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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0.09938 | -0.68% | |
0.7922 | 1.81% | |
0.000855 | -0.47% | |
0.3381 | -2.23% | |
0.004374 | 6.48% | |
0.000000001275 | 0.00% | |
0.00000730 | 1.53% | |
0.0002194 | -2.14% | |
0.000308 | 4.41% | |
2.7258 | 1.21% | |
0.008088 | 0.26% | |
0.00408 | -9.53% | |
0.1590 | -4.56% | |
0.000000047104 | 2.15% | |
0.002003 | -11.76% | |
0.005635 | -1.07% | |
0.747 | 0.67% | |
0.1947 | 3.73% | |
0.063422 | 1.68% | |
0.06200 | -0.24% | |
0.004936 | -0.88% | |
0.7188 | 39.28% | |
0.3490 | -1.36% | |
0.00000006476 | 2.45% | |
1.1279667 | 0.42% | |
0.0003647 | -17.28% | |
0.000356 | 0.56% | |
0.7063 | 1.54% | |
0.003058 | -5.00% | |
0.0040 | 0.00% | |
6.8894 | -0.64% | |
0.00001618 | 5.13% | |
0.2076 | 0.87% | |
0.000380 | -1.55% | |
0.00189 | 7.39% | |
1294 | -0.23% | |
0.002711 | -2.55% | |
1.0501 | -0.19% | |
0.00364 | 0.28% | |
0.3479 | -2.25% | |
139.94 | -0.11% | |
0.02275 | 1.34% | |
0.02958 | 0.96% | |
0.001560 | 0.00% | |
1.7185 | 5.11% | |
0.000724 | 1.69% | |
0.007442 | -2.72% | |
0.0030050 | -1.09% | |
0.3470 | 0.00% | |
0.1064 | 3.50% | |
0.0002248 | -0.75% | |
0.57104 | 5.42% | |
0.01464 | -0.34% | |
0.000757 | 13.32% | |
0.00004162 | -23.74% | |
9.606 | -0.45% | |
9.1204 | -8.81% | |
0.01350 | 14.41% | |
0.0200 | 1.01% | |
4.412 | 2.89% | |
0.0000503 | -2.52% | |
0.2062 | -9.24% | |
16.7693 | -2.27% | |
0.00460 | 2.22% | |
0.000694 | 15.67% | |
0.0425 | 1.19% | |
0.0094 | -21.67% | |
0.0000426 | 36.10% | |
0.00006741 | 0.46% | |
0.00001989 | 0.71% | |
0.0239 | 0.42% | |
15.97 | -1.90% | |
0.2413 | 0.00% | |
0.00888 | 11.00% | |
0.0600 | 2.21% | |
0.00146 | 44.55% | |
0.01090 | -4.64% | |
4.7461 | -3.00% | |
1.7628 | 4.57% | |
0.0140 | 9.38% | |
0.472 | 1.29% | |
0.0611 | 0.49% | |
13.58 | 10.32% | |
0.00013797 | -0.38% | |
0.00000629 | -1.56% | |
4.860 | -3.49% | |
0.4689 | 7.82% | |
0.01507 | 3.01% | |
0.1096 | 2.81% | |
0.001178 | -3.52% | |
0.00312546 | 3.97% | |
0.01095 | 1.39% | |
0.000000001717 | 5.99% | |
0.01091 | 3.51% | |
0.01247 | -0.08% | |
0.0062 | -4.62% | |
0.0836 | -0.59% | |
0.0004193 | 12.99% | |
0.012160 | 0.00% | |
0.0002912 | 6.32% | |
0.0000957 | 0.74% | |
0.0000158 | 10.49% | |
0.0476 | -2.86% | |
0.00942 | 10.18% | |
0.0009530 | 7.61% | |
0.0000580 | -3.33% | |
0.0000000131 | -2.96% | |
0.409 | -0.24% | |
0.0262 | 1.16% | |
0.01780 | 0.91% | |
0.000345 | 15.38% | |
0.00194 | 487.88% | |
0.04348 | 2.47% | |
305.3 | 2.55% | |
0.00004011 | -12.80% | |
0.01817 | 8.67% | |
0.0000244 | 2.95% | |
