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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0.000000001275 | -14.83% | |
0.004209 | 11.38% | |
0.1538 | -3.45% | |
0.000200620 | 0.80% | |
0.00696 | -4.53% | |
0.0592 | -1.33% | |
0.004880 | -2.22% | |
0.000600 | 0.00% | |
0.578 | 9.68% | |
0.04925 | 6.33% | |
0.000312 | -0.64% | |
0.005975 | -13.94% | |
0.002010 | -2.85% | |
0.000000446 | -10.08% | |
0.004951 | -0.80% | |
0.000358 | -0.83% | |
0.7075 | 1.58% | |
0.6489 | -3.18% | |
0.004206 | 1.67% | |
0.000392 | 2.08% | |
0.00322118 | -1.91% | |
0.6175 | -1.11% | |
0.002719 | -4.06% | |
0.000409 | -0.73% | |
0.3378 | -4.63% | |
0.01495 | -4.78% | |
19.1500 | 0.79% | |
0.003993 | 2.62% | |
0.001957 | -11.09% | |
0.0003691 | 1.60% | |
9.501 | 5.52% | |
0.0528 | 0.19% | |
0.766 | -4.37% | |
0.0799 | -1.11% | |
0.05673 | -25.39% | |
0.0875 | 59.09% | |
0.0030002 | 0.24% | |
0.01464 | -0.20% | |
0.002323 | -7.89% | |
0.0000015923 | -4.02% | |
0.1791 | -1.97% | |
7.26 | -2.81% | |
0.005933 | -6.02% | |
0.00006695 | -0.42% | |
0.0000465 | 5.20% | |
1.7628 | -0.07% | |
6.34 | -5.51% | |
0.000098 | 0.00% | |
0.0002771 | -14.24% | |
0.001811 | 0.17% | |
0.02759 | 4.59% | |
0.0000150 | -0.66% | |
0.474 | -4.44% | |
0.00000014169 | -2.13% | |
0.0428 | 1.18% | |
0.01999 | -9.18% | |
0.000795 | 12.29% | |
0.0120 | 34.83% | |
0.1861 | -1.06% | |
0.0000000387 | 6.03% | |
1.1555001 | 2.73% | |
0.1919 | -3.13% | |
0.001428 | -6.85% | |
0.013277 | -3.87% | |
0.063616 | -0.96% | |
0.000245 | -17.51% | |
0.3540 | -5.07% | |
0.0041 | -2.38% | |
27.16 | -1.70% | |
0.014946 | 2.10% | |
0.00449 | -1.75% | |
0.4861 | 1.17% | |
0.00000001188 | 0.25% | |
0.7587 | -8.07% | |
17.9409 | -3.86% | |
0.002987 | -0.93% | |
0.02324 | -0.13% | |
1.0859 | -1.59% | |
0.777 | -1.27% | |
0.0023 | 0.00% | |
0.001297 | -24.46% | |
0.01163 | -0.60% | |
1969.41 | -3.41% | |
0.00000003411 | -1.44% | |
0.0002421 | -5.58% | |
0.00944 | 11.45% | |
0.03006 | -7.02% | |
0.000884 | 11.34% | |
0.000506 | 1.40% | |
0.0027 | 12.50% | |
16.83 | -0.41% | |
0.01250 | 0.16% | |
0.06010 | 3.11% | |
0.002758 | -1.50% | |
10.86 | -3.12% | |
0.05045 | 14.97% | |
16.13 | 2.41% | |
0.007910 | 5.12% | |
0.6650 | -4.03% | |
0.85369 | 0.30% | |
0.0582 | -5.52% | |
0.03388 | -7.03% | |
0.0009700 | 1.57% | |
0.003922 | -1.11% | |
0.000726 | -24.14% | |
0.005835 | 3.64% | |
0.0006040 | -0.25% | |
0.1761 | -0.45% | |
0.01455 | -10.52% | |
0.0145 | 5.07% | |
17.13 | -5.52% | |
0.0158 | -3.07% | |
0.1700 | 2.04% | |
0.601 | 0.00% | |
0.01590 | -5.69% | |
8.35 | -2.11% | |
0.0003024 | -20.19% | |
0.51706 | -11.06% | |
6.3952 | 3.05% | |
1.748 | -1.24% | |
0.00210 | -2.78% | |
0.0003368 | -10.88% | |
0.000000001597 | -7.90% | |
0.000210 | -9.09% | |
0.02632 | -4.50% | |
