Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Blockchain validates transactions with consensus algorithms. Bitcoin and Ethereum use Proof-of-Work, while Polkadot and Cardano use Proof-of-Stake.

Other consensus protocols are used to verify transactions besides these two. This post focuses on Proof-of-Time (PoT), used by Analog, and Proof-of-History (PoH), used by Solana as a hybrid consensus protocol.

PoT and PoH may seem similar to users, but they are actually very different protocols.

Proof-of-Time (PoT)

Analog developed Proof-of-Time (PoT) based on Delegated Proof-of-Stake (DPoS). Users select "delegates" to validate the next block in DPoS. PoT uses a ranking system, and validators stake an equal amount of tokens. Validators also "self-select" themselves via a verifiable random function."

The ranking system gives network validators a performance score, with trustworthy validators with a long history getting higher scores. System also considers validator's fixed stake. PoT's ledger is called "Timechain."

Voting on delegates borrows from DPoS, but there are changes. PoT's first voting stage has validators (or "time electors" putting forward a block to be included in the ledger).

Validators are chosen randomly based on their ranking score and fixed stake. One validator is chosen at a time using a Verifiable Delay Function (VDF).

Validators use a verifiable delay function to determine if they'll propose a Timechain block. If chosen, they validate the transaction and generate a VDF proof before submitting both to other Timechain nodes.

This leads to the second process, where the transaction is passed through 1,000 validators selected using the same method. Each validator checks the transaction to ensure it's valid.

If the transaction passes, validators accept the block, and if over 2/3 accept it, it's added to the Timechain.

Proof-of-History (PoH)

Proof-of-History is a consensus algorithm that proves when a transaction occurred. PoH uses a VDF to verify transactions, like Proof-of-Time. Similar to Proof-of-Work, VDFs use a lot of computing power to calculate but little to verify transactions, similar to (PoW).

This shows users and validators how long a transaction took to verify.

PoH uses VDFs to verify event intervals. This process uses cryptography to prevent determining output from input.

The outputs of one transaction are used as inputs for the next. Timestamps record the inputs' order. This checks if data was created before an event.

PoT vs. PoH

PoT and PoH differ in that:

• PoT uses VDFs to select validators (or time electors), while PoH measures time between events.

• PoH uses a VDF to validate transactions, while PoT uses a ranking system.

• PoT's VDF-elected validators verify transactions proposed by a previous validator. PoH uses a VDF to validate transactions and data.

Conclusion

Both Proof-of-Time (PoT) and Proof-of-History (PoH) validate blockchain transactions differently. PoT uses a ranking system to randomly select validators to verify transactions.

PoH uses a Verifiable Delay Function to validate transactions, verify how much time has passed between two events, and allow validators to quickly verify a transaction without malicious actors knowing the input.

Would you abandon your bank for Apple?

Banks are struggling.

• not as a result of inflation

• not due to the economic downturn.

• not due to the conflict in Ukraine.

But because they’re underestimating Apple.

Slowly but surely, Apple is looking more like a bank.

An easy new savings account like Apple

Apple has a new savings account.

Apple says Apple Card users may set up and manage savings straight in Wallet.

• No more charges

• Colorfully high yields

• With no minimum balance

• No minimal down payments

Most consumer-facing banks will have to match Apple's offer or suffer disruption.

Users may set it up from their iPhones without traveling to a bank or filling out paperwork.

It’s built into the iPhone in your pocket.

So now more waiting for slow approval processes.

Once the savings account is set up, Apple will automatically transfer all future Daily Cash into it. Users may also add these cash to an Apple Cash card in their Apple Wallet app and adjust where Daily Cash is paid at any time.

Apple Pay and Apple Wallet VP Jennifer Bailey:

Savings enables Apple Card users to grow their Daily Cash rewards over time, while also saving for the future.

Bailey says Savings adds value to Apple Card's Daily Cash benefit and offers another easy-to-use tool to help people lead healthier financial lives.

Transfer money from a linked bank account or Apple Cash to a Savings account. Users can withdraw monies to a connected bank account or Apple Cash card without costs.

Once set up, Apple Card customers can track their earnings via Wallet's Savings dashboard. This dashboard shows their account balance and interest.

This product targets younger people as the easiest way to start a savings account on the iPhone.

Why would a Gen Z account holder travel to the bank if their iPhone could be their bank?

Using this concept, Apple will transform the way we think about banking by 2030.

Two other nightmares keep bankers awake at night

Apple revealed two new features in early 2022 that banks and payment gateways hated.

