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 | -5.56% | |
0.00450 | 0.00% | |
0.0008830 | -3.81% | |
0.00152 | -2.56% | |
1.419 | 5.58% | |
0.0598 | -3.86% | |
0.02202 | 15.77% | |
0.506 | -7.83% | |
0.000119 | 0.00% | |
0.00280 | -5.08% | |
0.008087 | 0.14% | |
0.475 | -6.50% | |
0.2666 | -2.84% | |
0.00039097 | -0.06% | |
0.000853 | 1.07% | |
0.01519 | -7.09% | |
6.32 | -11.98% | |
0.1610 | -11.29% | |
0.02047 | -6.70% | |
0.1894 | -5.82% | |
0.1600 | -3.03% | |
0.1135 | 0.44% | |
0.5800 | 28.43% | |
1.7628 | 0.00% | |
0.01045 | -16.33% | |
0.002714 | -9.05% | |
0.00728 | 0.55% | |
2.7272 | 1.55% | |
0.013794 | -0.98% | |
3111.31 | -1.23% | |
0.0000428 | -17.37% | |
0.00580 | -10.49% | |
0.002510 | -10.93% | |
0.00216 | -1.37% | |
18.2951 | -2.59% | |
0.9246 | -10.46% | |
0.0000000001866 | -3.81% | |
0.004098 | -8.69% | |
0.01610 | -7.42% | |
0.00006723 | -0.36% | |
0.000000444 | -12.43% | |
0.000360 | -3.23% | |
0.00005964 | -3.91% | |
0.004999 | 0.58% | |
0.1840 | -8.28% | |
0.6855 | 0.90% | |
0.008000 | 12.76% | |
7.8483 | -6.46% | |
0.013645 | -0.02% | |
0.1723 | -6.10% | |
0.00001155 | -4.55% | |
0.01101 | -4.51% | |
0.5789 | -5.15% | |
0.05847 | 3.38% | |
0.000203037 | 1.61% | |
0.00915 | -3.07% | |
0.4622 | -8.20% | |
0.000380 | -1.04% | |
0.00175 | -9.79% | |
2.627 | -8.24% | |
0.002746 | 5.66% | |
0.004074 | 4.60% | |
0.0004372 | 8.16% | |
0.0001971 | -10.08% | |
1.036 | -16.65% | |
0.0516 | -6.35% | |
0.005522 | -33.05% | |
0.00319916 | -6.17% | |
0.015740 | 4.93% | |
0.062949 | -2.25% | |
0.007773 | 1.13% | |
0.000840 | 6.60% | |
0.01467 | 0.20% | |
0.06716 | 6.33% | |
0.1727 | -5.63% | |
0.0029951 | -0.66% | |
0.0000136 | -17.07% | |
2.397 | -13.22% | |
0.002228 | 90.26% | |
0.8601 | -3.24% | |
0.002451 | 33.72% | |
0.000742 | 5.70% | |
0.753 | -8.84% | |
0.002048 | 2.40% | |
0.001503 | -5.23% | |
0.0113 | -4.24% | |
0.05575 | -3.95% | |
14.62 | -18.05% | |
1.0724 | -3.40% | |
0.3612 | -5.35% | |
0.0315 | -7.89% | |
0.0041 | -2.38% | |
0.310 | -6.91% | |
0.000288 | -14.03% | |
0.00454 | 0.67% | |
0.00001493 | -15.51% | |
0.00208 | -8.37% | |
0.015219 | -2.58% | |
0.00841 | -5.29% | |
0.002938 | -5.10% | |
0.00000014081 | -5.27% | |
7.29 | -3.19% | |
0.006467 | -6.13% | |
0.0666 | -5.53% | |
0.21966 | -13.57% | |
0.000297 | -1.66% | |
0.6460 | -6.02% | |
0.01145 | -4.42% | |
0.01696 | -2.58% | |
0.02688 | -8.97% | |
0.410 | -3.76% | |
0.004210 | 18.83% | |
0.01202 | -4.75% | |
0.774 | -7.19% | |
0.0112 | -50.66% | |
