713 | -3.81% | |
0.3612 | -5.35% | |
0.0315 | -7.89% | |
0.0041 | -2.38% | |
0.309 | -7.21% | |
0.000288 | -14.29% | |
0.00455 | 1.11% | |
0.00001491 | -15.57% | |
0.00208 | -8.77% | |
0.015212 | -1.71% | |
0.00843 | -4.31% | |
0.002939 | -4.58% | |
0.00000014042 | -5.54% | |
7.27 | -4.84% | |
0.006455 | -6.16% | |
0.0666 | -5.26% | |
0.21875 | -13.76% | |
0.000297 | -1.66% | |
0.6460 | -6.02% | |
0.01146 | -4.26% | |
0.01694 | -2.36% | |
0.02765 | -6.37% | |
0.410 | -3.76% | |
0.004186 | 19.09% | |
0.01201 | -4.91% | |
0.773 | -7.09% | |
0.0112 | -50.88% | |
0.01247 | 4.35% | |
0.0000238 | -0.83% | |
0.004824 | -9.60% | |
0.000000000237 | -0.42% | |
0.002303 | -8.32% | |
0.003872 | 18.48% | |
0.000224 | 7.69% | |
0.0002941 | -7.83% | |
0.001811 | -1.52% | |
16.66 | -2.00% | |
0.001649 | -9.15% | |
0.7442 | -24.60% | |
0.554 | -4.32% | |
0.00782 | -13.11% | |
0.478 | -4.59% | |
0.003440 | -3.21% | |
0.2026 | -8.98% | |
0.0000000405 | 11.88% | |
0.3679 | -8.51% | |
0.0000016715 | 0.75% | |
0.0479 | -2.64% | |
0.880 | -4.76% | |
0.0038 | -44.12% | |
0.00101 | -33.11% | |
0.00000003315 | -4.44% | |
0.85104 | -0.39% | |
0.000508 | -0.20% | |
0.001578 | -10.70% | |
0.001615 | -6.16% | |
0.3472 | 1.76% | |
0.0006030 | -1.68% | |
0.0420 | -4.33% | |
0.002032 | -7.43% | |
0.1664 | -5.35% | |
1981.78 | -2.80% | |
0.00003342 | -1.53% | |
0.0062 | 1.64% | |
0.1229 | -6.11% | |
0.0001760 | -25.01% | |
0.00153 | -10.00% | |
0.0003127 | -24.05% | |
17.73 | 5.47% | |
0.000506 | -30.01% | |
27.27 | -2.82% | |
0.001173 | -13.05% | |
5.305 | -1.87% | |
0.4114 | -3.72% | |
0.00000001175 | -1.43% | |
2.514 | -5.88% | |
4.726 | -6.21% | |
0.04743 | -8.24% | |
0.0258 | -3.73% | |
0.00233 | -2.92% | |
0.00000419 | -4.99% | |
0.03569 | -2.54% | |
0.3000 | -17.81% | |
0.2707 | -4.24% | |
0.0901 | -5.36% | |
0.07642 | -6.01% | |
0.1929 | -1.78% | |
0.01363 | -9.19% | |
0.000093 | -3.13% | |
0.0000550 | -2.48% | |
0.0000000903 | -0.66% | |
0.03687 | -11.33% | |
0.55363 | -5.44% | |
0.0002026 | -12.14% | |
0.03230 | -0.22% | |
0.001693 | -13.58% | |
0.031124 | 5.94% | |
0.01099 | 2.52% | |
0.0000002925 | 7.34% | |
0.01464 | -9.96% | |
0.0002448 | -8.25% | |
0.6603 | -5.85% | |
0.001321 | 5.34% | |
0.02282 | -5.90% | |
1.6882 | 8.25% | |
0.0731 | -5.19% | |
0.003897 | -4.01% | |
0.01809 | -2.06% | |
0.10800 | -8.55% | |
0.011987 | 0.01% | |
0.0007870 | 8.33% | |
0.0151 | -4.43% | |
1.741 | -6.25% | |
0.0860 | -5.70% | |
1.956 | -4.16% | |
0.1435 | -6.70% | |
0.2433 | -7.00% | |
