Let me tell you about "I am me." Two years ago, Rizwan from our mathematics research team was accepted into an EU exchange program from his graduate school in Istanbul and joined the University of Messina in Sicily. I visited him on a European trip starting from CERN (the particle accelerator) in Geneva.

A Seaside Conversation: The Appeal of "I Am Me"

It was a scorching June day. We were enjoying fish at a restaurant overlooking the sea in Palermo, Sicily. I mentioned how I loved the Italian phrase "IO SONO IO" (pronounced "io sono io," meaning "I am me")—the sound is so simple and the letters so round. Rizwan replied, "That's a mathematically beautiful phrase." That exchange, with the brilliant sea and clear sky as our backdrop, has stayed with me.

Solitude and Conviction in Mathematics

As you go deeper into mathematics, fewer and fewer people understand or empathize with you. There's a parallel in business with the beauty of craftspeople who quietly keep making products they're committed to. When you keep digging the same well, your companions dwindle. But in many situations, it's better not to bend your intuition or convictions.

The Harsh Reality of Scientific Research

Meanwhile, with science research budgets being cut worldwide, it's becoming harder to make a living as a full-time researcher while thinking "I am me." Rather than splitting life between a day job and nighttime hobbies, I think it's important to increase the number of people who can live 100% in their "I am me" field. Some of my colleagues are beginning to grasp that kind of life.

"The Flame of Passion" and Our Company's Mission

I respect serious, hardworking people who keep chasing the small flame of their passion. I want to do everything I can, personally and as a company, to bring even a little happiness to people whose dreams haven't been 100% fulfilled yet.

Come to think of it, there was a song by Ozaki Yutaka called "So That I Can Be Myself." The form is different from teenage angst, but I want to keep solving the difficult problem of "the scientist's struggle."

I've been studying the concept of "fixed points" for a while now. Mathematically it's quite niche so I'll skip that, but intuitively, it refers to the phenomenon of "returning to the original position." Think of it like landing on "Go Back to Start" in a board game, or circling around the same spot in Monopoly. The question is: what is "pinned down" in physical space or in society?

Ethical Fixed Points

Here's a concrete example: "Sexual violence against women must not be tolerated" is a fixed point. When someone at a media company gave an apology and said "times have changed," I don't think "times changing" is the essence of the matter. Rather, society has simply moved closer to the fixed point of "sexual violence is unacceptable." This framework can be applied to how different countries and religions have variations in their positions, or how Japan has come to emphasize the word "compliance" more strongly.

What's useful about this framework is that it addresses, for instance, those venting sessions at bars about "compliance fatigue." It moves beyond just complaining and helps you see solutions.

Edgy Humor Matters—That's a Fixed Point

I love comedy, so I believe edgy jokes are important. Isn't that a truth that applies to most people? The element of edge, like alcohol, plays a role in keeping our minds healthy and acts as a preventive measure against extreme behavior. In other words, "poison is medicine" can be seen as a fixed point in the context of humor and comedy.

Saying "all edge is bad" isn't good for society. Edgy humor, when handled properly, is an element that keeps society healthy. The key fixed point is that humans need edgy humor. When society tries to crack down on it, it's actually society that's lost its bearings and is wavering. The era is the thing that's wrong.

The Broad Applicability of Fixed Points

This concept of "fixed points" can be applied widely.

For example, which way trends are moving or who will become Japan's next prime minister are certainly important topics. But what matters more is identifying where the "fixed points for society and humanity" are. While changes in prime ministers and policies are important, universal fixed points should take priority.

The fixed point is that humans inherently have heightened violence and cruelty. The fact that we're seeing more of that kind of news lately is a sub-issue. So I think we need to tackle the handling of this fixed point head-on.

This might seem like an unusual endeavor, but I want to standardize what we call "dreams."

A dream should emerge from your passion. It should be something you're good at, something that brings you joy, something you can think about and work on from morning to night, 365 days a year, 24 hours a day. I believe a true dream is something you can keep doing, even if just a little bit each day.