0.01245 | 4.18% | |
0.0000240 | -1.23% | |
0.004835 | -9.47% | |
0.000000000226 | -5.04% | |
0.002309 | -8.04% | |
0.003879 | 18.08% | |
0.000224 | 7.69% | |
0.0002940 | -7.98% | |
0.001815 | -1.25% | |
16.65 | -2.17% | |
0.001648 | -9.20% | |
0.7460 | -24.36% | |
0.557 | -3.30% | |
0.00782 | -13.11% | |
0.478 | -4.78% | |
0.003436 | -3.37% | |
0.2028 | -9.02% | |
0.0000000405 | 11.88% | |
0.3678 | -8.21% | |
0.0000016667 | 0.45% | |
0.0480 | -2.64% | |
0.881 | -4.65% | |
0.0056 | -20.00% | |
0.00101 | -33.11% | |
0.00000003322 | -3.54% | |
0.85016 | -0.32% | |
0.000508 | -2.12% | |
0.001578 | -10.59% | |
0.001616 | -5.94% | |
0.3471 | 1.55% | |
0.0006017 | -1.86% | |
0.0420 | -4.33% | |
0.002032 | -7.43% | |
0.1664 | -5.35% | |
1981.78 | -2.80% | |
0.00003342 | -1.53% | |
0.0062 | 1.64% | |
0.1230 | -6.04% | |
0.0001760 | -25.07% | |
0.00155 | -8.82% | |
0.0003127 | -24.14% | |
17.66 | 5.06% | |
0.000511 | -29.42% | |
27.26 | -2.78% | |
0.001174 | -12.97% | |
5.275 | -2.50% | |
0.4118 | -3.85% | |
0.00000001189 | -1.65% | |
2.518 | -5.83% | |
4.727 | -6.19% | |
0.04736 | -8.23% | |
0.0257 | -3.75% | |
0.00233 | -2.92% | |
0.00000419 | -4.99% | |
0.03561 | -2.97% | |
0.3000 | -17.81% | |
0.2694 | -4.57% | |
0.0903 | -5.35% | |
0.07637 | -6.08% | |
0.1929 | -1.88% | |
0.01371 | -8.96% | |
0.000093 | -3.13% | |
0.0000550 | -2.65% | |
0.0000000901 | -0.99% | |
0.03683 | -11.27% | |
0.55347 | -5.27% | |
0.0002028 | -12.21% | |
0.03230 | -0.22% | |
0.001699 | -13.27% | |
0.031121 | 4.81% | |
0.01100 | 3.48% | |
0.0000002925 | 7.34% | |
0.01464 | -9.96% | |
0.0002472 | -7.55% | |
0.6609 | -5.77% | |
0.001313 | 9.05% | |
0.02285 | -5.89% | |
1.6923 | 8.84% | |
0.0732 | -5.06% | |
0.003900 | -3.92% | |
0.01809 | -2.11% | |
0.10793 | -8.61% | |
0.011987 | 0.01% | |
0.0007631 | 18.16% | |
0.0151 | -4.43% | |
1.743 | -6.29% | |
0.0861 | -5.80% | |
1.958 | -4.21% | |
0.1436 | -6.57% | |
0.2435 | -6.92% | |
0.000908 | -14.10% | |
0.01220 | -6.44% | |
0.450 | -3.85% | |
0.784 | -6.11% | |
0.2494 | -5.28% | |
0.0000464 | -3.33% | |
2.173 | -0.64% | |
0.00597 | -7.73% | |
0.02661 | -3.94% | |
0.1217 | -7.80% | |
0.1967 | -16.48% | |
0.592 | -6.62% | |
0.2460 | -3.00% | |
0.237 | -5.95% | |
0.00000000008480 | -11.39% | |
0.000246 | 25.51% | |
0.0209 | -10.30% | |
0.005998 | 3.45% | |
0.0000002623 | 2.18% | |
0.01889 | -10.05% | |
0.00000001640 | -2.21% | |
0.0614 | -5.83% | |
0.03350 | -8.39% | |
0.3119 | -14.50% | |
0.0157 | -8.19% | |