0.000098 | 7.69% | |
0.05101 | 1.13% | |
0.0018818 | -1.96% | |
0.0000000738 | -10.55% | |
0.000450 | -40.32% | |
0.001973 | 0.00% | |
0.0000000381 | 0.79% | |
0.015910 | -14.27% | |
0.3356 | 2.32% | |
4.46 | -2.41% | |
2.213 | -2.55% | |
0.02455 | -9.41% | |
0.001750 | -2.78% | |
0.02733 | 0.22% | |
0.0480 | 1.27% | |
0.00228 | -1.72% | |
0.00930 | 1.31% | |
31.0000 | 0.00% | |
0.3326 | -3.00% | |
0.0002447 | 1.62% | |
0.00598 | -1.16% | |
0.011343 | 4.11% | |
2.943 | 2.22% | |
0.005410 | 0.60% | |
0.000202 | -8.60% | |
0.1658 | -6.01% | |
0.00530 | 0.76% | |
0.4455 | -2.67% | |
0.002335 | 16.46% | |
0.000001459 | 6.11% | |
0.0208 | -8.77% | |
0.000823 | -0.72% | |
0.004235 | 8.26% | |
0.000030 | -34.78% | |
0.04051 | -1.60% | |
0.00953 | 7.20% | |
0.5520 | -12.12% | |
0.1028 | -0.96% | |
0.7591 | 14.89% | |
10.99 | 2.04% | |
0.0100 | -10.71% | |
0.002835 | 3.77% | |
0.513 | -0.19% | |
0.0655 | 5.31% | |
0.003111 | -11.14% | |
0.002267 | -0.53% | |
0.02420 | -5.54% | |
0.02352 | 2.75% | |
15.16 | 1.40% | |
0.537 | 1.13% | |
0.00000001144 | 0.62% | |
0.04345 | 0.72% | |
0.2389 | -2.69% | |
0.006362 | -0.17% | |
0.0177 | 7.93% | |
0.1220 | 1.92% | |
0.06186 | 0.63% | |
0.2923 | -3.44% | |
0.02605 | 0.62% | |
0.01057 | -2.58% | |
0.0004091 | 26.30% | |
0.1324 | 0.61% | |
0.03377 | -1.52% | |
0.02743 | 4.34% | |
1.470 | -12.45% | |
0.002584 | 8.07% | |
0.010991 | -8.31% | |
0.012754 | 1.33% | |
0.006373 | 9.41% | |
0.0806 | 1.90% | |
0.547 | 7.47% | |
0.0000561 | -6.34% | |
0.5500 | 2.77% | |
0.00000001393 | 6.25% | |
0.06220 | 0.97% | |
0.1059 | -7.67% | |
0.01310 | 1.87% | |
0.000194315 | -3.14% | |
3.488 | 1.87% | |
0.249693 | -0.15% | |
0.0000000800 | 10.19% | |
0.00000013283 | 1.72% | |
0.024139 | -0.33% | |
0.0000000001867 | 2.47% | |
0.00000000001435 | -23.02% | |
0.002335 | -5.81% | |
6.47 | 1.89% | |
0.001521 | 8.41% | |
0.00200 | 47.06% | |
5.373 | 2.38% | |
27.19 | 2.68% | |
0.0095 | 4.40% | |
0.002899 | -0.17% | |
0.0514 | 1.58% | |
0.00561 | -6.03% | |
0.003099 | -2.33% | |
0.0001886 | 2.78% | |
0.00661 | -2.51% | |
0.0087 | -13.00% | |
0.2941 | -0.37% | |
0.000908 | -7.44% | |
0.1893 | -3.76% | |
0.0004626 | -13.53% | |
0.7607 | -0.08% | |
0.0052 | 108.00% | |
0.001935 | 1.15% | |
0.0511 | -40.86% | |
0.004308 | -13.93% | |
0.00000353 | -0.84% | |
0.003482 | -26.82% | |
0.0972 | 2.64% | |
0.00000391 | -6.68% | |
0.003985 | 2.13% | |
0.0004049 | 3.82% | |
0.002848 | 3.56% | |
0.04416 | 4.84% | |
0.0602 | 2.21% | |
0.01450 | -1.83% | |
0.03350 | 0.36% | |
0.002900 | 38.10% | |
20.99 | 11.71% | |