0.002477 | -1.16% | |
0.4767 | -2.77% | |
0.003532 | 7.36% | |
0.478 | -2.25% | |
0.07058 | 4.35% | |
5.392 | 1.89% | |
0.9446 | -1.44% | |
0.00849 | 1.43% | |
0.599 | -1.32% | |
0.00782 | -7.35% | |
0.000532 | -5.00% | |
0.00063 | -14.86% | |
0.00003363 | -6.14% | |
0.000086 | -8.51% | |
0.010825 | -0.28% | |
0.0107 | 3.88% | |
0.00006021 | 0.82% | |
2.549 | -1.51% | |
0.002339 | 0.39% | |
12.73 | -1.24% | |
0.1270 | 0.79% | |
1.7730 | 4.27% | |
2.6779 | -0.06% | |
0.000697 | -2.92% | |
0.001535 | -16.21% | |
0.004169 | -8.15% | |
0.01355 | -12.97% | |
0.0000545 | -1.45% | |
9.627 | -1.08% | |
0.01363 | -4.01% | |
0.01841 | 1.60% | |
0.03669 | -2.99% | |
0.004992 | 17.21% | |
0.000001299 | -6.75% | |
0.0000000852 | -5.65% | |
0.841 | -2.55% | |
0.0004388 | -10.23% | |
0.011990 | 0.04% | |
0.2486 | -1.00% | |
0.01160 | 3.66% | |
0.0007401 | 30.88% | |
0.03230 | -0.19% | |
0.2485 | -1.07% | |
0.003009 | -0.13% | |
0.04194 | 0.94% | |
0.0002010 | -6.64% | |
3123.99 | 1.11% | |
0.06413 | -10.06% | |
0.0061 | -1.61% | |
5.437 | -0.82% | |
0.000001470 | -3.16% | |
0.4163 | -0.34% | |
0.03467 | -3.93% | |
0.0258 | 0.39% | |
0.2455 | -2.39% | |
0.1895 | 0.80% | |
0.002877 | 17.43% | |
0.0112 | -50.66% | |
0.003455 | -1.00% | |
0.002365 | -5.02% | |
0.0618 | -2.98% | |
0.0618 | -0.32% | |
0.001832 | -10.11% | |
0.002505 | -1.57% | |
0.1068 | -5.82% | |
0.0000285 | -40.38% | |
0.00901 | -22.06% | |
0.01851 | 28.36% | |
0.000232 | 20.83% | |
0.002033 | -2.45% | |
0.0863 | -5.27% | |
7.4456 | -5.48% | |
0.0004020 | -0.59% | |
4.318 | -2.92% | |
0.02844 | 11.31% | |
0.001129 | -2.00% | |
0.0844 | -4.95% | |
0.0110 | -1.79% | |
0.001550 | -1.34% | |
0.7618 | 0.05% | |
0.01888 | -4.11% | |
0.310 | -1.90% | |
0.00000000008314 | -8.73% | |
5.1166 | -2.19% | |
0.1054 | -3.83% | |
0.002844 | 17.42% | |
0.237 | -3.66% | |
0.00173 | 13.82% | |
0.0000002580 | -4.41% | |
0.0001899 | 5.09% | |
0.1993 | 0.15% | |
0.000640 | 1.59% | |
0.2735 | 0.70% | |
0.03644 | -3.50% | |
0.0139 | -7.33% | |
0.02791 | -14.70% | |
2.134 | -0.84% | |
0.00000001355 | -15.21% | |
0.0211 | 1.93% | |
0.00001149 | -2.71% | |
0.0000020 | -4.76% | |
0.00002287 | 0.31% | |
0.05118 | 0.31% | |
0.00956 | 1.49% | |
0.014716 | -9.36% | |
0.21739 | -2.16% | |
2.959 | -1.14% | |
0.0047 | -76.73% | |
0.1476 | -0.54% | |
1.040 | 0.00% | |
0.000796 | -1.12% | |
2.385 | -0.29% | |
0.01126 | -5.30% | |
0.006515 | -2.89% | |
0.001711 | -3.88% | |
0.0910 | -2.15% | |
1312 | -7.54% | |
0.2177 | 6.72% | |
0.17386 | -1.02% | |
0.0051094 | 0.15% | |
0.0593 | 0.00% | |
0.1899 | -1.35% | |
0.0000000000000138 | -3.50% | |
55.74 | -2.86% | |
0.0000088 | -1.12% | |
0.1225 | -6.56% | |
0.547 | -0.55% | |
307.7 | 0.46% | |
0.003876 | 2.46% | |
0.3046 | -0.29% | |
0.01545 | -14.07% | |