6.38 | -5.48% | |
0.02313 | 0.13% | |
0.0004101 | -18.53% | |
0.2685 | -4.62% | |
0.001134 | -3.90% | |
0.003052 | 4.23% | |
0.00932 | -4.61% | |
0.01395 | -10.98% | |
0.003941 | -0.53% | |
0.002953 | -14.31% | |
15.95 | -4.26% | |
0.01330 | -2.92% | |
0.004599 | -5.85% | |
0.538 | -7.56% | |
0.0648 | -0.61% | |
0.1044 | -8.10% | |
0.0000000000000141 | -3.42% | |
0.000001502 | -1.38% | |
305.9 | -0.91% | |
0.0003472 | -6.01% | |
0.1058 | -7.92% | |
0.2982 | -10.42% | |
0.0620 | -1.27% | |
0.0780 | -5.11% | |
1.830 | 2.81% | |
0.0000580 | -10.63% | |
0.01147 | -3.04% | |
0.7614 | -0.01% | |
2.120 | -3.42% | |
0.00000001258 | -6.54% | |
0.002983 | -10.61% | |
0.002229 | -1.37% | |
0.0000259 | -1.52% | |
0.05030 | -5.36% | |
0.012252 | -1.09% | |
2.945 | -5.73% | |
0.00030000 | 0.00% | |
0.1876 | -3.65% | |
8.31 | -5.25% | |
0.00622 | -30.89% | |
0.001569 | -3.92% | |
0.00000000001066 | -8.73% | |
0.1183 | -8.93% | |
0.000303 | 14.77% | |
0.0051050 | -0.14% | |
0.00097 | 4.30% | |
0.0106 | 8.16% | |
0.0002899 | -6.87% | |
0.0000091 | -2.15% | |
0.1028 | -28.56% | |
0.004222 | -8.24% | |
0.0612 | -1.45% | |
0.0171 | -50.86% | |
0.1220 | -11.66% | |
0.00000652 | -9.94% | |
0.0135 | -8.78% | |
0.000278 | -5.44% | |
0.0003561 | -9.48% | |
0.0104 | 8.33% | |
0.09173 | -7.33% | |
0.01542 | -7.22% | |
0.01004 | -4.65% | |
0.003223 | -9.95% | |
0.001102 | 6.78% | |
0.0048 | 6.67% | |
0.002500 | 1.01% | |
16.01 | -4.82% | |
0.0864 | 44.00% | |
0.02924 | -13.97% | |
0.006101 | -7.14% | |
0.0521 | -0.76% | |
0.2626 | -6.55% | |
0.001027 | -3.57% | |
0.00419 | 0.96% | |
39.73 | -3.75% | |
0.02664 | -12.83% | |
0.7280 | 0.50% | |
0.0005487 | -1.75% | |
0.00002889 | 8.12% | |
0.001337 | -5.24% | |
0.002395 | -16.23% | |
0.0000000465 | -3.93% | |
0.017744 | -2.63% | |
0.0098 | -2.00% | |
0.381 | -3.79% | |
69.3 | -4.15% | |
0.0000021 | 0.00% | |
0.0002640 | -7.66% | |
0.4718 | -5.49% | |
0.02840 | 373.33% | |
0.002958 | -14.51% | |
0.0000591 | -3.27% | |
0.2573 | 1.86% | |
0.0000000745 | -0.67% | |
0.006500 | -2.99% | |
0.1301 | -3.91% | |
0.0484 | -10.20% | |
0.004742 | 4.98% | |
4.365 | -4.80% | |
0.0096 | -2.04% | |
0.01257 | -10.15% | |
0.005460 | -4.16% | |
0.00126 | -3.82% | |
6.2329 | -0.88% | |
13.35 | -4.44% | |
0.00756 | -5.50% | |
0.0564 | -15.19% | |
1344 | -6.08% | |
0.1734 | -6.77% | |
0.010807 | -6.06% | |
0.0575 | -7.85% | |
0.2480 | -11.90% | |
0.0005537 | -11.70% | |
0.0000031 | -11.43% | |
0.1258 | -9.30% | |
56.21 | -20.71% | |