A Financial Foundation for Continuity

To sustain your dream around the clock, every day of the year, you need a modest amount of money. Not for a luxurious lifestyle, but as a basic foundation to keep your activities going. The question is: how do you secure that funding? That's where creativity comes in.

Expanding to Delight Your Stakeholders

If you're going to keep at it anyway, your activities should bring joy to the stakeholders involved. In other words, you need to scale what you're doing and make it bigger. To do that, focus on what you're truly great at and delegate everything else to people who excel in those areas. This means building a team, creating systems and structures. Think of it as building a "machine" that combines human talent, hardware, and software.

Contributing to Others' Happiness

Your work must connect to the happiness of others. It should make someone's boring life more enjoyable, or help someone who isn't feeling very happy to feel a little bit happier. That should be your purpose. It should never end in self-satisfaction.

Tackling Uncharted Territory

From a more scientific perspective, I want to work on things that haven't been attempted in human history. For challenges where data and stories already exist, you can look to the past to find the method. But I want to try new approaches and solutions even in areas where the probability of success is low. I want to pursue challenges where either "the problem itself is new" or "the solution is new."

Building a Team with People Who Get It

Finally, I want to move forward with people who say "I feel you" and truly understand. It doesn't have to be a large group. Whether it's a small team or a large one, meeting people who face the same direction and forming a wonderful team is what gives you the power to realize your dreams.

International Standards That Inform This "Standardization of Dreams"

ISO 26000 (Guidance on Social Responsibility)

Relevant elements: Contributing to others' happiness, stakeholder considerations

Why it's useful: ISO 26000 provides comprehensive guidelines for organizations to fulfill their social responsibilities. The essay's emphasis on "others' happiness" and "stakeholder delight" aligns with ISO 26000's seven core subjects: organizational governance, human rights, labor practices, the environment, fair operating practices, consumer issues, and community involvement and development. It's relevant for ensuring that realizing your dream doesn't end in self-satisfaction but creates social value.

ISO 56000 Series (Innovation Management)

Relevant elements: Tackling uncharted territory, new problems and solutions

Why it's useful: The international standard for innovation management directly connects to the core of this essay regarding "creating new value." ISO 56002 provides a framework for organizations to systematically manage innovation, offering useful methodologies for working on "things not yet attempted in human history." The techniques for structuring challenges in areas of high uncertainty are particularly relevant.

ISO 9001 (Quality Management System)

Relevant elements: Continuity, building systems and structures, constructing the machine

Why it's useful: The idea of creating "a system that allows you to continue your dream 365 days a year" shares common ground with ISO 9001's process approach. It's rich with methodologies for turning dreams into sustainable activities: continuous improvement (PDCA cycle), process standardization, and clear role definition. The division-of-labor philosophy of "focus on what you're good at and delegate the rest" aligns with ISO 9001's efficient resource management thinking.

There are several important SVP and CVP benchmarks in mathematics and computer science:

TU Darmstadt Lattice Challenge

https://www.latticechallenge.org/

The most well-known benchmark is the TU Darmstadt Lattice Challenge (available at latticechallenge.org), which provides lattice bases for testing and comparing lattice reduction algorithms. These challenges are designed so that solving SVP in one lattice implies solutions for all lattices of a certain smaller dimension, making them particularly suitable for worst-case analysis.

Recent Progress

The benchmark has seen steady progress over the years:

• As of February 2021, researchers from CWI (Centrum Wiskunde & Informatica) solved the SVP Challenge for dimension 180 in 52 days using specialized hardware with 1.5 TB of RAM and four AI-capable graphics cards.

• In June 2019, dimension 157 was solved using the General Sieve Kernel (G6K) implementation.

• Earlier work solved a 128-dimensional ideal lattice challenge, which required approximately 30,000 CPU hours.

Darmstadt LWE Challenge

There's also the Darmstadt LWE (Learning With Errors) Challenge, which is related to lattice-based cryptography security. This challenge is particularly relevant for assessing the security of post-quantum cryptographic schemes.

Why These Benchmarks Matter

SVP and CVP are central to lattice-based cryptography, which is being considered for post-quantum cryptography since these problems are believed to be hard even for quantum computers. These benchmarks help researchers evaluate algorithm performance and inform secure parameter choices for next-generation cryptographic systems.