0.2744 | -0.22% | |
0.2697 | -0.19% | |
0.6586 | -3.22% | |
0.000267 | -9.49% | |
0.004914 | -0.18% | |
0.00000657 | -2.81% | |
0.0104 | 8.33% | |
0.004481 | -4.31% | |
0.0339 | 5.28% | |
0.1103 | -17.93% | |
0.09126 | -3.43% | |
16.00 | -1.48% | |
0.001339 | -2.05% | |
0.00920 | -11.88% | |
0.1249 | -0.40% | |
13.67 | 0.37% | |
0.001656 | -16.07% | |
0.011604 | 8.07% | |
0.00424 | -3.20% | |
0.3500 | -1.69% | |
0.0503 | 1.62% | |
0.8084 | -1.74% | |
0.1520 | -0.46% | |
0.01199 | 99.83% | |
0.01170 | -3.39% | |
0.00091 | -8.08% | |
0.00002669 | -4.58% | |
0.00000001340 | 3.47% | |
0.000239 | -21.64% | |
0.2127 | 1.62% | |
0.0002584 | -5.35% | |
0.6344 | -12.86% | |
0.0005613 | -3.54% | |
0.012200 | 0.00% | |
0.001950 | 62.36% | |
0.560 | -2.44% | |
0.00947 | -1.97% | |
0.0812 | -2.17% | |
0.0548 | 8.09% | |
0.00000000000040 | 0.00% | |
0.001057 | 1.34% | |
0.0003901 | -10.07% | |
0.00155 | -2.52% | |
0.00000000001872 | -3.51% | |
0.002223 | -0.45% | |
0.0483 | 0.21% | |
0.0100 | 1.01% | |
0.0000033 | -19.51% | |
0.1314 | 0.00% | |
0.01141 | 0.00% | |
0.0423 | -0.47% | |
0.3470 | -0.63% | |
0.456 | 1.33% | |
0.1172 | 3.17% | |
0.0994 | 0.00% | |
8.39 | -0.36% | |
0.1101 | 0.00% | |
0.0019559 | -2.51% | |
2.184 | 0.23% | |
0.386 | 0.00% | |
0.786 | -1.26% | |
0.000853 | 1.07% | |
0.001155 | -3.67% | |
19.09 | -4.26% | |
0.02032 | 3.89% | |
0.10934 | -1.92% | |
0.003254 | -1.48% | |
0.0748 | 0.54% | |
0.0848 | 0.12% | |
0.0004084 | 6.58% | |
0.2506 | -0.52% | |
0.00000411 | 0.00% | |
0.715 | -0.42% | |
0.00001124 | 30.55% | |
0.0000562 | -0.88% | |
0.1081 | -2.70% | |
0.008749 | -2.79% | |
0.4305 | 0.75% | |
0.0256 | -13.51% | |
0.0000000747 | -1.32% | |
0.0592 | 14.73% | |
0.00000000164 | 5.81% | |
0.0609 | -1.77% | |
0.00764 | -1.93% | |
6.48 | 0.15% | |
0.00000000000229 | -2.55% | |
1.978 | -1.00% | |
0.000345 | -4.43% | |
0.0773 | 2.52% | |
0.04076 | -2.63% | |
16.42 | -1.02% | |
0.001067 | -0.65% | |
0.0002963 | -2.47% | |
0.00000226 | -21.25% | |
0.649 | -6.48% | |
4.807 | -0.89% | |
0.01483 | -2.75% | |
0.01529 | -1.42% | |
0.00705 | -0.70% | |
2.711 | 0.78% | |
0.1159 | -7.13% | |
0.000862 | -14.82% | |
0.0873 | -2.13% | |
0.3014 | -3.40% | |
0.0000085 | -3.41% | |
0.000091 | 0.00% | |
0.301 | -59.87% | |
0.0000551 | 24.94% | |
0.0000000615 | 5.13% | |
0.003591 | 52.48% | |
0.006064 | 2.40% | |
0.02814 | 5.00% | |
0.000475 | -15.63% | |
0.566 | 0.00% | |
0.2784 | -2.66% | |
0.1896 | 0.37% | |
0.030394 | -2.58% | |
0.00000000001383 | -2.26% | |
0.1520 | -1.30% | |
0.0096 | 0.00% | |
0.00000724 | 0.28% | |
0.00614 | 0.16% | |
1.344 | -1.61% | |
0.3371 | -0.91% | |
0.0000000134 | 5.51% | |
0.001581 | -3.66% | |
0.662 | 0.30% | |
0.000659 | -2.08% | |
0.0228 | -1.30% | |
0.004204 | 0.10% | |
0.2654 | -1.30% | |