0.09238 | 1.47% | |
8.41 | 0.24% | |
0.0003358 | 2.75% | |
0.00016 | -20.00% | |
0.0002545 | 0.16% | |
6.3140 | 2.15% | |
0.03827 | 6.78% | |
0.000197 | -5.74% | |
0.0000002505 | 0.20% | |
0.0002041 | 1.34% | |
0.599 | 3.10% | |
0.000825 | -4.51% | |
0.01155 | -2.61% | |
0.01396 | 2.42% | |
0.0396 | 3.13% | |
2.206 | 8.62% | |
0.000784 | -2.97% | |
0.002191 | -3.27% | |
0.003449 | 4.55% | |
0.001708 | 3.14% | |
0.0546 | -5.21% | |
0.0000020 | 0.00% | |
0.0000544 | 0.00% | |
0.1421 | -0.42% | |
0.0000000512 | 6.44% | |
0.0578 | -0.34% | |
0.0029 | 31.82% | |
0.0051000 | -0.10% | |
0.481 | 2.56% | |
0.01974 | 2.71% | |
0.00931 | -14.11% | |
0.001525 | 0.93% | |
0.0090 | 80.00% | |
59.37 | 3.49% | |
0.305 | 0.99% | |
0.000098 | 22.50% | |
0.10428 | -1.79% | |
16.79 | 2.00% | |
0.030121 | 0.01% | |
0.0097 | -2.02% | |
0.000283 | 11.42% | |
0.707 | 1.58% | |
0.00000000003205 | -3.14% | |
0.000067 | 21.82% | |
0.5236 | 4.57% | |
0.000498 | -3.30% | |
0.003146 | -20.29% | |
0.00000001470 | 4.48% | |
0.01121 | 0.72% | |
0.760 | -0.39% | |
0.00000013002 | -52.55% | |
0.1232 | -0.40% | |
0.000000000226 | -1.74% | |
1.731 | 1.52% | |
0.0286 | -4.35% | |
0.7580 | -4.49% | |
0.017330 | -2.33% | |
0.1848 | 0.16% | |
0.003426 | 2.33% | |
0.2422 | 1.38% | |
0.00843 | 0.84% | |
0.00000000000344 | -11.57% | |
0.007994 | -0.05% | |
0.0000085 | 3.66% | |
0.00705 | -0.70% | |
0.00210 | 0.96% | |
0.0000080 | -6.98% | |
0.003099 | -0.39% | |
0.0485 | 1.25% | |
0.0834 | 0.12% | |
0.8457 | -1.58% | |
0.003645 | -7.06% | |
0.06038 | 2.22% | |
0.0000039 | 0.00% | |
0.04480 | -0.44% | |
0.001650 | -2.42% | |
0.01238 | 8.69% | |
0.05920 | 2.00% | |
0.01115 | 6.29% | |
0.0155 | 4.73% | |
0.0532 | 0.95% | |
0.000000091 | -2.15% | |
0.00003186 | 0.60% | |
0.001184 | -4.59% | |
0.001030 | 1.38% | |
0.000491 | 1.24% | |
0.004729 | -0.04% | |
0.000515 | -3.92% | |
1.304 | 3.08% | |
0.0756 | -6.67% | |
0.0899 | -0.99% | |
0.00898 | 6.65% | |
0.00000285 | 1.06% | |
0.000261 | 4.40% | |
0.4164 | 3.20% | |
22.510 | 1.57% | |
0.1101 | 1.10% | |
4.878 | 1.41% | |
0.000594 | 0.17% | |
0.000962 | 16.89% | |
0.1714 | 1.60% | |
0.000000000000805 | -7.47% | |
0.003505 | 16.52% | |
0.00010000 | -9.08% | |
0.01809 | -12.78% | |
0.00003445 | 2.07% | |
0.000001772 | -14.40% | |
0.0000000000000136 | 3.03% | |
0.0555 | -1.25% | |
0.014453 | 2.11% | |
0.05267 | -8.00% | |
0.0000016751 | 1.88% | |
48.213 | 0.22% | |
0.02644 | -0.75% | |
0.1884 | 2.56% | |
0.6520 | 0.88% | |
0.03765 | 1.29% | |
0.001107 | -7.98% | |
0.0000000590 | 1.72% | |
1.930 | 0.00% | |