0.000891 | -15.70% | |
0.01200 | -8.12% | |
0.447 | -4.89% | |
0.781 | -6.47% | |
0.2490 | -5.25% | |
0.0000464 | -3.33% | |
2.174 | -0.59% | |
0.00597 | -7.59% | |
0.02655 | -4.19% | |
0.1217 | -7.80% | |
0.1964 | -16.92% | |
0.592 | -6.18% | |
0.2458 | -3.04% | |
0.237 | -5.58% | |
0.00000000008471 | -11.48% | |
0.000246 | 28.80% | |
0.0207 | -11.16% | |
0.006002 | 3.27% | |
0.0000002629 | 2.06% | |
0.01886 | -10.53% | |
0.00000001640 | -2.55% | |
0.0615 | -5.67% | |
0.03352 | -8.47% | |
0.3119 | -14.05% | |
0.0157 | -8.19% | |
6.37 | -5.49% | |
0.02310 | -0.35% | |
0.0004091 | -19.04% | |
0.2685 | -4.58% | |
0.001134 | -3.65% | |
0.003051 | 4.20% | |
0.00932 | -4.61% | |
0.01392 | -10.83% | |
0.003941 | -0.53% | |
0.002949 | -14.55% | |
15.94 | -4.21% | |
0.01332 | -2.63% | |
0.004598 | -5.88% | |
0.537 | -7.57% | |
0.0646 | -0.77% | |
0.1044 | -7.94% | |
0.0000000000000139 | -4.79% | |
0.000001502 | -1.83% | |
305.8 | -0.78% | |
0.0003488 | 2.08% | |
0.1059 | -8.07% | |
0.2978 | -10.33% | |
0.0620 | -1.27% | |
0.0781 | -4.99% | |
1.826 | 2.82% | |
0.0000578 | -10.94% | |
0.01142 | -2.73% | |
0.7614 | -0.01% | |
2.117 | -3.64% | |
0.00000001258 | -6.54% | |
0.003002 | -10.04% | |
0.002231 | -1.24% | |
0.0000259 | -1.52% | |
0.05035 | -5.16% | |
0.012252 | -1.09% | |
2.945 | -5.64% | |
0.00030000 | 0.00% | |
0.1873 | -3.65% | |
8.30 | -5.47% | |
0.00622 | -30.89% | |
0.001558 | -4.65% | |
0.00000000001071 | -9.16% | |
0.1182 | -9.01% | |
0.000303 | 14.77% | |
0.0051015 | -0.06% | |
0.00097 | 4.30% | |
0.0101 | 3.06% | |
0.0002890 | -7.10% | |
0.0000089 | -4.30% | |
0.1031 | -28.25% | |
0.004212 | -8.47% | |
0.0612 | -1.13% | |
0.0171 | -50.86% | |
0.1221 | -11.46% | |
0.00000653 | -9.81% | |
0.0136 | -8.11% | |
0.000284 | 1.07% | |
0.0003561 | -9.44% | |
0.0104 | 8.33% | |
0.09162 | -7.40% | |
0.01541 | -7.45% | |
0.00998 | -5.40% | |
0.003219 | -9.96% | |
0.001099 | 6.29% | |
0.0051 | 13.33% | |
0.002500 | 1.01% | |
16.01 | -4.65% | |
0.0864 | 44.00% | |
0.02928 | -14.01% | |
0.006101 | -7.22% | |
0.0519 | -1.52% | |
0.2624 | -6.98% | |
0.001014 | -5.14% | |
0.00420 | 1.94% | |
39.64 | -3.86% | |
0.02665 | -12.79% | |
0.7280 | 0.50% | |
0.0005480 | -1.63% | |
0.00002875 | 7.52% | |
0.001336 | -5.65% | |
0.002394 | -16.41% | |
0.0000000462 | -2.53% | |
0.017744 | -2.63% | |
0.0098 | -2.00% | |
0.380 | -4.28% | |
69.2 | -4.68% | |
0.0000021 | 0.00% | |
0.0002635 | -7.80% | |
0.4713 | -5.53% | |
0.02840 | 373.33% | |
0.002958 | -14.51% | |
0.0000591 | -3.27% | |
0.2573 | 1.86% | |