0.002791 | 18.56% | |
0.01139 | 0.53% | |
0.909 | -1.30% | |
0.0662 | 2.64% | |
0.1070 | -0.09% | |
5.43 | -4.23% | |
70.1 | 0.86% | |
0.00002023 | 0.70% | |
0.01774 | -4.11% | |
0.0652 | -3.83% | |
1.432 | -2.12% | |
15.61 | 0.84% | |
0.0005521 | 0.33% | |
0.668 | -3.33% | |
0.003982 | -1.46% | |
0.0308 | 2.33% | |
0.001147 | 8.62% | |
0.5423 | 3.97% | |
0.8224 | -0.54% | |
0.000412 | 0.49% | |
0.0234 | 0.86% | |
0.0872 | -0.91% | |
0.0575 | -2.21% | |
0.00003076 | 0.03% | |
0.000008 | -27.27% | |
0.0006534 | -2.55% | |
0.1176 | -3.53% | |
0.2573 | -1.38% | |
0.00681 | -2.30% | |
0.0000582 | 0.00% | |
0.001793 | -0.50% | |
39.23 | -2.12% | |
0.1902 | -0.11% | |
0.003074 | -2.51% | |
0.0052 | -1.89% | |
0.001624 | 0.06% | |
0.000023 | -4.17% | |
0.00031 | -3.13% | |
0.000038 | -9.52% | |
5.699 | -0.56% | |
0.01346 | 2.28% | |
143.18 | -4.96% | |
0.1922 | -1.08% | |
0.1158 | -0.17% | |
1.215 | 0.16% | |
0.0762 | -2.68% | |
0.00001726 | 8.01% | |
0.00000000000014 | 0.00% | |
0.00008773 | -2.07% | |
0.00012384 | -2.49% | |
0.00000000001173 | 1.03% | |
0.00042 | 40.00% | |
101.25 | -1.34% | |
0.0323 | 0.94% | |
0.00000356 | -1.39% | |
0.0000000453 | -3.21% | |
0.00000018000 | -37.89% | |
0.2958 | -6.36% | |
0.1451 | 2.54% | |
12.22 | -6.86% | |
0.00000000000019 | -5.00% | |
0.0004947 | 3.43% | |
0.5095 | -0.89% | |
0.000062 | 5.08% | |
0.00877 | -9.77% | |
0.3802 | 0.98% | |
22.663 | -0.84% | |
0.8761 | 1.29% | |
0.00755 | -0.13% | |
0.000000000000840 | 3.96% | |
0.0076 | -8.43% | |
0.000600 | 0.00% | |
1.702 | -4.27% | |
0.003503 | 0.06% | |
0.00000000000476 | 12.26% | |
0.0000008 | 100.00% | |
0.000000000301 | -27.99% | |
0.0433 | -2.48% | |
0.00016 | -23.81% | |
0.00014 | 100.00% | |
0.0295 | -1.34% | |
0.0783 | 2.09% | |
0.000350 | 0.29% | |
0.0003586 | 4.06% | |
0.0799 | -6.98% | |
0.0001100 | -2.57% | |
0.03346 | -6.87% | |
1.286 | 1.18% | |
0.1255 | -4.27% | |
0.2171 | -0.09% | |
0.01191 | -0.75% | |
0.2410 | -5.71% | |
0.0050 | -27.54% | |
0.00189 | -16.00% | |
0.2985 | -1.00% | |
0.0000512 | -16.75% | |
0.00002 | -33.33% | |
16.12 | -0.80% | |
0.0424 | -2.75% | |
0.2223 | 2.30% | |
0.04192 | 3.02% | |
0.0013 | 8.33% | |
0.01270 | 18.80% | |
0.0000239 | 0.42% | |
0.00748 | -1.71% | |
0.000002066 | -8.79% | |
0.4954 | 2.25% | |
0.000000000235 | -3.69% | |
0.02216 | 0.14% | |
0.5487 | -1.22% | |
0.000001655 | 4.09% | |
2.822 | -4.47% | |
0.03718 | -8.92% | |
0.00743 | -4.01% | |
0.002700 | 4.98% | |
0.003410 | -2.10% | |
0.005978 | 37.11% | |
0.0006999 | -3.18% | |
0.0694 | 0.73% | |
0.05911 | -1.42% | |
0.1247 | -2.20% | |
0.000018 | 0.00% | |
0.000000000004600 | -1.90% | |
0.0000008 | -20.00% | |
0.01039 | -7.15% | |
0.00000000003312 | 0.00% | |
2.023 | -0.39% | |
0.0005 | 0.00% | |
0.00002 | -60.00% | |