• Tap to Pay with Apple

• Late Apple Pay

They startled the industry.

Tap To Pay converts iPhones into mobile POS card readers. Apple Pay Later is pushing the BNPL business in a consumer-friendly direction, hopefully ending dodgy lending practices.

Tap to Pay with Apple

iPhone POS

Millions of US merchants, from tiny shops to huge establishments, will be able to accept Apple Pay, contactless credit and debit cards, and other digital wallets with a tap.

No hardware or payment terminal is needed.

Revolutionary!

Stripe has previously launched this feature.

Tap to Pay on iPhone will provide companies with a secure, private, and quick option to take contactless payments and unleash new checkout experiences, said Bailey.

Apple's solution is ingenious. Brilliant!

Bailey says that payment platforms, app developers, and payment networks are making it easier than ever for businesses of all sizes to accept contactless payments and thrive.

I admire that Apple is offering this up to third-party services instead of closing off other functionalities.

Slow POS terminals, farewell.

Late Apple Pay

Pay Apple later.

Apple Pay Later enables US consumers split Apple Pay purchases into four equal payments over six weeks with no interest or fees.

The Apple ecosystem integration makes this BNPL scheme unique. Nonstick. No dumb forms.

Frictionless.

Just double-tap the button.

Apple Pay Later was designed with users' financial well-being in mind. Apple makes it easy to use, track, and pay back Apple Pay Later from Wallet.

Apple Pay Later can be signed up in Wallet or when using Apple Pay. Apple Pay Later can be used online or in an app that takes Apple Pay and leverages the Mastercard network.

Apple Pay Order Tracking helps consumers access detailed receipts and order tracking in Wallet for Apple Pay purchases at participating stores.

Bad BNPL suppliers, goodbye.

Most bankers will be caught in Apple's eye playing mini golf in high-rise offices.

The big problem:

• Banks still think about features and big numbers just like other smartphone makers did not too long ago.

• Apple thinks about effortlessness, seamlessness, and frictionlessness that just work through integrated hardware and software.

Let me know what you think Apple’s next power moves in the banking industry could be.

These quotes will change your perspective.

I try to reflect on these quotes daily. Reading it in the morning can affect your day, decisions, and priorities. Let's start.

1. Friedrich Nietzsche once said, "He who has a why to live for can bear almost any how."

What's your life goal?

80% of people don't know why they live or what they want to accomplish in life if you ask them randomly.

Even those with answers may not pursue their why. Without a purpose, life can be dull.

Your why can guide you through difficult times.

Create a life goal. Growing may change your goal. Having a purpose in life prevents feeling lost.

2. Seneca said, "He who fears death will never do anything fit for a man in life."

FAILURE STINKS Yes.

This quote is great if you're afraid to try because of failure. What if I'm not made for it? What will they think if I fail?

This wastes most of our lives. Many people prefer not failing over trying something with a better chance of success, according to studies.

Failure stinks in the short term, but it can transform our lives over time.

3. Two men peered through the bars of their cell windows; one saw mud, the other saw stars. — Dale Carnegie

It’s not what you look at that matters; it’s what you see.

The glass-full-or-empty meme is everywhere. It's hard to be positive when facing adversity.

This is a skill. Positive thinking can change our future.

We should stop complaining about our life and how easy success is for others.

Seductive pessimism. Realize this and start from first principles.

4. “Smart people learn from everything and everyone, average people from their experiences, and stupid people already have all the answers.” — Socrates.

Knowing we're ignorant can be helpful.

Every person and situation teaches you something. You can learn from others' experiences so you don't have to. Analyzing your and others' actions and applying what you learn can be beneficial.

Reading (especially non-fiction or biographies) is a good use of time. Walter Issacson wrote Benjamin Franklin's biography. Ben Franklin's early mistakes and successes helped me in some ways.

Knowing everything leads to disaster. Every incident offers lessons.

5. “We must all suffer one of two things: the pain of discipline or the pain of regret or disappointment.“ — James Rohn

My favorite Jim Rohn quote.

Exercise hurts. Healthy eating can be painful. But they're needed to get in shape. Avoiding pain can ruin our lives.

Always choose progress over hopelessness. Myth: overnight success Everyone who has mastered a craft knows that mastery comes from overcoming laziness.

Turn off your inner critic and start working. Try Can't Hurt Me by David Goggins.

6. “A champion is defined not by their wins, but by how they can recover when they fail.“ — Serena Williams

Have you heard of Traf-o-Data?