0.0000000743 | -1.07% | |
0.006500 | -2.99% | |
0.1300 | -3.99% | |
0.0484 | -9.87% | |
0.004731 | 4.76% | |
4.360 | -4.93% | |
0.0096 | -2.04% | |
0.01263 | -9.14% | |
0.005431 | -4.82% | |
0.00126 | -3.82% | |
6.2310 | -0.90% | |
13.35 | -4.23% | |
0.00757 | -5.49% | |
0.0564 | -15.19% | |
1342 | -6.09% | |
0.1732 | -6.93% | |
0.010826 | -5.61% | |
0.0575 | -7.85% | |
0.2470 | -12.29% | |
0.0005530 | -11.84% | |
0.0000031 | -11.43% | |
0.1258 | -9.30% | |
56.15 | -20.79% | |
0.0887 | -3.27% | |
0.0832 | -4.59% | |
0.1099 | -7.34% | |
0.1502 | -6.01% | |
0.1085 | -4.49% | |
0.06006 | -15.76% | |
0.008899 | 5.93% | |
0.2782 | -5.82% | |
19.19 | -9.31% | |
0.004521 | -10.49% | |
0.000635 | -12.41% | |
0.018559 | -9.74% | |
0.03539 | -1.48% | |
0.2500 | -7.20% | |
0.04051 | -11.82% | |
0.002844 | -5.45% | |
0.00769 | -6.11% | |
0.0000000124 | -17.33% | |
0.01134 | -5.66% | |
0.0004279 | 7.92% | |
0.5461 | -4.13% | |
15.33 | -7.43% | |
0.2991 | -13.80% | |
1.196 | -5.53% | |
0.2455 | -6.26% | |
0.000345 | -4.43% | |
0.000600 | -7.69% | |
0.2111 | -3.52% | |
0.000168 | -3.45% | |
0.001714 | -6.80% | |
145.58 | -1.77% | |
0.000936 | -4.39% | |
0.4234 | -3.05% | |
0.01453 | -11.73% | |
0.3313 | -5.29% | |
0.00000226 | -21.25% | |
0.001662 | -10.36% | |
0.0000008 | 14.29% | |
0.003371 | -7.69% | |
0.655 | -13.59% | |
101.67 | 0.95% | |
0.1866 | -2.35% | |
0.0006753 | 1.14% | |
0.00977 | -6.06% | |
0.0984 | -3.24% | |
0.0004000 | -5.03% | |
0.0004912 | 3.58% | |
0.00000000155 | 8.39% | |
0.00000724 | 0.00% | |
0.01124 | -4.50% | |
0.005694 | -10.12% | |
0.0779 | 1.30% | |
5.47 | -7.45% | |
0.04583 | 10.49% | |
0.0000551 | 24.66% | |
0.000676 | 3.84% | |
0.000002073 | -14.62% | |
0.1599 | -4.82% | |
0.0150 | -8.54% | |
0.0232 | -2.11% | |
11.12 | -2.71% | |
0.000816 | 0.12% | |
0.3393 | -5.17% | |
0.706 | -3.81% | |
12.78 | -2.96% | |
0.1968 | -4.42% | |
0.00710 | -3.53% | |
0.002350 | -11.32% | |
0.000527 | -4.53% | |
0.8059 | -1.23% | |
0.000000001300 | -13.16% | |
0.002634 | -6.20% | |
0.04511 | -0.66% | |
0.885 | -7.62% | |
0.1063 | -10.07% | |
0.0000000624 | -2.35% | |
0.002434 | -25.38% | |
0.1077 | -7.08% | |
0.1890 | -0.58% | |
0.2612 | -6.98% | |
0.0225 | -5.06% | |
0.01127 | -2.59% | |
0.01456 | -8.60% | |
1.3114 | -6.32% | |
0.04130 | -1.43% | |
0.0012 | 100.00% | |
0.655 | -3.39% | |
0.00692 | -1.42% | |
1.337 | -3.19% | |
0.0860 | -6.11% | |
0.01400 | -11.56% | |
0.003864 | -6.40% | |
0.000000000000819 | 1.11% | |
0.667 | -6.19% | |
0.1777 | -3.42% | |