0.000000000019 | 0.00% | |
0.001197 | 0.00% | |
0.003880 | -3.60% | |
0.00000006 | 0.00% | |
0.0000032 | 10.34% | |
0.00998 | 1.53% | |
0.003938 | -0.10% | |
0.04453 | -1.50% | |
0.010200 | 0.99% | |
0.000000000037 | -7.50% | |
0.1764 | -1.73% | |
0.00000000003543 | 0.60% | |
0.00000000000652 | 0.15% | |
0.00010999 | 80.10% | |
0.01222 | -4.75% | |
0.0000063 | -37.00% | |
0.05600 | 0.52% | |
0.0151 | 12.69% | |
0.001000 | -4.03% | |
0.000000000765 | 0.00% | |
0.1605 | -0.43% | |
0.0000000000000158 | -3.66% | |
0.01788 | 5.92% | |
1.2886 | -4.49% | |
0.4417 | -0.99% | |
0.1709 | -0.18% | |
0.00599 | -0.33% | |
0.0001623 | 1.56% | |
0.0012 | 0.00% | |
0.03420 | -0.29% | |
0.000122 | 3.39% | |
0.000167 | -5.11% | |
0.00002 | -75.00% | |
0.00004 | 0.00% | |
0.1119 | -1.76% | |
2.2869 | -0.20% | |
50.0000 | 0.00% | |
0.02406 | -9.96% | |
0.02049 | 10.28% | |
0.0658 | -1.94% | |
0.02803 | -19.20% | |
0.0896 | 0.79% | |
0.000000001934 | 20.05% | |
0.024504 | 0.00% | |
0.0000509 | 0.39% | |
0.00001 | 0.00% | |
0.0984 | -1.01% | |
0.0000082 | -3.53% | |
0.001859 | -7.83% | |
0.00412 | -1.44% | |
0.000920 | -3.46% | |
0.000000084 | -15.15% | |
0.00006 | -53.85% | |
2.202 | 2.18% | |
0.0306 | -1.29% | |
0.000794 | -6.26% | |
0.02693 | -1.79% | |
0.000119 | 0.00% | |
0.00236 | -4.84% | |
0.1208 | -5.48% | |
0.0000194 | -37.42% | |
0.001615 | -9.83% | |
0.0114 | 4.59% | |
0.0007 | 0.00% | |
0.0001 | 0.00% | |
0.6997 | -0.01% | |
0.000019 | 0.00% | |
0.0098 | 0.00% | |
0.00004358 | 0.62% | |
0.01749 | -1.58% | |
0.000900 | 49.50% | |
0.00000000015902 | 1.24% | |
0.00000051 | 0.00% | |
0.00000000000101 | 1.00% | |
0.00010 | 42.86% | |
0.003484 | -3.06% | |
0.0000239 | 9.13% | |
0.00482 | -2.82% | |
0.0005783 | -3.62% | |
0.0002 | 0.00% | |
48.691 | -0.38% | |
0.000022 | -8.33% | |
1.061 | -1.49% | |
0.000000000001597 | 2.63% | |
0.0000213 | 0.47% | |
0.004521 | -5.20% | |
0.0782 | -1.01% | |
0.00013885 | -0.28% | |
0.000001955 | -0.71% | |
0.0000094 | -31.88% | |
0.00083 | -19.42% | |
0.0116 | -3.33% | |
0.01468 | -4.61% | |
0.000064 | 0.00% | |
0.000024 | -27.27% | |
0.0740 | -1.99% | |
0.6778 | -1.85% | |
0.0000056 | -8.20% | |
0.0000442 | 34.35% | |
0.000000000525 | 16.93% | |
0.00000000000289 | 0.70% | |
0.000005 | -28.57% | |
0.0000001300 | 0.00% | |
0.000001300 | -45.83% | |
0.001263 | 0.00% | |
0.0000119 | 0.00% | |
0.000189410 | 0.11% | |
0.000028 | 3.70% | |
0.000000000009 | 0.00% | |
0.00009149 | -4.12% | |
0.000011 | 0.00% | |
0.00113 | 44.87% | |
0.0000000109 | 105.66% | |
0.00000000051 | -5.56% | |
0.0009 | 0.00% | |
0.007999 | -0.01% | |
0.0000193 | 0.52% | |
0.00004398 | 0.00% | |
0.0629 | -1.41% | |
0.3838 | 7.09% | |
1.0689 | -5.78% | |
0.01240 | 0.65% | |
0.5384 | -1.90% | |
0.0970 | -1.22% | |
0.01540 | 1.12% | |