Gates and Allen founded Traf-O-Data. After some success, it failed. Traf-o-Data's failure led to Microsoft.

Allen said Traf-O-Data's setback was important for Microsoft's first product a few years later. Traf-O-Data was a business failure, but it helped them understand microprocessors, he wrote in 2017.

“The obstacle in the path becomes the path. Never forget, within every obstacle is an opportunity to improve our condition.” — Ryan Holiday.

Bonus Quotes

More helpful quotes:

“Those who cannot change their minds cannot change anything.” — George Bernard Shaw.

“Do something every day that you don’t want to do; this is the golden rule for acquiring the habit of doing your duty without pain.” — Mark Twain.

“Never give up on a dream just because of the time it will take to accomplish it. The time will pass anyway.” — Earl Nightingale.

“A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.” — George Bernard Shaw.

“We don’t stop playing because we grow old; we grow old because we stop playing.” — George Bernard Shaw.

Conclusion

Words are powerful. Utilize it. Reading these inspirational quotes will help you.

Research on preventing disease, extending life, and caring for your body from the inside out

Grapefruit and pomegranates aren't on the list, so ignore that. Mostly, I enjoyed the visual, but those fruits are healthful, too.

15 (or 17 if you consider the photo) different foods a day sounds like a lot. If you're not used to it  — it is.

These lists don't aim for perfection. Instead, use this article and the science below to eat more of these foods. If you can eat 5 foods one day and 5 the next, you're doing well. This list should be customized to your requirements and preferences.

“Every time you eat or drink, you are either feeding disease or fighting it” -Heather Morgan.

The 15 Foods That You Should Consume Daily and Why:

1. Dark/Red Berries

(blueberries, blackberries, acai, goji, cherries, strawberries, raspberries)

The 2010 Global Burden of Disease Study is the greatest definitive analysis of death and disease risk factors in history. They found the primary cause of both death, disability, and disease inside the United States was diet.

Not eating enough fruit, and specifically berries, was one of the best predictors of disease (1).

What's special about berries? It's their color! Berries have the most antioxidants of any fruit, second only to spices. The American Cancer Society found that those who ate the most berries were less likely to die of cardiovascular disease.

2. Beans

Soybeans, black beans, kidney beans, lentils, split peas, chickpeas.

Beans are one of the most important predictors of survival in older people, according to global research (2).

For every 20 grams (2 tablespoons) of beans consumed daily, the risk of death is reduced by 8%.

Soybeans and soy foods are high in phytoestrogen, which reduces breast and prostate cancer risks. Phytoestrogen blocks the receptors' access to true estrogen, mitigating the effects of weight gain, dairy (high in estrogen), and hormonal fluctuations (3).

3. Nuts

(almonds, walnuts, pecans, pistachios, Brazil nuts, cashews, hazelnuts, macadamia nuts)

Eating a handful of nuts every day reduces the risk of chronic diseases like heart disease and diabetes. Nuts also reduce oxidation, blood sugar, and LDL (bad) cholesterol, improving arterial function (4).

Despite their high-fat content, studies have linked daily nut consumption to a slimmer waistline and a lower risk of obesity (5).

4. Flaxseed

(milled flaxseed)

2013 research found that ground flaxseed had one of the strongest anti-hypertensive effects of any food. A few tablespoons (added to a smoothie or baked goods) lowered blood pressure and stroke risk 23 times more than daily aerobic exercise (6).

Flax shouldn't replace exercise, but its nutritional punch is worth adding to your diet.

5. Other seeds

(chia seeds, hemp seeds, pumpkin seeds, sesame seeds, fennel seeds)

Seeds are high in fiber and omega-3 fats and can be added to most dishes without being noticed.

When eaten with or after a meal, chia seeds moderate blood sugar and reduce inflammatory chemicals in the blood (7). Overall, a great daily addition.

6. Dates

Dates are one of the world's highest sugar foods, with 80% sugar by weight. Pure cake frosting is 60%, maple syrup is 66%, and cotton-candy jelly beans are 70%.

Despite their high sugar content, dates have a low glycemic index, meaning they don't affect blood sugar levels dramatically. They also improve triglyceride and antioxidant stress levels (8).

Dates are a great source of energy and contain high levels of dietary fiber and polyphenols, making 3-10 dates a great way to fight disease, support gut health with prebiotics, and satisfy a sweet tooth (9).