Top Funded PQC Startups

1. SandboxAQ (USA, Palo Alto)

• Total funding: $950M+ across 5 rounds
• Latest: $450M Series E (April 2025) with investors including Google, NVIDIA, Ray Dalio, BNP Paribas, Horizon Kinetics
• Valuation: $5.6B
• Spun out from Alphabet in 2022

2. ID Quantique (Switzerland, Geneva)

• $65M+ investment from SK Telecom (2018), plus additional investments from Deutsche Telecom
• Total funding: $10.8M across 12 rounds (not including the SK Telecom investment)
• Founded in 2001
• Acquired by IonQ in 2025

3. Quantum Xchange (USA, Bethesda)

• Total funding: $39.6M-$45.6M over 2 rounds
• Series A: $13.5M (2021) at $59M post-money valuation, plus initial $10M funding

4. PQShield (UK, Oxford)

• Series B: $37M (June 2024) led by Addition
• Total funding: ~$37M+ (includes earlier Series A)
• Founded in 2018

5. QuSecure (USA, San Mateo)

• Series A: $28M total (February 2025) led by Two Bear Capital with Accenture Ventures participation
• Founded in 2019

6. QuintessenceLabs (Australia)

• Total funding: ~$50M over several rounds
• Investors include Australian Government and In-Q-Tel
• Founded in 2006

Other Notable Funded Companies

Qrypt (USA)

• Amount not disclosed, but active in quantum-secure encryption

Post-Quantum (UK)

• Funding amount not publicly disclosed

Crypto Quantique (UK, London)

• Founded 2016
• Funding amount not publicly disclosed

Quantum Dice (UK, Oxford)

• Founded 2019
• Funding amount not publicly disclosed

Qubitrium (Turkey)

• €1.5M seed funding (2024)

Agnostiq (Canada, Toronto)

• Founded 2018
• Funding amount not publicly disclosed

Quantum Blockchains (Poland)

• Founded 2018
• Funding amount not publicly disclosed

Note: SandboxAQ is significantly ahead with nearly $1B in funding, though it focuses broadly on quantum AI applications beyond just PQC. The purely PQC-focused companies range from ~$10M to $50M in funding, with PQShield and QuSecure being recent well-funded entrants in the pure-play PQC space.

Algorithm Development:

• Designing cryptographic schemes provably secure against both classical and quantum attacks
• Balancing security assumptions with practical constraints
• Limited mathematical foundations compared to classical crypto (RSA, ECC)

Implementation Challenges:

• Much larger key and signature sizes (often 10-100x larger than classical schemes)
• Higher computational overhead for operations
• Side-channel attack resistance is harder to achieve
• Memory constraints on embedded devices

Performance Trade-offs:

• Significantly slower operations in many cases
• Memory usage concerns, especially for constrained devices
• Network bandwidth impact from larger message sizes
• Battery life implications for mobile devices

Standardization & Migration:

• NIST standardization process revealed vulnerabilities in several candidates
• Hybrid approaches needed during transition period
• Legacy system compatibility issues
• Coordinating industry-wide migration

Security Analysis:

• Relatively new algorithms with less cryptanalytic scrutiny
• Quantum attack models still evolving
• Conservative parameter selection leads to larger sizes

Practical Deployment:

• Integration with existing protocols (TLS, VPNs, etc.)
• Hardware acceleration support still developing
• Crypto-agility in systems design

RSA encryption has been a cornerstone of internet security for decades. Today, you don't need to build your own cryptographic infrastructure from scratch. Here's a breakdown of the types of SaaS platforms that leverage RSA encryption to keep your data secure.

Key Management & Encryption

The foundation of any crypto strategy starts with managing your keys properly. Cloud providers like AWS KMS, Azure Key Vault, and Google Cloud KMS offer robust key management services that handle RSA keys at scale. You'll also find Encryption-as-a-Service platforms that abstract away the complexity, and cloud-based Hardware Security Module (HSM) services for those who need that extra layer of physical security.