0.0005029 | -1.87% | |
0.000000440 | 0.00% | |
0.002570 | -0.77% | |
0.02700 | 0.00% | |
0.07507 | -4.30% | |
0.0000562 | -3.10% | |
0.661 | 1.38% | |
0.0607 | 0.83% | |
0.0045 | -18.18% | |
0.000001461 | -0.41% | |
0.00220 | 11.68% | |
0.0412 | -55.56% | |
0.2471 | 2.36% | |
0.5070 | 2.88% | |
0.00003580 | 16.38% | |
0.1681 | -4.49% | |
0.0000086 | 86.96% | |
0.1890 | -0.42% | |
0.4317 | 3.48% | |
0.001300 | 1.33% | |
0.0006323 | 7.66% | |
0.000000000001507 | 1.14% | |
16.01 | 2.37% | |
0.01036 | -3.99% | |
0.00756 | 0.67% | |
0.003505 | 4.97% | |
13.20 | -0.30% | |
0.00009006 | -0.63% | |
0.000851 | -0.12% | |
0.00000016200 | -16.92% | |
0.1199 | 1.78% | |
0.1012 | -11.38% | |
0.001124 | 9.55% | |
0.000450 | -13.46% | |
2.048 | -6.14% | |
0.00002261 | -0.04% | |
12.15 | 1.33% | |
0.00839 | 5.93% | |
0.1064 | 0.85% | |
1.2086 | 1.55% | |
5.47 | 1.48% | |
0.00834 | 6.38% | |
0.000024 | -11.11% | |
0.0111 | 0.00% | |
0.0643 | -0.31% | |
0.9456 | 2.95% | |
0.6581 | -1.70% | |
0.05284 | -0.43% | |
0.00000867 | -22.86% | |
0.0000008 | 0.00% | |
0.00002 | -33.33% | |
0.0762 | -2.06% | |
2.352 | 7.06% | |
0.00487 | 2.31% | |
0.0000002377 | 12.23% | |
0.1024 | 1.89% | |
0.0832 | -2.23% | |
0.00000000188 | 3.87% | |
0.04161 | 8.19% | |
0.00818 | -4.33% | |
0.00285 | -3.06% | |
0.1891 | 1.34% | |
0.05033 | 0.66% | |
0.1031 | 1.18% | |
0.01140 | 2.33% | |
0.0671 | -0.89% | |
0.385 | 2.94% | |
0.0240 | -4.76% | |
0.1072 | 4.08% | |
0.007399 | -0.03% | |
0.0417 | 0.97% | |
0.000000002080 | 6.94% | |
0.1232 | 0.16% | |
0.704 | 19.32% | |
0.01731 | -2.04% | |
0.0055 | -20.29% | |
0.003039 | 3.33% | |
0.000031 | -18.42% | |
1.400 | 2.71% | |
0.0002201 | 0.05% | |
0.9746 | 0.00% | |
0.0000000030216 | 0.00% | |
0.1190 | -2.94% | |
16.04 | 1.71% | |
0.00151 | -0.66% | |
0.1670 | 1.77% | |
0.001650 | -9.89% | |
0.00006800 | 54.62% | |
0.01156 | -1.78% | |
0.05575 | 0.00% | |
0.0391 | -1.76% | |
39.98 | 2.96% | |
8.20 | 0.12% | |
0.611 | 4.09% | |
0.0000516 | 2.79% | |
0.01508 | 0.67% | |
0.356 | 18.27% | |
0.000092 | 1.10% | |
0.01372 | 3.24% | |
0.7827 | 1.06% | |
0.003835 | -1.77% | |
69.2 | 1.47% | |
0.000068 | 119.35% | |
0.03324 | -0.92% | |
0.1173 | -3.46% | |
0.003933 | -0.08% | |
0.02639 | -7.50% | |
1.2314 | 1.19% | |
0.0000512 | -19.24% | |
0.000433 | 0.46% | |
0.001348 | 0.90% | |
0.0951 | -6.21% | |
0.0079 | 17.91% | |
0.0000221 | -18.15% | |
0.2073 | -1.24% | |
0.0097 | 203.13% | |
0.000350 | 0.29% | |
0.0001708 | 5.24% | |
0.0778 | 1.17% | |
0.0737 | 1.94% | |
0.00072 | -11.11% | |
0.1124 | 0.45% | |
0.00000000000189 | -17.11% | |