0.000412 | 0.49% | |
0.00003 | 50.00% | |
0.00490 | -5.59% | |
0.002243 | -7.66% | |
22.380 | -2.39% | |
0.000018 | -65.38% | |
5.604 | -5.29% | |
0.8335 | 0.28% | |
0.0304 | -3.49% | |
0.00000000000021 | 16.67% | |
0.5402 | -2.07% | |
0.0752 | -4.93% | |
16.42 | -3.35% | |
0.6793 | -7.94% | |
0.0809 | -4.94% | |
0.00225 | 14.80% | |
0.590 | -4.38% | |
0.00031 | -3.13% | |
0.0000565 | -9.31% | |
2.126 | -6.47% | |
0.02476 | -15.00% | |
0.00008786 | -2.04% | |
0.002582 | -4.83% | |
0.750 | 0.00% | |
0.1157 | -5.24% | |
0.0419 | -6.47% | |
0.00000000000014 | 0.00% | |
0.310 | -3.73% | |
0.2135 | -6.65% | |
0.0506 | -6.81% | |
0.00009121 | -2.84% | |
0.00002238 | -3.37% | |
0.00000000001295 | -2.41% | |
0.000009 | -18.18% | |
0.03676 | -2.65% | |
0.00000000000039 | -2.50% | |
0.00000014000 | -51.69% | |
0.0000213 | -4.91% | |
0.0074 | -10.84% | |
0.0000061 | 10.91% | |
0.001018 | -4.23% | |
0.5141 | -2.63% | |
2.843 | -3.76% | |
0.2040 | -4.54% | |
0.000000000004690 | 0.02% | |
0.01234 | -3.59% | |
6.196 | -4.85% | |
0.000840 | -0.83% | |
0.00020 | -20.00% | |
0.0000080 | -6.98% | |
0.000600 | 0.00% | |
0.0679 | -5.17% | |
0.00867 | -12.69% | |
0.00113 | 0.00% | |
0.2979 | -10.73% | |
0.005978 | 11.14% | |
0.0768 | -2.78% | |
0.000351 | 0.86% | |
0.000000000001584 | -14.10% | |
0.03910 | -6.59% | |
0.0000579 | -13.58% | |
0.0050 | -29.58% | |
0.0003675 | -7.01% | |
0.000024 | 0.00% | |
0.000058 | -1.69% | |
0.000000097 | -7.62% | |
0.1206 | -8.57% | |
0.00000861 | 3.61% | |
0.001602 | 0.25% | |
0.0289 | -8.25% | |
1.251 | -3.55% | |
8.34 | -2.00% | |
0.00002010 | -0.84% | |
0.00609 | -2.25% | |
0.4868 | -3.68% | |
0.0013 | 8.33% | |
0.04498 | -14.58% | |
0.00000000000235 | 12.44% | |
0.000074 | 25.42% | |
0.000000000449 | -15.76% | |
1.254 | -6.07% | |
0.000013 | -48.00% | |
0.2167 | 3.04% | |
0.02182 | -5.42% | |
0.00030 | -3.23% | |
0.1424 | -1.86% | |
0.0528 | -5.04% | |
0.2125 | -4.41% | |
0.17875 | -0.86% | |
0.0000000000000165 | -3.51% | |
0.05401 | 1.98% | |
0.0431 | -2.05% | |
0.05973 | -0.38% | |
0.0531 | 3.31% | |
0.1232 | -9.21% | |
0.001100 | -47.59% | |
0.1128 | -1.40% | |
0.0007 | 0.00% | |
0.003501 | -3.74% | |
0.0115 | 0.00% | |
0.004188 | -0.24% | |
0.002700 | 5.02% | |
0.000000000019 | 0.00% | |
0.01069 | 0.09% | |
0.0000032 | 10.34% | |
3.8900 | 54.80% | |
0.000000000003 | -40.00% | |
0.000833 | -9.06% | |
0.010200 | 0.99% | |
4.60 | -7.63% | |
0.0002100 | -4.59% | |
0.00753 | -1.95% | |
0.0317 | -5.09% | |
0.00000000003622 | 5.44% | |