0.000913 | -2.35% | |
0.09613 | 0.96% | |
0.416 | 0.97% | |
0.00011 | -15.38% | |
0.1048 | 0.58% | |
0.002147 | 2.43% | |
0.001275 | -1.62% | |
1.4252 | -3.59% | |
58.5600 | 0.00% | |
0.001115 | 1.92% | |
0.004657 | 3.49% | |
0.0001450 | 0.00% | |
0.0443 | -5.94% | |
0.02899 | 0.07% | |
17.412 | -6.46% | |
0.0003495 | 0.00% | |
0.08113 | -0.22% | |
0.0006276 | -7.27% | |
0.003187 | -5.43% | |
0.00385 | 0.00% | |
0.0009012 | 0.00% | |
0.005289 | -6.55% | |
0.0003946 | 0.74% | |
0.001643 | -6.49% | |
0.000057 | -1.72% | |
0.0007993 | 0.00% | |
5.956 | -0.27% | |
0.1915 | -6.36% | |
0.0000579 | -1.03% | |
0.001225 | -10.06% | |
0.002813 | -5.57% | |
0.002594 | -2.63% | |
0.002258 | -2.67% | |
0.2162 | 2.51% | |
1899.00 | 0.00% | |
0.4190 | 2.97% | |
1.72 | -1.15% | |
0.0975 | -0.20% | |
0.1054 | -11.87% | |
0.04291 | -1.70% | |
0.000115 | -0.86% | |
0.4916 | -2.81% | |
0.000858 | 13.19% | |
0.1267 | -0.47% | |
1.275 | 4.34% | |
0.0390 | -1.27% | |
0.00206 | -0.48% | |
0.00000285 | -1.04% | |
0.00997 | 0.50% | |
3.8900 | 0.00% | |
2.78 | -3.47% | |
0.547 | 3.80% | |
0.1037 | 4.64% | |
1.000000 | 0.00% | |
0.1764 | 2.26% | |
0.3771 | 0.00% | |
0.5732 | 0.00% | |
1.878 | 6.40% | |
2.691 | 0.22% | |
0.0341 | -3.40% | |
0.0520 | -0.95% | |
0.000000050 | 16.28% | |
0.0001320 | 0.00% | |
0.1329 | 0.45% | |
0.07022 | 0.37% | |
0.00737 | 0.68% | |
0.633 | -1.71% | |
0.0700 | 0.00% | |
0.000000000003 | 0.00% | |
0.001104 | -0.54% | |
0.00000080 | 0.00% | |
0.1654 | 0.24% | |
0.000216 | 0.00% | |
0.0000000030216 | 0.02% | |
1.5000 | 0.00% | |
3.9889 | 0.00% | |
0.0791 | 0.13% | |
1.1371 | 0.00% | |
0.000079 | 0.00% | |
0.4424 | 0.00% | |
0.0376 | -3.84% | |
0.0517 | 1.77% | |
0.000378 | 2.44% | |
0.0071 | 0.00% | |
0.01572 | -0.82% | |
0.000210 | 0.00% | |
1.396 | 0.50% | |
0.00777 | -1.02% | |
0.1500 | -1.06% | |
6.80 | -1.31% | |
0.0417 | -2.11% | |
0.000452 | 0.00% | |
0.0271 | 0.00% | |
0.230000 | 0.00% | |
0.000000002465 | 2.11% | |
0.00000011220 | 0.00% | |
0.00000043 | 2.38% | |
0.1204 | 0.00% | |
0.004000 | 0.00% | |
4.67 | -1.27% | |
0.000300 | 0.00% | |
0.00035 | 0.00% | |
0.000000041 | -4.65% | |
0.0005 | 0.00% | |
0.00033 | 0.00% | |
0.011926 | 0.00% | |
0.001100 | 0.00% | |
0.000365 | 0.00% | |
0.0063 | 0.00% | |
0.0000002593 | 0.00% | |
0.00001584 | 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% | |
0.2464 | 0.16% | |
0.000902 | 0.00% | |
0.0230 | -7.63% | |
0.000000000768 | -3.40% | |
0.0001 | 0.00% | |
0.0009 | 0.00% | |
0.0560 | 0.00% | |
0.000453 | 0.44% | |
0.00000103 | 0.00% | |
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 | 0.00% | |
0.000000008400 | 0.00% | |
0.0000002150 | -9.13% | |
0.000427 | 0.00% | |
0.0063 | 0.00% | |
0.000310 | 0.00% | |
0.3284 | 0.00% | |
0.9900 | 0.00% | |