0.0887 | -3.27% | |
0.0833 | -4.58% | |
0.1100 | -7.49% | |
0.1503 | -6.00% | |
0.1086 | -4.40% | |
0.06006 | -15.76% | |
0.008899 | 5.93% | |
0.2784 | -5.88% | |
19.17 | -9.49% | |
0.004527 | -10.25% | |
0.000651 | -10.58% | |
0.018559 | -9.74% | |
0.03545 | -1.14% | |
0.2504 | -7.02% | |
0.04054 | -11.52% | |
0.002850 | -5.06% | |
0.00769 | -6.11% | |
0.0000000123 | -18.00% | |
0.01136 | -6.19% | |
0.0004279 | 7.89% | |
0.5464 | -4.02% | |
15.36 | -7.08% | |
0.2991 | -13.90% | |
1.195 | -5.76% | |
0.2458 | -6.15% | |
0.000345 | -4.43% | |
0.000600 | -7.69% | |
0.2125 | -2.92% | |
0.000169 | -2.87% | |
0.001716 | -6.79% | |
146.16 | -1.37% | |
0.000931 | -4.61% | |
0.4233 | -2.89% | |
0.01452 | -12.05% | |
0.3313 | -5.34% | |
0.00000226 | -21.25% | |
0.001658 | -10.96% | |
0.0000008 | 14.29% | |
0.003346 | -8.33% | |
0.655 | -13.70% | |
101.67 | 0.95% | |
0.1870 | -2.30% | |
0.0006758 | 1.26% | |
0.00979 | -5.87% | |
0.0983 | -3.63% | |
0.0004004 | -5.03% | |
0.0004913 | 3.61% | |
0.00000000155 | 8.39% | |
0.00000724 | 0.00% | |
0.01124 | -4.66% | |
0.005692 | -10.11% | |
0.0779 | 1.04% | |
5.47 | -7.45% | |
0.04619 | 11.30% | |
0.0000551 | 24.66% | |
0.000675 | 3.69% | |
0.000002072 | -14.94% | |
0.1600 | -4.82% | |
0.0150 | -8.54% | |
0.0232 | -2.11% | |
11.13 | -2.54% | |
0.000816 | 0.12% | |
0.3398 | -5.19% | |
0.707 | -3.81% | |
12.79 | -3.03% | |
0.1968 | -4.28% | |
0.00712 | -3.39% | |
0.002350 | -11.32% | |
0.000466 | -14.50% | |
0.8059 | -1.14% | |
0.000000001300 | -13.16% | |
0.002633 | -6.23% | |
0.04511 | -0.81% | |
0.887 | -7.22% | |
0.1064 | -9.98% | |
0.0000000624 | -2.35% | |
0.002434 | -25.43% | |
0.1079 | -6.74% | |
0.1890 | -0.58% | |
0.2614 | -7.01% | |
0.0224 | -6.28% | |
0.01128 | -2.67% | |
0.01460 | -8.00% | |
1.3121 | -6.41% | |
0.04130 | -1.43% | |
0.0012 | 100.00% | |
0.654 | -3.68% | |
0.00692 | -1.42% | |
1.339 | -3.11% | |
0.0861 | -5.90% | |
0.01400 | -14.37% | |
0.003869 | -8.17% | |
0.000000000000819 | -0.49% | |
0.666 | -6.46% | |
0.1779 | -3.42% | |
0.000412 | 0.49% | |
0.00002 | -33.33% | |
0.00490 | -5.59% | |
0.002243 | -7.73% | |
22.374 | -2.49% | |
0.000018 | -65.38% | |
5.614 | -5.34% | |
0.8352 | 0.44% | |
0.0304 | -3.49% | |
0.00000000000021 | 16.67% | |
0.5397 | -2.28% | |
0.0752 | -4.81% | |
16.42 | -3.30% | |
0.6803 | -7.83% | |
0.0811 | -4.81% | |
0.00225 | 14.80% | |
0.590 | -4.38% | |
0.00031 | -3.13% | |
0.0000565 | -9.31% | |
2.123 | -6.56% | |
0.02479 | -14.87% | |
0.00008786 | -2.04% | |