0.00000000000872 | 33.95% | |
0.00010999 | 80.10% | |
0.1875 | -5.16% | |
0.000000000765 | 1.59% | |
0.0000071 | -29.00% | |
0.002499 | 20.03% | |
0.00000354 | -6.10% | |
0.4380 | -2.90% | |
0.0000004 | -60.00% | |
0.0660 | -5.44% | |
0.0001623 | 1.56% | |
0.003866 | -7.02% | |
0.0003495 | -12.63% | |
0.03420 | -0.29% | |
0.000001671 | 5.09% | |
0.001120 | -2.95% | |
0.03372 | 0.03% | |
0.07925 | -0.78% | |
50.0000 | 0.00% | |
0.00000000001940 | 0.26% | |
0.0650 | -8.19% | |
0.0342 | -4.74% | |
0.00023 | -36.11% | |
0.02005 | 1.98% | |
0.000000001696 | -1.85% | |
0.0875 | -4.37% | |
0.3579 | -4.05% | |
0.001022 | -4.93% | |
0.00000051 | -1.92% | |
0.00248 | -9.82% | |
0.000000002017 | -5.57% | |
0.550 | -1.43% | |
0.000092 | 0.00% | |
0.008231 | 0.00% | |
0.0000509 | 0.79% | |
0.00006 | -14.29% | |
0.0985 | -4.18% | |
0.024504 | 0.00% | |
0.0000055 | 14.58% | |
0.000001317 | -3.94% | |
0.000937 | -2.80% | |
0.000000000790 | 6.18% | |
0.00410 | -6.39% | |
0.0008 | 60.00% | |
0.000000000573 | 37.08% | |
0.1662 | -8.78% | |
1.384 | -0.93% | |
0.0943 | -6.82% | |
0.000000000009 | 0.00% | |
0.00510 | 0.00% | |
0.0006895 | -6.80% | |
0.001791 | 0.06% | |
0.0019267 | -9.32% | |
0.00000006 | 0.00% | |
17.325 | -3.21% | |
0.0084 | 27.27% | |
0.1009 | -2.32% | |
0.6998 | -0.01% | |
0.000019 | 0.00% | |
0.001518 | -23.60% | |
0.0946 | -9.39% | |
0.00000103 | 3.00% | |
0.00008 | -38.46% | |
0.003463 | -11.50% | |
0.01730 | -4.63% | |
0.0009 | 0.00% | |
1.73 | -27.92% | |
0.00004 | -20.00% | |
0.01512 | -3.57% | |
0.00000000000101 | 1.00% | |
0.0271 | -0.37% | |
0.000018 | -28.00% | |
0.0001450 | 0.00% | |
0.001927 | -7.36% | |
0.00010 | 42.86% | |
0.9900 | 0.00% | |
0.0063 | -1.56% | |
0.0000345 | 8.49% | |
0.00000011220 | -28.39% | |
0.0005780 | -5.60% | |
0.0002 | -50.00% | |
0.0000002124 | -6.14% | |
0.000000000040 | -42.03% | |
1.045 | -6.86% | |
0.0192 | -45.30% | |
0.00046 | -6.12% | |
0.00000000000287 | 0.35% | |
0.0765 | -8.16% | |
0.001994 | -10.46% | |
0.0000021 | -84.78% | |
0.00000285 | -3.72% | |
0.00000000000423 | -1.40% | |
0.00083 | -19.42% | |
0.0000000204 | -0.97% | |
0.0001320 | 28.16% | |
0.00995 | -0.50% | |
0.001035 | 47.65% | |
0.000064 | 72.97% | |
0.00000000054 | 1.89% | |
0.000042 | 2.44% | |
0.0727 | -7.74% | |
0.000000000112 | 0.90% | |
0.0195 | 82.24% | |
0.0000001300 | 0.00% | |
0.001263 | 0.00% | |
0.0055 | -3.51% | |
0.000011 | 0.00% | |
0.0000000109 | 105.66% | |
0.000258 | 0.39% | |
0.000079 | 2.60% | |
0.00000011 | 37.50% | |
0.00004398 | 0.00% | |