0.000353 | -13.69% | |
0.0009 | 0.00% | |
0.02709 | -0.26% | |
0.00000003512 | -0.20% | |
0.00000000001765 | -5.21% | |
0.001159 | 2.66% | |
0.0005613 | 3.79% | |
0.746 | -2.48% | |
0.1525 | 1.19% | |
0.008231 | 0.00% | |
0.0003757 | -9.12% | |
0.000000000705 | -2.22% | |
0.0175 | 16.67% | |
0.00005024 | 12.65% | |
0.00755 | 0.00% | |
0.00000000000871 | 33.59% | |
16.28 | 0.93% | |
0.0006443 | 1.43% | |
0.1555 | -1.64% | |
0.000288 | 0.00% | |
1.972 | 2.23% | |
0.00093 | 5.68% | |
0.00000006 | -45.45% | |
1.0271 | -3.18% | |
0.0383 | -30.36% | |
0.00000000000015 | -25.00% | |
0.0334 | 0.60% | |
0.0012 | 20.00% | |
9.193 | 0.98% | |
0.4450 | 0.00% | |
0.006500 | 116.67% | |
17.8750 | -5.64% | |
0.01447 | 0.84% | |
0.01540 | 1.18% | |
0.000167 | -2.34% | |
0.660 | 2.17% | |
0.2135 | 2.79% | |
0.01764 | 1.55% | |
0.000561 | 0.00% | |
0.01454 | -0.07% | |
0.0309 | 6.92% | |
0.2120 | 1.34% | |
449.00 | -0.22% | |
0.00006 | 0.00% | |
0.00121 | -17.69% | |
15.73 | 2.68% | |
0.0073 | -13.10% | |
0.1888 | 2.28% | |
0.000001780 | -16.82% | |
0.00012 | 9.09% | |
0.1439 | -0.35% | |
0.589 | 0.86% | |
0.0005 | 0.00% | |
0.00030000 | 0.00% | |
0.04057 | 18.63% | |
0.0005908 | -0.12% | |
0.0000055 | -1.79% | |
1.246 | -2.12% | |
0.005768 | -0.89% | |
0.0000119 | 0.00% | |
0.0000069538 | 1.06% | |
0.000001656 | 4.09% | |
0.00004140 | -5.18% | |
0.1683 | 2.75% | |
0.0334 | -13.47% | |
0.0004020 | 1.64% | |
0.0092 | -2.13% | |
0.003266 | 24.70% | |
0.0003071 | 0.46% | |
0.000022 | -8.33% | |
0.004157 | -0.43% | |
0.002026 | -0.20% | |
0.0000192 | -9.00% | |
0.1735 | 2.85% | |
0.3227 | -11.42% | |
0.0002998 | -14.22% | |
0.000869 | 6.23% | |
0.0006 | 0.00% | |
0.003512 | -9.48% | |
0.0001 | 0.00% | |
0.0000000000000158 | -4.82% | |
0.01523 | 1.47% | |
0.00000000000013 | -7.14% | |
0.1168 | 0.86% | |
0.00113 | 0.00% | |
0.002187 | -0.41% | |
0.02049 | 0.00% | |
2.404 | -6.79% | |
0.000453 | 0.22% | |
0.0028 | -20.00% | |
0.01735 | 2.18% | |
0.2413 | -1.19% | |
0.0015 | -16.67% | |
0.0000579 | 0.00% | |
0.0071 | 0.00% | |
0.2166 | 0.00% | |
0.00679 | -0.29% | |
1.73 | 1.17% | |
0.00008822 | 0.60% | |
0.000000000004640 | 18.37% | |
0.00151 | -10.65% | |
0.0217 | 0.46% | |
0.000092 | 0.00% | |
0.0295 | 0.00% | |
0.001581 | -0.06% | |
0.0305 | -4.39% | |
0.02100 | 32.08% | |
0.0999 | 2.36% | |
0.000000000021 | 50.00% | |
0.00000000000231 | -16.30% | |
0.1190 | -0.42% | |
0.03790 | 1.31% | |
0.004390 | -12.20% | |
0.0023 | 0.00% | |
0.0000071 | -18.39% | |
0.0969 | 1.47% | |
0.000000000786 | 2.21% | |
0.0000002930 | 0.17% | |