0.002586 | -4.58% | |
0.750 | 0.00% | |
0.1156 | -5.32% | |
0.0419 | -6.47% | |
0.00000000000014 | 0.00% | |
0.309 | -4.04% | |
0.2135 | -6.73% | |
0.0507 | -7.14% | |
0.00009111 | -3.00% | |
0.00002240 | -3.16% | |
0.00000000001553 | 12.54% | |
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% | |
0.001023 | -3.85% | |
0.5141 | -2.63% | |
2.852 | -3.45% | |
0.2040 | -4.67% | |
0.000000000004690 | 0.02% | |
0.01236 | -3.59% | |
6.184 | -5.04% | |
0.000839 | -1.06% | |
0.00020 | -20.00% | |
0.0000080 | -6.98% | |
0.000600 | 0.00% | |
0.0680 | -5.03% | |
0.00868 | -12.76% | |
0.00113 | 0.00% | |
0.2977 | -10.57% | |
0.005978 | 11.14% | |
0.0769 | -2.78% | |
0.000351 | 0.86% | |
0.000000000001558 | -15.46% | |
0.03903 | -6.92% | |
0.0000579 | -13.58% | |
0.0050 | -29.58% | |
0.0003663 | -7.34% | |
0.000024 | 0.00% | |
0.000058 | -1.69% | |
0.000000097 | -7.62% | |
0.1207 | -8.63% | |
0.00000861 | 3.61% | |
0.001604 | 0.44% | |
0.0288 | -8.86% | |
1.260 | -2.85% | |
8.36 | -2.11% | |
0.00002009 | -0.89% | |
0.00610 | -2.09% | |
0.4869 | -3.72% | |
0.0013 | 8.33% | |
0.04467 | -14.70% | |
0.00000000000235 | 12.44% | |
0.000069 | 16.95% | |
0.000000000449 | -15.76% | |
1.259 | -5.69% | |
0.000013 | -48.00% | |
0.2167 | 3.04% | |
0.02184 | -5.45% | |
0.00030 | -3.23% | |
0.1423 | -1.86% | |
0.0523 | -4.74% | |
0.2140 | -3.30% | |
0.17927 | -0.71% | |
0.0000000000000163 | -4.68% | |
0.05432 | 2.57% | |
0.0426 | -3.40% | |
0.05943 | -0.92% | |
0.0533 | 3.90% | |
0.1231 | -9.49% | |
0.001100 | -47.59% | |
0.1129 | -1.22% | |
0.0007 | 0.00% | |
0.003501 | -3.74% | |
0.0111 | 0.00% | |
0.004189 | -0.71% | |
0.002700 | 5.02% | |
0.000000000019 | 0.00% | |
0.01069 | 0.09% | |
0.0000032 | 10.34% | |
3.8900 | 54.80% | |
0.000000000003 | -40.00% | |
0.000835 | -8.74% | |
0.010200 | 0.99% | |
4.61 | -7.24% | |
0.0002100 | -4.59% | |
0.00753 | -2.59% | |
0.0318 | -4.79% | |
0.00000000003610 | 2.47% | |
0.00000000000872 | 33.95% | |
0.00010999 | 80.10% | |
0.1877 | -5.11% | |
0.000000000765 | 0.00% | |
0.0000071 | -29.00% | |
0.002510 | 20.73% | |
0.00000360 | -4.76% | |
0.4382 | -3.25% | |
0.0000004 | -60.00% | |
0.0660 | -5.58% | |
0.0001623 | 1.56% | |
0.003870 | -7.59% | |
0.0003495 | -12.63% | |
0.03420 | -0.29% | |
0.000001671 | 5.09% | |
0.001121 | -2.78% | |
0.03372 | 0.00% | |
0.07925 | -0.63% | |
50.0000 | 0.00% | |
0.00000000001940 | 0.26% | |
0.0649 | -8.33% | |
0.0342 | -4.74% | |
0.00023 | -36.11% | |
0.01956 | 3.27% | |