0.0663 | 3.43% | |
0.01748 | -7.46% | |
0.000709 | -4.70% | |
1.1074 | -1.56% | |
0.5388 | -0.48% | |
0.09345 | -2.99% | |
0.00013 | 8.33% | |
0.000883 | -14.93% | |
0.001296 | 1.33% | |
1.4337 | -8.34% | |
58.5600 | 0.00% | |
0.00004313 | -2.51% | |
0.0459 | -16.39% | |
0.002101 | -5.53% | |
0.02905 | -0.45% | |
0.001799 | -7.60% | |
0.0006691 | 2.20% | |
0.003173 | -8.06% | |
0.00385 | 0.00% | |
0.0009012 | 0.00% | |
0.0000119 | 0.00% | |
0.0003988 | 0.61% | |
0.0007993 | 0.00% | |
5.938 | -2.54% | |
0.0000329 | 0.00% | |
0.003398 | 6.65% | |
0.000027 | 3.85% | |
0.011079 | 3.71% | |
0.002554 | -13.57% | |
0.002272 | -6.92% | |
1899.00 | 0.00% | |
0.4084 | -1.23% | |
0.1159 | -11.66% | |
0.04273 | -9.93% | |
0.000114 | -5.79% | |
0.4897 | -10.82% | |
0.000760 | 3.26% | |
0.1297 | -8.66% | |
0.000001969 | 3.63% | |
1.262 | -1.02% | |
0.0399 | 1.27% | |
0.001141 | -6.40% | |
0.02741 | -2.35% | |
0.00210 | 0.96% | |
0.000119 | 0.00% | |
0.0819 | 5.81% | |
0.00970 | -0.51% | |
2.80 | -6.67% | |
1.000000 | 0.00% | |
0.1700 | -2.97% | |
0.3771 | 0.00% | |
0.549 | -7.26% | |
0.5732 | 0.00% | |
48.532 | -0.23% | |
1.783 | -1.76% | |
2.658 | -2.85% | |
0.000000038 | -62.00% | |
0.1315 | -5.40% | |
0.06916 | -2.87% | |
0.640 | -3.18% | |
0.6427 | -4.98% | |
0.0700 | 0.00% | |
0.00000000015708 | 0.00% | |
0.001110 | -2.97% | |
0.00000080 | 0.00% | |
0.1642 | -4.09% | |
0.000216 | 0.00% | |
0.0000000030210 | 0.00% | |
1.412 | -7.77% | |
1.5000 | 0.00% | |
3.9889 | 0.00% | |
1.1371 | 0.00% | |
0.4424 | 0.00% | |
0.2156 | 0.37% | |
0.0381 | -5.22% | |
0.000375 | -0.53% | |
0.0071 | 0.00% | |
0.01550 | -3.61% | |
0.000210 | 0.00% | |
0.00781 | -1.76% | |
2.010 | -4.69% | |
0.1517 | -3.56% | |
6.72 | -4.82% | |
0.0411 | -4.86% | |
0.000452 | 0.00% | |
0.230000 | 0.00% | |
0.000000002360 | -2.36% | |
0.000188227 | -1.71% | |
0.00000042 | 0.00% | |
0.1204 | 0.00% | |
2.736 | 3.01% | |
1.032 | -1.99% | |
0.004000 | 0.00% | |
0.000300 | 0.00% | |
0.0023 | 0.00% | |
0.00035 | 0.00% | |
0.0112 | 0.00% | |
0.000000040 | 2.56% | |
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% | |
0.0000002593 | 0.00% | |
0.000007 | 0.00% | |
0.00001584 | 0.00% | |
0.000091 | 0.00% | |
0.0000001013 | 0.00% | |
0.00005 | 0.00% | |
0.00006187 | 0.00% | |
0.000077 | 0.00% | |
0.001405 | 0.00% | |
0.2473 | 0.32% | |
0.000902 | 0.00% | |
0.0230 | 1.32% | |
0.000000000734 | -0.81% | |
0.0001 | 0.00% | |
0.0009 | 0.00% | |
0.0560 | 0.00% | |
0.00012800 | 37.63% | |
0.000451 | -0.22% | |