0.000000000099 | -6.60% | |
0.9900 | 0.00% | |
0.04813 | 11.18% | |
0.00069 | 9.52% | |
0.00639 | -17.65% | |
0.000063 | 1.61% | |
0.07144 | -2.84% | |
0.003282 | -1.77% | |
0.1520 | 0.00% | |
0.00150 | -11.76% | |
0.000265 | -0.38% | |
0.000000001868 | 0.00% | |
0.1161 | 0.69% | |
0.00000000000102 | 0.99% | |
0.0000301 | -37.68% | |
0.00000000001042 | -6.80% | |
0.001594 | -1.12% | |
0.2469 | 0.20% | |
0.000000000728 | -7.02% | |
0.0005896 | 2.79% | |
0.0000980 | -10.83% | |
0.0765 | -0.39% | |
0.0003827 | 10.42% | |
0.00000000031 | -42.59% | |
0.000022 | 0.00% | |
0.00000000016003 | 0.64% | |
0.0000000042 | -6.67% | |
1.815 | 1.23% | |
0.00787 | 4.24% | |
0.00000000003653 | 2.79% | |
0.00400 | 3.90% | |
0.000000000447 | -14.86% | |
0.0103 | 0.00% | |
0.000000040 | 2.56% | |
0.0009 | 50.00% | |
0.00000240 | 1.69% | |
0.00023474 | -1.56% | |
0.000055 | -1.79% | |
0.0000111 | 0.00% | |
0.0413 | 0.98% | |
0.000024 | 33.33% | |
0.00204 | 2.00% | |
0.00004 | 0.00% | |
0.000035 | -43.55% | |
0.01428 | 8.59% | |
0.0009 | -40.00% | |
0.000000000009 | 12.50% | |
0.000000008399 | -0.01% | |
0.0623 | -2.04% | |
0.00000058 | 13.73% | |
0.00023 | -8.00% | |
0.0001320 | 0.00% | |
0.000110 | -23.61% | |
0.00000000000095 | -3.06% | |
1.269 | 1.85% | |
0.0647 | 0.94% | |
0.0599 | 4.90% | |
0.0005376 | -2.63% | |
0.01683 | 0.12% | |
0.000681 | -0.73% | |
0.2758 | 0.69% | |
0.3026 | 2.06% | |
0.3587 | 3.25% | |
0.01164 | -2.68% | |
0.5353 | 1.21% | |
0.4277 | 1.04% | |
0.09263 | 0.90% | |
0.02831 | 6.11% | |
0.2622 | -4.72% | |
0.2850 | 2.78% | |
0.00012 | 0.00% | |
0.002121 | 1.58% | |
1.013 | 0.80% | |
0.2123 | -0.14% | |
58.5600 | 0.00% | |
0.001031 | -5.59% | |
0.0001451 | 0.07% | |
0.0461 | 5.01% | |
6.079 | -2.53% | |
0.000891 | -2.52% | |
0.02840 | -0.28% | |
0.0756 | -1.43% | |
18.009 | 2.86% | |
0.004603 | -0.15% | |
0.0009012 | 0.00% | |
0.17689 | 5.20% | |
0.005225 | 3.49% | |
0.00699 | 0.00% | |
0.0007993 | 0.00% | |
6.095 | 2.66% | |
0.2170 | 9.54% | |
0.001712 | -3.82% | |
0.02565 | -5.94% | |
0.001231 | -0.81% | |
2.6716 | 0.97% | |
0.002904 | 3.68% | |
0.02062 | 5.47% | |
0.0000467 | 0.00% | |
0.002420 | -5.76% | |
0.002360 | -5.71% | |
0.0013 | 0.00% | |
0.4177 | 3.06% | |
0.000113 | 0.89% | |
0.5011 | 4.29% | |
0.000879 | 6.16% | |
0.1222 | 1.75% | |
0.02656 | 0.15% | |
0.00405 | 3.85% | |
0.00496 | 14.55% | |
0.0753 | -9.17% | |
0.00910 | -1.30% | |
3.8900 | 0.00% | |
0.001112 | -0.09% | |
0.1038 | -3.62% | |
0.1733 | -0.29% | |
0.3771 | 0.00% | |
0.5732 | 0.00% | |
0.0486 | -4.89% | |
2.701 | -2.98% | |