7. Cruciferous Veggies

(broccoli, Brussel sprouts, horseradish, kale, cauliflower, cabbage, boy choy, arugula, radishes, turnip greens)

Cruciferous vegetables contain an active ingredient that makes them disease-fighting powerhouses. Sulforaphane protects our brain, eyesight, against free radicals and environmental hazards, and treats and prevents cancer (10).

Unless you eat raw cruciferous vegetables daily, you won't get enough sulforaphane (and thus, its protective nutritional benefits). Cooking destroys the enzyme needed to create this super-compound.

If you chop broccoli, cauliflower, or turnip greens and let them sit for 45 minutes before cooking them, the enzyme will have had enough time to work its sulforaphane magic, allowing the vegetables to retain the same nutritional value as if eaten raw. Crazy, right? For more on this, see What Chopping Your Vegetables Has to Do with Fighting Cancer.

8. Whole grains

(barley, brown rice, quinoa, oats, millet, popcorn, whole-wheat pasta, wild rice)

Whole-grains are one of the healthiest ways to consume your daily carbs and help maintain healthy gut flora.

This happens when fibre is broken down in the colon and starts a chain reaction, releasing beneficial substances into the bloodstream and reducing the risk of Type 2 Diabetes and inflammation (11).

9. Spices

(turmeric, cumin, cinnamon, ginger, saffron, cloves, cardamom, chili powder, nutmeg, coriander)

7% of a person's cells will have DNA damage. This damage is caused by tiny breaks in our DNA caused by factors like free-radical exposure.

Free radicals cause mutations that damage lipids, proteins, and DNA, increasing the risk of disease and cancer. Free radicals are unavoidable because they result from cellular metabolism, but they can be avoided by consuming anti-oxidant and detoxifying foods.

Including spices and herbs like rosemary or ginger in our diet may cut DNA damage by 25%. Yes, this damage can be improved through diet. Turmeric worked better at a lower dose (just a pinch, daily). For maximum free-radical fighting (and anti-inflammatory) effectiveness, use 1.5 tablespoons of similar spices (12).

10. Leafy greens

(spinach, collard greens, lettuce, other salad greens, swiss chard)

Studies show that people who eat more leafy greens perform better on cognitive tests and slow brain aging by a year or two (13).

As we age, blood flow to the brain drops due to a decrease in nitric oxide, which prevents blood vessels from dilatation. Daily consumption of nitrate-rich vegetables like spinach and swiss chard may prevent dementia and Alzheimer's.

11. Fermented foods

(sauerkraut, tempeh, kombucha, plant-based kefir)

Miso, kimchi, and sauerkraut contain probiotics that support gut microbiome.

Probiotics balance the good and bad bacteria in our bodies and offer other benefits. Fermenting fruits and vegetables increases their antioxidant and vitamin content, preventing disease in multiple ways (14).

12. Sea vegetables

(seaweed, nori, dulse flakes)

A population study found that eating one sheet of nori seaweed per day may cut breast cancer risk by more than half (15).

Seaweed and sea vegetables may help moderate estrogen levels in the metabolism, reducing cancer and disease risk.

Sea vegetables make up 30% of the world's edible plants and contain unique phytonutrients. A teaspoon of these super sea-foods on your dinner will help fight disease from the inside out.

13. Water

I'm less concerned about whether you consider water food than whether you drink enough. If this list were ranked by what single item led to the best health outcomes, water would be first.

Research shows that people who drink 5 or more glasses of water per day have a 50% lower risk of dying from heart disease than those who drink 2 or less (16).

Drinking enough water boosts energy, improves skin, mental health, and digestion, and reduces the risk of various health issues, including obesity.

14. Tea

All tea consumption is linked to a lower risk of stroke, heart disease, and early death, with green tea leading for antioxidant content and immediate health benefits.

Green tea leaves may also be able to interfere with each stage of cancer formation, from the growth of the first mutated cell to the spread and progression of cancer in the body. Green tea is a quick and easy way to support your long-term and short-term health (17).

15. Supplemental B12 vitamin

B12, or cobalamin, is a vitamin responsible for cell metabolism. Not getting enough B12 can have serious consequences.

Historically, eating vegetables from untreated soil helped humans maintain their vitamin B12 levels. Due to modern sanitization, our farming soil lacks B12.

B12 is often cited as a problem only for vegetarians and vegans (as animals we eat are given B12 supplements before slaughter), but recent studies have found that plant-based eaters have lower B12 deficiency rates than any other diet (18).

Article Sources:

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