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Image source: infzm.comAccording to Xinhua News Agency
, on September 24, at the 6th Heidelberg International Mathematics and Computer Science Laureate Forum held in Heidelberg, Germany, the 89-year-old famous British mathematician, Abel Prize and Fields Medal winner Michael Attia proposed A simple train of thought to prove Riemanns conjecture, and said that Riemanns conjecture can be proved along this train of thought.
The new idea proposed by Attia is based on the deduction of an important dimensionless number in physics—the fine structure constant. The deduction process combines the earlier theories of von Neumann and other scientists, and introduces a new The so-called TODD function, which is regarded as the core of proving the Riemann Hypothesis. Attias line of proof is still subject to peer review, though.What is the relationship between the Riemann Hypothesis and the blockchain? If the Riemann Hypothesis is proved, what impact will it have on the real world? What is the impact on the blockchain?
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Riemann conjecture
First, lets look at what the Riemann Hypothesis is.The Riemann Hypothesis is one of the seven major mathematical problems in the world, which was proposed by the German mathematician Bernhard Riemann in 1859.Riemann conjecture(RH) is aboutRiemann zeta function
Conjectures for the zero distribution of ζ(s).
A more popular mathematical expression is as follows:
ζ(s) = 1 + 1 / 2^s + 1 / 3^s + 1 / 4^s + ... = 0 All non-trivial solutions lie on the line x=1/2.that isThe guess is
: All non-trivial zeros of the Riemann function ζ(s) are located on a straight line whose real part is 1/2.
The trivial zeros here are the periodic zeros of a trigonometric sin function; the nontrivial zeros are the zeros of the Zeta function itself.So what does the Riemann Hypothesis have to do with the distribution of prime numbers (also known as prime numbers)?
Lets look at another deformation formula of it:The conjecture assumes that the law of the distribution of prime numbers is random and uniform, closely related to non-trivial zeros.
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Applications of Prime Numbers in Cryptography
So, why is it necessary to prove the distribution law of prime numbers? How do prime numbers affect real-world applications?
The distribution of prime numbers among natural numbers is extremely important in both pure and applied mathematics.
Prime numbers refer to those integers that can only be divisible by 1 and itself, and each integer can be expressed as the product of a finite number of prime numbers, so prime numbers can be regarded as atoms in the natural number system.Although the Riemann Hypothesis assumes that the distribution of prime numbers is random and uniform, no one has proved this conjecture so far. At present, the latest achievement in proving this conjecture is that a French team uses a computer to derive the Riemann conjecture to the first ten trillion non-trivial zeros of the Zeta function, all of which conform to the Riemann conjecture, and there is no counterexample.
then,Mathematicians apply this characteristic of prime numbers to cryptographyMathematicians apply this characteristic of prime numbers to cryptography
. Because people have not yet discovered the law of prime numbers, if it is used as a key for encryption, the cracker must perform a large number of calculations, even if the fastest computer is used, the process of finding prime numbers will take too long and lose the meaning of cracking .RSA public key encryption algorithm is widely used in major banks now.: It is very easy to multiply two large prime numbers, but it is extremely difficult to factorize the product, so the product can be made public as an encryption key.
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If the Riemann Hypothesis is proved, what impact will it have on the real world?
Professor Ouyang, Department of Mathematics, University of Science and Technology of China said
Unless Attia proves that the Riemann conjecture is not true, or proposes a new law of prime numbers, it will not have much impact on practical applications.
The application of number theory to cryptography, including information security and cyberspace security, and even quantum computing, occurs in limited situations (prime numbers currently used do not exceed 150 digits). The range of possible counterexamples to the Riemann Hypothesis has far exceeded the range of numbers in practical applications.
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What is the relationship between the Riemann Hypothesis and the blockchain?What are the problems of cryptography?：
There are three main types of classic research problems based on public key cryptography
(1) The problem of prime number decomposition of large integers (RSA encryption algorithm belongs to this field);
(2) Discrete logarithm problems (ECDLP) on elliptic curves, etc. (elliptic curve encryption algorithms belong to this field);
(3) Discrete logarithm problem (DLP) over finite fields;
Song Chenggen, CTO of Beijing Ouchain Technology Co., Ltd. saidIn the blockchain, the most used correlation algorithm based on elliptic curves is not directly related to prime numbers. It remains to be seen what connection the elliptic curve has with the Riemann Hypothesis or the tools used to prove the Riemann Hypothesis.