0.000000049 | 0.00% | |
0.1345 | 2.20% | |
0.00083 | 0.00% | |
0.617 | 0.33% | |
0.6358 | 3.08% | |
0.0713 | 1.42% | |
0.0737 | -0.54% | |
0.001097 | 1.20% | |
0.00000080 | 0.00% | |
0.00000000000041 | 0.00% | |
0.000216 | 0.00% | |
0.451 | 1.81% | |
1.424 | 0.85% | |
1.5000 | 0.00% | |
3.9889 | 0.00% | |
0.0782 | 1.16% | |
1.1371 | 0.00% | |
0.867 | 1.40% | |
5.632 | 2.18% | |
0.000076 | -2.56% | |
0.02221 | -0.27% | |
0.4424 | 0.00% | |
0.0327 | -2.10% | |
0.0371 | 3.63% | |
0.000357 | -2.72% | |
0.2011 | 2.65% | |
0.0071 | 0.00% | |
0.2673 | 1.79% | |
0.000210 | 0.00% | |
0.2624 | 1.23% | |
0.0226 | 1.35% | |
0.1468 | 0.75% | |
6.65 | 0.45% | |
0.003902 | 3.01% | |
0.2352 | 1.47% | |
0.000452 | 0.00% | |
0.1985 | -0.55% | |
0.000000002436 | -0.41% | |
0.000190131 | 1.56% | |
0.00000041 | -2.38% | |
0.1204 | 0.00% | |
2.716 | 0.30% | |
1.038 | 1.17% | |
0.004000 | 0.00% | |
0.000300 | 0.00% | |
0.00035 | 0.00% | |
0.011926 | 0.00% | |
0.0000193 | 0.00% | |
0.4593 | 0.00% | |
0.001100 | 0.00% | |
0.000365 | 0.00% | |
0.001880 | 0.00% | |
0.0063 | 0.00% | |
0.0000002593 | 0.00% | |
0.00001584 | 0.00% | |
0.0000001013 | 0.00% | |
0.00006187 | 0.00% | |
0.001405 | 0.00% | |
0.000510 | -1.16% | |
0.000902 | 0.00% | |
0.0001 | 0.00% | |
0.0009 | 0.00% | |
0.0560 | 0.00% | |
0.0119 | 1.71% | |
0.00000103 | 0.00% | |
0.0000000104 | 0.00% | |
0.00000007 | 16.67% | |
0.00000000001605 | 0.00% | |
0.001000 | 0.00% | |
0.0000000106 | 0.00% | |
0.000000000375 | 0.00% | |
0.0063 | 0.00% | |
0.000310 | 0.00% | |
0.3284 | 0.00% | |
0.0055 | 0.00% | |
0.000405 | 0.00% | |
-- | -- | |
0.00000011 | 0.00% | |
0.0000006594 | 0.00% | |
0.001000 | 0.00% | |
0.001000 | 0.00% | |
0.000058 | 0.00% | |
1.6799 | 0.00% | |
0.00000000002387 | 0.00% | |
0.00425 | 0.00% | |
0.0007670 | 1.52% | |
0.000112 | 0.00% | |
0.00037 | 0.00% | |
0.001963 | 0.00% | |
0.00000055 | 0.00% | |
0.2993 | 0.00% | |
0.00006767 | 0.00% | |
0.001263 | 0.00% | |
0.001210 | 0.00% | |
0.00171 | 0.00% | |
0.0195 | 0.00% | |
0.05056 | 0.00% | |
0.000024 | 0.00% | |
0.001234 | 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% | |
0.006490 | 0.00% | |
0.000363 | 0.00% | |
0.0012 | 0.00% | |
6.2788 | 0.00% | |
0.001000 | 0.00% | |
0.0192 | 0.00% | |
0.0006 | 0.00% | |
0.0786 | 0.00% | |
0.001200 | 0.00% | |
0.00000000000540 | 0.00% | |
0.000028 | 0.00% | |
0.000999 | 0.00% | |
0.001801 | 0.00% | |
0.0200 | 0.00% | |
0.0093 | 0.00% | |
0.0006 | 0.00% | |
65.1101 | 0.00% | |
3.7189 | 0.00% | |
0.000082 | 0.00% | |
0.016111 | 0.00% | |
4.1000 | 0.00% | |
0.0489 | 0.00% | |