Digital Signatures & Authentication

Remember when signing documents meant printing, signing, scanning, and emailing? Electronic signature platforms like DocuSign and Adobe Sign use RSA-based digital signatures to make this process seamless and legally binding. Digital certificate authorities like DigiCert, Let's Encrypt, and GlobalSign issue the certificates that verify identities online. And if you're shipping software, code signing services ensure your users know it's really from you.

PKI & Certificate Management

Public Key Infrastructure (PKI) can be a headache to manage on your own. PKI-as-a-Service platforms handle the heavy lifting, while certificate lifecycle management platforms make sure your certificates don't expire at 3am on a Saturday (we've all been there). SSL/TLS certificate management tools keep your websites secure and your browser bars green.

Identity & Access

Your users need to prove who they are. Identity and Access Management (IAM) platforms, multi-factor authentication (MFA) services, and Privileged Access Management (PAM) solutions all use RSA encryption under the hood to verify identities and control access to sensitive resources.

API & Data Security

APIs are the backbone of modern applications, and they need protection. API security gateways with RSA encryption, data encryption platforms, and secure file transfer services (SFTP) ensure your data stays private as it moves between systems.

Compliance & Document Security

For industries with strict compliance requirements, document encryption services, secure email gateways, and blockchain-based authentication platforms provide the audit trails and security guarantees you need to sleep at night.

The Bottom Line

Most cloud providers and security vendors bundle RSA encryption capabilities into broader security suites rather than offering standalone RSA-only products. This is actually good news—it means you get RSA's proven security as part of a comprehensive solution.

The key is finding the right combination of services for your specific needs. Whether you're protecting customer data, signing documents, or managing API access, there's likely a SaaS solution that can help.

Daisuke Ishii - dai@kiara.team

1. 伊藤清と現代ファイナンスを支える見えない柱

20世紀の確率論を語るとき、伊藤清という名前を抜きにすることはできません。彼は、ブラウン運動（ウィーナー過程）に対する厳密な数学的基盤を築き、伊藤積分、さらには伊藤の定理を生み出しました。この功績は、単に数学の世界にとどまらず、経済学、物理学、そしてとりわけ金融工学の発展に決定的な影響を与えました。

たとえば、ブラック＝ショールズ方程式。この式が株価オプションの理論価格を算出する手法として世界に広まり、1997年にはノーベル経済学賞にまでつながったことは有名です。しかし、その根底にあるのはまさに伊藤清の確率微分方程式です。ブラック＝ショールズ理論が「巨人の肩に乗った小人」と呼ばれるのは、そのためです。

株価の動きは本質的にランダムです。過去に上がっていたからといって、翌日も上がる保証はどこにもありません。伊藤の定理は、期待値の観点からはある程度の予測ができることを示していますが、それはあくまで「平均的な話」。実際の価格は、正規分布に従うランダムな振れ幅の中を漂い、誰にも確定的な未来を見せてはくれないのです。

2. なぜNASDAQやNVIDIAは上がり続けるように見えるのか？

最近では、NASDAQやNVIDIAなど、一部の銘柄がまるで一直線に上がり続けているかのような印象を受けます。しかし確率論の視点から見れば、これは単に「そういう結果が、たまたま起きた」だけにすぎません。企業業績が良ければ投資が集まりやすく、それに伴って価格が上がるのは自然な流れですが、それもまた需給バランスという仕組みの中での話。つまり、上がった理由があるように見えても、未来の動きはやはりフラットで、上にも下にも転ぶ可能性が常に共存しているのです。

証券会社のアナリストたちが声を揃えて予想を語ります。「上がる」「下がる」、その言葉には根拠があるようで、実際は過去データに基づく統計的傾向を語っているにすぎません。市場が不確実であるからこそ、多くの人が多様な視点で未来を測ろうとします。しかし、確率論的には、未来に対して「当たり」を事前に断定することはできません。そこには、少し残酷ともいえる現実があります。

3. 夫婦関係にも通じる確率論的なまなざし

この「明日はどうなるかわからない」という視点は、私たちの日常にも活かせます。たとえば、関係が悪化した夫婦のケース。過去の言い争い、すれ違い、不信感。履歴だけを見れば、「もう終わりだ」と思いたくなるのも無理はありません。