0.000000001695 | -1.91% | |
0.0876 | -4.26% | |
0.3571 | -4.60% | |
0.001022 | -4.93% | |
0.00000051 | -3.77% | |
0.00248 | -9.82% | |
0.000000002137 | 0.05% | |
0.549 | -1.79% | |
0.000092 | 0.00% | |
0.008231 | 0.00% | |
0.0000509 | 0.79% | |
0.00006 | -14.29% | |
0.0986 | -4.09% | |
0.024504 | 0.00% | |
0.0000055 | 14.58% | |
0.000001307 | -4.25% | |
0.000940 | -2.49% | |
0.000000000808 | 7.59% | |
0.00410 | -7.45% | |
0.0008 | 60.00% | |
0.000000000573 | 37.08% | |
0.1664 | -8.67% | |
1.384 | -1.00% | |
0.0945 | -6.62% | |
0.000000000009 | 0.00% | |
0.00510 | 0.00% | |
0.0006895 | -6.80% | |
0.001791 | 0.06% | |
0.0019272 | -9.24% | |
0.00000006 | 0.00% | |
17.320 | -3.23% | |
0.0084 | 27.27% | |
0.1009 | -2.42% | |
0.6998 | -0.01% | |
0.000019 | 0.00% | |
0.001518 | -23.60% | |
0.0951 | -9.17% | |
0.00000103 | 3.00% | |
0.00008 | -38.46% | |
0.003470 | -11.00% | |
0.01728 | -4.74% | |
0.0009 | 0.00% | |
1.73 | -27.92% | |
0.00004 | -20.00% | |
0.01512 | -3.76% | |
0.00000000000099 | 2.06% | |
0.0271 | -0.37% | |
0.000018 | -28.00% | |
0.0001450 | 0.00% | |
0.001957 | 1.24% | |
0.00010 | 42.86% | |
0.9900 | 0.00% | |
0.0063 | -1.56% | |
0.0000249 | 8.73% | |
0.00000011220 | -28.39% | |
0.0005769 | -5.74% | |
0.0002 | -50.00% | |
0.0000002326 | 3.38% | |
0.000000000040 | -42.03% | |
1.050 | -6.50% | |
0.0192 | -45.30% | |
0.00046 | -6.12% | |
0.00000000000288 | 1.41% | |
0.0768 | -7.91% | |
0.001995 | -10.42% | |
0.0000021 | -84.78% | |
0.00000286 | -2.72% | |
0.00000000000426 | 0.71% | |
0.00083 | -19.42% | |
0.0000000200 | -0.50% | |
0.0001320 | 28.16% | |
0.00995 | -0.50% | |
0.001035 | 47.65% | |
0.000064 | 72.97% | |
0.00000000053 | -1.85% | |
0.000042 | 2.44% | |
0.0728 | -7.73% | |
0.000000000108 | 2.86% | |
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% | |
0.000080 | 1.27% | |
0.00000011 | 37.50% | |
0.00004398 | 0.00% | |
0.0663 | 2.79% | |
0.01752 | -7.20% | |
0.000709 | -4.70% | |
1.1075 | -1.56% | |
0.5389 | -0.42% | |
0.09291 | -2.70% | |
0.00013 | 8.33% | |
0.000884 | -14.75% | |
0.001300 | 1.64% | |
1.3974 | -10.82% | |
58.5600 | 0.00% | |
0.00004315 | -2.46% | |
0.0460 | -16.21% | |
0.002101 | -7.44% | |
0.02906 | -0.45% | |
0.001802 | -7.35% | |
0.0006694 | 2.20% | |
0.003170 | -7.90% | |
0.00385 | 0.00% | |
0.0009012 | 0.00% | |
0.0000119 | 0.00% | |
0.0003989 | 0.63% | |
0.0007993 | 0.00% | |
5.931 | -2.75% | |
0.0000329 | 0.00% | |
0.003402 | 6.68% | |
0.000029 | 11.54% | |
0.011168 | 3.79% | |
