Christopher Janz of Point Nine Capital created the SaaS napkin in 2016. This post shows how founders have raised cash in the last 6 years. View raw data.

Round size

Unsurprisingly, round sizes have expanded and will taper down in 2022. In 2016, pre-seed rounds were $200k to $500k; currently, they're $1-$2m. Despite the macroeconomic scenario, Series A have expanded from $3m to $12m in 2016 to $6m and $18m in 2022.

Valuation

There are hints that valuations are rebounding this year. Pre-seed valuations in 2022 are $12m from $3m in 2016, and Series B prices are $270m from $100m in 2016.

Compared to public SaaS multiples, Series B valuations more closely reflect the market, but Seed and Series A prices seem to be inflated regardless of the market.

I'd like to know how each annual cohort performed for investors, based on the year they invested and the valuations. I can't access this information.

ARR

Seed firms' ARR forecasts have risen from $0 to $0.6m to $0 to $1m. 2016 expected $1.2m to $3m, 2021 $0.5m to $4m, and this year $0.5m to $2.5m, suggesting that Series A firms may raise with less ARR today. Series B minutes fell from $4.2m to $3m.

Capitalization Rate

2022 is the year that VCs start discussing capital efficiency in portfolio meetings. Given the economic shift in the markets and the stealthy VC meltdown, it's not surprising. Christopher Janz added capital efficiency to the SaaS Napkin as a new statistic for Series A (3.5x) and Series B. (2.5x). Your investors must live under a rock if they haven't asked about capital efficiency. If you're unsure:

The Capital Efficiency Ratio is the ratio of how much a company has spent growing revenue and how much they’re receiving in return. It is the broadest measure of company effectiveness in generating ARR

What next?

No one knows what's next, including me. All startup and growing enterprises around me are tightening their belts and extending their runways in anticipation of a difficult fundraising ride. If you're wanting to raise money but can wait, wait till the market is more stable and access to money is easier.

The comeback tour continues…

First, he founded a $47 billion co-working company (sorry, a “tech company”).

He established WeLive to disrupt apartment life.

Then he created WeGrow, a school that tossed aside the usual curriculum to feed children's souls and release their potential.

He raised the world’s consciousness.

Then he blew it all up (without raising the world’s consciousness). (He bought a wave pool.)

Adam Neumann's WeWork business burned investors' money. The founder sailed off with unimaginable riches, leaving long-time employees with worthless stocks and the company bleeding money. His track record, which includes a failing baby clothing company, should have stopped investors cold.

Once the dust settled, folks went on. We forgot about the Neumanns! We forgot about the private jets, company retreats, many houses, and WeWork's crippling. In that moment, the prodigal son of entrepreneurship returned, choosing the blockchain as his industry. His homecoming tour began with Flowcarbon, which sold Goddess Nature Tokens to lessen companies' carbon footprints.

Did it work?

Of course not.

Despite receiving $70 million from Andreessen Horowitz's a16z, the project has been halted just two months after its announcement.

This triumph should lower his grade.

Neumann seems to have moved on and has another revolutionary idea for the future of living. Flow (not Flowcarbon) aims to help people live in flow and will launch in 2023. It's the classic Neumann pitch: lofty goals, yogababble, and charisma to attract investors.

It's a winning formula for one investment fund. a16z has backed the project with its largest single check, $350 million. It has a splash page and 3,000 rental units, but is valued at over $1 billion. The blog post praised Neumann for reimagining the office and leading a paradigm-shifting global company.

Flow's mission is to solve the nation's housing crisis. How? Idk. It involves offering community-centric services in apartment properties to the same remote workforce he once wooed with free beer and a pingpong table. Revolutionary! It seems the goal is to apply WeWork's goals of transforming physical spaces and building community to apartments to solve many of today's housing problems.

The elevator pitch probably sounded great.

At least a16z knows it's a near-impossible task, calling it a seismic shift. Marc Andreessen opposes affordable housing in his wealthy Silicon Valley town. As details of the project emerge, more investors will likely throw ethics and morals out the window to go with the flow, throwing money at a man known for burning through it while building toxic companies, hoping he can bank another fantasy valuation before it all crashes.

Insanity is repeating the same action and expecting a different result. Everyone on the Neumann hype train needs to sober up.

Like WeWork, this venture Won’tWork.

Like before, it'll cause a shitstorm.

University entrepreneurship is like a Willy Wonka Factory of ideas. Classes, roommates, discussions, and the cafeteria all inspire new ideas. I've seen people establish a business without knowing its roots.

Chicken or egg? On my mind: I've asked university founders around the world whether the problem or solution came first.

The Problem

One African team I met started with the “instant noodles” problem in their academic ecosystem. Many of us have had money issues in college, which may have led to poor nutritional choices.

Many university students in a war-torn country ate quick noodles or pasta for dinner.

Noodles required heat, water, and preparation in the boarding house. Unreliable power from one hot plate per blue moon. What's healthier, easier, and tastier than sodium-filled instant pots?

BOOM. They were fixing that. East African kids need affordable, nutritious food.

This is a real difficulty the founders faced every day with hundreds of comrades.

This sparked their serendipitous entrepreneurial journey and became their business's cornerstone.

The Solution

I asked a UK team about their company idea. They said the solution fascinated them.

The crew was fiddling with social media algorithms. Why are some people more popular? They were studying platforms and social networks, which offered a way for them.

Solving a problem? Yes. Long nights of university research lead them to it. Is this like world hunger? Social media influencers confront this difficulty regularly.

It made me ponder something. Is there a correct response?

In my heart, yes, but in my head…maybe?

I believe you should lead with empathy and embrace the problem, not the solution. Big or small, businesses should solve problems. This should be your focus. This is especially true when building a social company with an audience in mind.

Philosophically, invention and innovation are occasionally accidental. Also not penalized. Think about bugs and the creation of Velcro, or the inception of Teflon. They tackle difficulties we overlook. The route to the problem may look different, but there is a path there.

There's no golden ticket to the Chicken-Egg debate, but I'll keep looking this summer.

They depend heavily on open source..

Discord users send billions of messages daily. Users wish to search these messages. How do we index these to search by message keywords?

Let’s find out.

1. Discord utilizes Elasticsearch. Elasticsearch is a free, open search engine for textual, numerical, geographical, structured, and unstructured data. Apache Lucene powers Elasticsearch.
   

2. How does elastic search store data? It stores it as numerous key-value pairs in JSON documents.
   

3. How does elastic search index? Elastic search's index is inverted. An inverted index lists every unique word in every page and where it appears.

4. Elasticsearch indexes documents and generates an inverted index to make data searchable in near real-time. The index API adds or updates JSON documents in a given index.

1. Let's examine how discord uses Elastic Search. Elasticsearch prefers bulk indexing. Discord couldn't index real-time messages. You can't search posted messages. You want outdated messages.

6. Let's check what bulk indexing requires.
1. A temporary queue for incoming communications.
2. Indexer workers that index messages into elastic search.

1. Discord's queue is Celery. The queue is open-source. Elastic search won't run on a single server. It's clustered. Where should a message go? Where?

8. A shard allocator decides where to put the message. Nevertheless. Shattered? A shard combines elastic search and index on. So, these two form a shard which is used as a unit by discord. The elastic search itself has some shards. But this is different, so don’t get confused.

1. Now, the final part is service discovery — to discover the elastic search clusters and the hosts within that cluster. This, they do with the help of etcd another open source tool.
   

A great thing to notice here is that discord relies heavily on open source systems and their base implementations which is very different from a lot of other products.

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.