でも、確率論の視点では、明日という日は過去と必ずしも連動していない、という見方ができるのです。関係が悪化しているからといって、翌日も必ず悪化し続けるわけではない。逆にいえば、終わったと決めつけてしまったその瞬間に、未来の可能性を自分の手で閉ざしてしまっているかもしれない。冷徹とも思える確率論的視点は、裏を返せば「明日がまだ白紙である」という希望を差し出してくれているのです。

4. ボラティリティという名の「振れ幅」で世界を捉え直す

金融の世界では「ボラティリティ（volatility）」という言葉があります。価格の1日あたりの動きの大きさ、つまり「振れ幅」です。この概念を気候にたとえると、四季の変化がはっきりしている日本は振れ幅が大きく、ロサンゼルスのように年間を通して穏やかな気候の地域は振れ幅が小さい。

人間関係でも、この「振れ幅」は応用できます。感情の起伏が激しい夫婦や家族の関係は、まさに高ボラティリティの状態にあります。そしてその背後には、職場のストレス、介護、経済的不安など、さまざまな外的要因が潜んでいます。関係を修復したいなら、自分と相手だけでなく、こうした環境要因を分解し、どの振れ幅が何に由来するのかを見極めることが必要です。

5. 明日に何をするか——トレンドとボラティリティを味方にする

確率論に従えば、明日の結果は「五分五分」であると仮定できます。つまり、過去がどうであれ、明日は新しい選択ができる日であるということ。だからこそ、ゼロベースでポジティブなアクションを試してみる価値があります。たとえば、冷え込んだ夫婦関係においても、たった一言の声がけや、食事に誘うだけで、明日を少しだけ変える可能性があるのです。

そして、ボラティリティが高いときは状況が不安定であるがゆえに、ちょっとした一手で大きく状況が変わることもあります。一方でボラティリティが下がれば、関係は安定に向かい、冷静な判断がしやすくなる。この「安定と攻略」という二段階は、人間関係と確率論の交差点として、とても面白い構造を示しています。

6. SNSという市場と「終わったことにしない」力

YouTuberやSNSマーケティングの世界にも、確率的な波は存在します。一時期、誰もが参入し、バズり、注目された時代がありました。今では参入者も増え、注目を集めるのが難しくなり、「もう終わった」と言われがちです。

でも、本当にそうでしょうか？　確率的に見れば、ブレ幅が大きくなった今こそ、予想外の動きが生まれるタイミングともいえます。確率の世界では、過去の平均的な傾向が未来の全てを決めることはありません。今日の振れ幅が大きいことは、明日、突如として「新しい成功」が生まれる余地があることを意味しているのです。

7. The end is not the end.

「諦めたら試合終了ですよ」——これは漫画『スラムダンク』で有名になった言葉です。一見すると精神論のように響きますが、確率論の観点から見れば、これは深い真理を突いています。「終わった」と思ったその時点で、自ら未来の可能性を放棄してしまうのです。

たとえば、野球の試合で一方がリードしていても、試合終了まで何が起きるかわかりません。確率過程においても同じことが言えます。明日の値動きは誰にも予測できない。だからこそ、「The end is not the end.」という言葉には、冷静で理性的でありながら、希望を手放さない姿勢が込められているのです。

結びにかえて

伊藤清という偉大な学者の理論が、なぜ一般にはあまり知られていないのか。それは、確率論という分野が高度であると同時に、日々の流行やトレンドの中で注目を集めにくいという背景があるからでしょう。今はK-POPが世界を席巻し、古典音楽や数学は脇に追いやられているかもしれません。でも、それらの価値が失われたわけではありません。

私たちが、伊藤の定理と夫婦関係という、一見つながりのなさそうなテーマを重ねたのは、「確率論は人間の生き方を支えるヒントを与えてくれる」からです。株式市場の急変、人間関係の軋轢、すべては過去に縛られず、未来に開かれています。だからこそ、私たちは明日も歩き続けることができるのです。

The end is not the end. それは、未来に対して心を閉ざさないという意思表明なのです。