0.00008773 | 0.00% | |
0.0131 | 0.00% | |
4.4022 | 0.00% | |
0.0745 | 0.00% | |
0.001120 | 0.00% | |
0.000412 | 0.00% | |
0.001100 | 0.00% | |
0.3882 | 0.00% | |
0.001000 | 0.00% | |
0.076250 | 0.00% | |
0.0150 | 0.00% | |
0.0036 | 0.00% | |
0.001815 | -0.55% | |
0.1769 | 0.00% | |
2.2869 | 0.00% | |
0.0000000204 | 2.51% | |
0.000258 | 0.00% | |
0.000701 | 0.00% | |
0.03000 | 0.00% | |
0.000946 | 0.00% | |
0.013728 | 0.00% | |
0.4820 | 0.00% | |
0.0490 | 0.00% | |
0.0096 | 0.00% | |
0.004189 | 0.62% | |
1.76670591 | 0.00% | |
0.000399 | 0.00% | |
0.0000000000270 | 0.00% | |
0.0000002850 | 0.00% | |
0.6700 | 0.00% | |
0.00011 | 0.00% | |
0.000835 | 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% | |
0.0650 | 0.00% | |
0.00125 | 0.00% | |
1.0100 | 0.00% | |
0.010200 | 0.00% | |
0.88686 | 0.00% | |
0.03644 | 0.00% | |
0.0000164 | 0.00% | |
0.1723 | 0.00% | |
0.01463 | 0.00% | |
0.00614 | 0.00% | |
0.4606 | 0.00% | |
0.001800 | 0.00% | |
0.00126 | 0.00% | |
0.000001000 | 0.00% | |
104.52 | 0.00% | |
0.0000008 | 0.00% | |
1.3388 | 1.76% | |
0.00390 | 0.00% | |
0.0000194 | 0.00% | |
0.0000325 | 0.00% | |
1.0000 | 0.00% | |
0.34211 | 0.00% | |
0.00130 | 0.00% | |
0.0000077 | 0.00% | |
0.0005 | 0.00% | |
0.001277 | 0.00% | |
0.03520 | 0.00% | |
0.0000023 | 0.00% | |
0.000000005 | 0.00% | |
0.001200 | 0.00% | |
0.001518 | 0.00% | |
0.000313 | 0.00% | |
0.0000032 | 0.00% | |
0.0007000 | 0.00% | |
0.00200 | 0.00% | |
0.000000000568 | 0.00% | |
0.0048 | 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% | |
0.0000063 | 0.00% | |
0.001745 | 0.00% | |
0.00625 | 0.00% | |
0.0900 | 0.00% | |
0.00006 | 0.00% | |
0.000506 | 0.00% | |
1939.10 | 0.00% | |
0.01030 | 0.00% | |
3.7449 | 0.00% | |
0.00233 | 0.00% | |
0.00070 | 0.00% | |
0.0000269 | 0.00% | |
0.0000000500 | 0.00% | |
0.0000001300 | 0.00% | |
0.000900 | 0.00% | |
0.000426832 | 0.00% | |
0.00002803 | 0.00% | |
0.0810 | 0.00% | |
0.0000245 | 0.00% | |
0.000064 | 0.00% | |
0.1197 | 0.00% | |
0.00056 | 0.00% | |
0.0030487 | 0.00% | |
0.000003726 | 0.00% | |
0.000510 | 0.00% | |
0.00200 | 0.00% | |
0.0001100 | 0.00% | |
0.3101 | 0.00% | |
1.4371 | 0.00% | |
0.0002100 | 0.00% | |
0.00236 | 0.00% | |
0.0000257 | 0.00% | |
0.00625 | 0.00% | |
0.6003 | 0.00% | |
1899.00 | 0.00% | |
0.002686 | 0.00% | |
0.250 | 0.00% | |
0.3358 | 1.18% | |
0.001106 | 0.00% | |
0.0249 | 0.00% | |
0.6608 | 0.00% | |
0.00500 | 0.00% | |
3.58 | 0.00% | |
0.00981 | 1.34% | |
0.00538 | 0.00% | |
0.4282 | -1.59% | |
5155.00 | 0.00% | |
1.195 | 1.88% | |
1.334 | 1.06% | |
0.0091 | 0.00% |