0.0055 | 0.00% | |
0.000405 | 0.00% | |
-- | -- | |
0.00000000000101 | 0.00% | |
0.001290 | 0.00% | |
0.00000011 | 0.00% | |
0.0000006646 | -0.06% | |
0.001000 | 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% | |
0.0010 | 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% | |
0.000000000118 | 3.51% | |
0.05056 | 0.00% | |
1.3575 | 0.00% | |
0.00136 | 0.00% | |
0.000092 | 0.00% | |
0.000042 | 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% | |
0.0084 | 0.00% | |
0.018559 | 0.00% | |
0.9990 | 0.00% | |
0.0000111 | 0.00% | |
0.00000151 | 0.00% | |
0.006500 | 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% | |
0.0192 | 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% | |
1.257 | -1.02% | |
3.7189 | 0.00% | |
0.00000011 | 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% | |
0.001100 | 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% | |
0.1769 | 0.00% | |
0.0000000195 | -4.41% | |
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% | |
0.04422 | -2.56% | |
0.0550 | 0.00% | |
0.004248 | -2.32% | |
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% | |
0.00023 | 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 | -2.79% | |
0.0000085 | -3.41% | |
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% | |
1.3203 | -0.53% | |
0.00995 | 0.00% | |
0.00390 | 0.00% | |
0.0000325 | 0.00% | |
0.017744 | 0.00% | |
1.0000 | 0.00% | |
0.00450 | 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% | |
0.1600 | 0.00% | |
0.000000005 | 0.00% | |
0.001035 | 0.00% | |
0.001518 | 0.00% | |
0.00083 | 0.00% | |
0.000313 | 0.00% | |
0.0007000 | 0.00% | |
0.00011 | 0.00% | |
0.00101 | 0.00% | |
0.00200 | 0.00% | |
0.0032 | 0.00% | |
0.3905 | 0.00% | |
0.000495 | 0.00% | |
0.00046 | 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% | |
0.000700 | 0.00% | |
0.01030 | 0.00% | |
3.7449 | 0.00% | |
0.008231 | 0.00% | |
0.00233 | 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% | |
0.00622 | 0.00% | |
0.000000000129 | 0.00% | |
0.000426832 | 0.00% | |
0.00002801 | 0.00% | |
6.4004 | 0.00% | |
0.00776 | 0.00% | |
0.0810 | 0.00% | |
0.0000245 | 0.00% | |
0.1197 | 0.00% | |
0.00056 | 0.00% | |
0.0030487 | 0.00% | |
0.000003726 | 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% | |
0.0000211 | 0.00% | |
0.4400 | 0.00% | |
1.4371 | 0.00% | |
0.0002100 | 0.00% | |
0.0000259 | 0.00% | |
0.00625 | 0.00% | |
0.6000 | 0.00% | |
0.0000002925 | 0.00% | |
0.05575 | 0.00% | |
0.250 | 0.00% | |
0.001106 | 0.00% | |
0.0249 | 0.00% | |
0.6608 | 0.00% | |
0.000000000763 | -4.86% | |
0.00500 | 0.00% | |
3.58 | 0.00% | |
0.0020 | 0.00% | |
0.00538 | 0.00% | |
0.02665 | 1.22% | |
0.4240 | -2.35% | |
0.317 | 0.32% | |
0.000000001868 | 0.00% | |
0.0018 | 0.00% | |
5155.00 | 0.00% | |
0.0091 | 0.00% |