0.004025 | 0.00% | |
0.0116 | -1.69% | |
9.640 | -0.79% | |
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 | 9.09% | |
0.000000008400 | 0.00% | |
0.000427 | 0.00% | |
0.0063 | 0.00% | |
0.000310 | 0.00% | |
0.3284 | 0.00% | |
0.000405 | 0.00% | |
-- | -- | |
0.00000000000101 | 0.00% | |
0.001290 | 0.00% | |
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% | |
0.000098 | 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% | |
0.00037 | 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% | |
0.0001000 | 0.00% | |
0.05056 | 0.00% | |
1.3575 | 0.00% | |
0.00136 | 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% | |
0.00003075 | 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% | |
0.00012700 | 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% | |
0.00000000000540 | 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% | |
0.0320 | -3.03% | |
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% | |
0.0036 | 0.00% | |
0.1769 | 0.00% | |
2.2915 | 0.00% | |
0.0005 | 0.00% | |
0.000632 | 0.00% | |
0.0099 | 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% | |
0.0550 | 0.00% | |
0.004287 | 3.75% | |
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% | |
0.0001 | 0.00% | |
0.6700 | 0.00% | |
0.00011 | 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% | |
0.0889 | -2.09% | |
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% | |
0.00774 | 0.00% | |
0.1725 | 0.00% | |
0.00008 | 0.00% | |
0.03786 | 0.00% | |
0.01463 | 0.00% | |
0.01367 | -2.08% | |
0.0000073 | -16.09% | |
0.00614 | 0.00% | |
0.4606 | 0.00% | |
0.00021 | 0.00% | |
0.001800 | 0.00% | |
0.01200 | 0.00% | |
0.000001000 | 0.00% | |
0.0000008 | 0.00% | |
1.3150 | -1.52% | |
0.00390 | 0.00% | |
0.0000310 | 0.00% | |
0.0000325 | 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% | |
0.00083 | 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% | |
0.0900 | 0.00% | |
0.00006 | 0.00% | |
0.000700 | 0.00% | |
0.01030 | 0.00% | |
3.7449 | 0.00% | |
0.0422 | -3.21% | |
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% | |
0.000055 | 0.00% | |
0.3101 | 0.00% | |
0.00074 | 0.00% | |
0.0000211 | 0.00% | |
0.00756 | 0.00% | |
0.4400 | 0.00% | |
1.4371 | 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% | |
0.02639 | 1.89% | |
0.00500 | 0.00% | |
3.58 | 0.00% | |
0.0020 | 0.00% | |
0.00538 | 0.00% | |
0.02610 | -4.78% | |
0.4236 | -1.24% | |
0.000000001868 | 0.00% | |
0.0018 | 0.00% | |
5155.00 | 0.00% | |
0.0091 | 0.00% | |
0.0301 | -4.14% | |
0.547 | 3.99% |