10 min
World-leading Computer Scientists: Lenstra, Lenstra and Lenstra ASecuritySite Podcast
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- Technology
Related blog: https://medium.com/asecuritysite-when-bob-met-alice/mathematics-in-the-blood-the-lenstra-family-bf188c686e74
Introduction
I know it’s a strange question to pose, but which family has most advanced the Internet and Cybersecurity? Well, the Lenstra family has a strong claim to that title. From their Dutch roots, they have contributed so much to our modern world — both from a theoretical and a practical point of view. I suppose there’s something in the nature of the Dutch that not only wants to solve real problems, but do it in a scientific way. That approach is also the beating heart of academic research — to take major problems and solve them through collaborative efforts, and where each researcher breaks solves part of the puzzle. The Internet — and in fact our modern world — has been created through the coming together of all the amazing work of researchers over many decades.
Meet the Cryptography and Problem-Solving Brothers My grandfather was an electrician, and my father was one too. I suppose electrical things are in my blood. It was where I started my career, and I have always had a love for everything that relates to electrons. I must admit I gave myself a little too many electrical shocks when I was a child, as the temptation to take things apart just seemed too strong for me. And, it still amazes me that we often just take electricity — and all its applications in our modern world — for granted. Where would we be without our control of electricity and all things electrical? You certainly wouldn’t be reading this article, now.
So, sometimes, there’s something in our blood that defines our future careers. And for the Lenstra family that was certainly the case, and from their Dutch roots, Hendrik, Arjen, Andries and Jan Karel have become important mathematicians.
One of the most famous of the brothers for those who have studied networking is the mighty Jan Karel Lenstra (J.K. Lenstra) and whose many major breakthroughs include scheduling, local searches and the travelling salesman problem. We can thus all thank Jan for his work on routing problems, and which led to the creation of routing protocols on the Internet:
The solving of the routing problem on the Internet, allowed the Internet to scale to levels that we see now, and where we have almost instant access to information from any part of the planet. We can thank J.K. Lenstra for providing that foundation.
Arjen followed a cryptography focus for his work, including many classic papers such as those related to the factorization of polynomials and a famous paper entitled “Ron was wrong. White is right” [here]:
But, Arjen’s most cited paper included his brother (Hendrik W. Lenstra Jr.) as a co-author [3]:
And, in these days of Microsoft Word and LaTeX, don’t you just love the pen markup on the paper? The brothers also collaborated on another classic paper — and which included the mighty J.M Pollard [2]:
Lenstra–Lenstra–Lovász (LLL) When the two brothers worked together they created some of their best work, and it was the classic Factorizing Polynomials with Rational Coefficients paper [3] that led to the Lenstra–Lenstra–Lovász (LLL) method [paper]. The paper also included mighty Laszlo Lovász [here] (who has an h-index of 109):
This will use this method — defined as Lenstra–Lenstra–Lovász (LLL) — to crack the signature, and discover the private key used to digitally sign the message. This will search for the private key that has been used to sign a message with ECDSA. In this case we will generate two signatures, and then search for a private key.
One of the most common signatures is ECDSA (Elliptic Curve Digital Signature Algorithm) and which is used with Bitcoin and Ethereum. With this, Bob creates a random private key (priv), and then a public key from:
Next, in order to create a signature for a message of M, he creates a random number (k) and gen
Related blog: https://medium.com/asecuritysite-when-bob-met-alice/mathematics-in-the-blood-the-lenstra-family-bf188c686e74
Introduction
I know it’s a strange question to pose, but which family has most advanced the Internet and Cybersecurity? Well, the Lenstra family has a strong claim to that title. From their Dutch roots, they have contributed so much to our modern world — both from a theoretical and a practical point of view. I suppose there’s something in the nature of the Dutch that not only wants to solve real problems, but do it in a scientific way. That approach is also the beating heart of academic research — to take major problems and solve them through collaborative efforts, and where each researcher breaks solves part of the puzzle. The Internet — and in fact our modern world — has been created through the coming together of all the amazing work of researchers over many decades.
Meet the Cryptography and Problem-Solving Brothers My grandfather was an electrician, and my father was one too. I suppose electrical things are in my blood. It was where I started my career, and I have always had a love for everything that relates to electrons. I must admit I gave myself a little too many electrical shocks when I was a child, as the temptation to take things apart just seemed too strong for me. And, it still amazes me that we often just take electricity — and all its applications in our modern world — for granted. Where would we be without our control of electricity and all things electrical? You certainly wouldn’t be reading this article, now.
So, sometimes, there’s something in our blood that defines our future careers. And for the Lenstra family that was certainly the case, and from their Dutch roots, Hendrik, Arjen, Andries and Jan Karel have become important mathematicians.
One of the most famous of the brothers for those who have studied networking is the mighty Jan Karel Lenstra (J.K. Lenstra) and whose many major breakthroughs include scheduling, local searches and the travelling salesman problem. We can thus all thank Jan for his work on routing problems, and which led to the creation of routing protocols on the Internet:
The solving of the routing problem on the Internet, allowed the Internet to scale to levels that we see now, and where we have almost instant access to information from any part of the planet. We can thank J.K. Lenstra for providing that foundation.
Arjen followed a cryptography focus for his work, including many classic papers such as those related to the factorization of polynomials and a famous paper entitled “Ron was wrong. White is right” [here]:
But, Arjen’s most cited paper included his brother (Hendrik W. Lenstra Jr.) as a co-author [3]:
And, in these days of Microsoft Word and LaTeX, don’t you just love the pen markup on the paper? The brothers also collaborated on another classic paper — and which included the mighty J.M Pollard [2]:
Lenstra–Lenstra–Lovász (LLL) When the two brothers worked together they created some of their best work, and it was the classic Factorizing Polynomials with Rational Coefficients paper [3] that led to the Lenstra–Lenstra–Lovász (LLL) method [paper]. The paper also included mighty Laszlo Lovász [here] (who has an h-index of 109):
This will use this method — defined as Lenstra–Lenstra–Lovász (LLL) — to crack the signature, and discover the private key used to digitally sign the message. This will search for the private key that has been used to sign a message with ECDSA. In this case we will generate two signatures, and then search for a private key.
One of the most common signatures is ECDSA (Elliptic Curve Digital Signature Algorithm) and which is used with Bitcoin and Ethereum. With this, Bob creates a random private key (priv), and then a public key from:
Next, in order to create a signature for a message of M, he creates a random number (k) and gen
10 min