0.002554 | -13.51% | |
0.002272 | -6.92% | |
1899.00 | 0.00% | |
0.4089 | -1.09% | |
0.1159 | -11.73% | |
0.04282 | -9.72% | |
0.000114 | -5.79% | |
0.4909 | -10.66% | |
0.000762 | 3.25% | |
0.1297 | -8.08% | |
0.000001969 | 3.63% | |
1.264 | -1.02% | |
0.0396 | 1.28% | |
0.001140 | -6.48% | |
0.02738 | -2.80% | |
0.00210 | 0.48% | |
0.000119 | 0.00% | |
0.0817 | 5.56% | |
0.00976 | -0.81% | |
2.80 | -6.67% | |
1.000000 | 0.00% | |
0.1703 | -2.63% | |
0.3771 | 0.00% | |
0.549 | -7.42% | |
0.5732 | 0.00% | |
48.534 | -0.23% | |
1.784 | -1.65% | |
2.663 | -2.67% | |
0.000000046 | -54.00% | |
0.1317 | -5.79% | |
0.06923 | -2.82% | |
0.641 | -2.88% | |
0.6445 | -4.86% | |
0.0700 | 0.00% | |
0.00000000015708 | 0.00% | |
0.001110 | -2.97% | |
0.00000080 | 0.00% | |
0.1643 | -4.25% | |
0.000216 | 0.00% | |
0.0000000030210 | 0.00% | |
1.416 | -7.51% | |
1.5000 | 0.00% | |
3.9889 | 0.00% | |
1.1371 | 0.00% | |
0.4424 | 0.00% | |
0.2151 | 0.05% | |
0.0381 | -5.46% | |
0.000375 | -1.32% | |
0.0071 | 0.00% | |
0.01554 | -3.24% | |
0.000210 | 0.00% | |
0.00782 | -1.76% | |
2.010 | -4.69% | |
0.1518 | -4.05% | |
6.73 | -4.94% | |
0.0411 | -4.64% | |
0.000452 | 0.00% | |
0.230000 | 0.00% | |
0.000000002418 | 1.00% | |
0.000191711 | -1.10% | |
0.00000043 | -2.27% | |
0.1204 | 0.00% | |
2.736 | 2.74% | |
1.032 | -2.18% | |
0.004000 | 0.00% | |
0.000300 | 0.00% | |
0.0023 | 0.00% | |
0.00035 | 0.00% | |
0.0112 | 0.00% | |
0.000000040 | 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% | |
0.0000002593 | 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% | |
0.2468 | 0.37% | |
0.000902 | 0.00% | |
0.0226 | -2.16% | |
0.000000000783 | 1.42% | |
0.0001 | 0.00% | |
0.0009 | 0.00% | |
0.0560 | 0.00% | |
0.00012800 | 37.63% | |
0.000446 | -1.55% | |
0.004025 | 0.00% | |
0.0114 | -3.39% | |
9.629 | -0.96% | |
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% | |
0.004234 | 2.57% | |
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% | |
0.0922 | -0.97% | |
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% | |
0.01369 | -1.93% | |
0.0000082 | -4.65% | |
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% | |
1.3101 | -0.52% | |
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% | |
0.02636 | 1.74% | |
0.00500 | 0.00% | |
3.58 | 0.00% | |
0.0020 | 0.00% | |
0.00538 | 0.00% | |
0.02609 | -4.85% | |
0.4236 | -1.94% | |
0.000000001868 | 0.00% | |
0.0018 | 0.00% | |
5155.00 | 0.00% | |
0.0091 | 0.00% | |
0.0301 | -4.14% | |
0.546 | 3.41% |