**"For their pioneering contributions to mathematical cryptography, combinatorics and the theory of computer science."**

## Adi Shamir

The Wolf Prize in Mathematics for 2024 is awarded to Professor Adi Shamir

"For his pioneering contributions to mathematical cryptography."

Adi Shamir Shamir Adi (born in Israel 1952) is a professor at the Weizmann Institute in the Department of Computer Science and Applied Mathematics, an expert in the fields of encryption and information interpretation and a world-renowned senior scientist.

From a young age, Shamir showed an interest in science and participated in academic programs for youth and the summer camps of the Weizmann Institute of Science. After graduating with high honors in his first degree in mathematics at Tel Aviv University (1973), Shamir continued his studies at the Weizmann Institute, focusing on computer science and receiving a master's degree in 1975, followed by a doctorate in 1977. In his doctoral thesis, he examined the properties of mathematical functions certain that are relevant to the semantics of programming languages. After completing his doctorate, he moved to the University of Warwick in England and then continued his academic journey at the Massachusetts Institute of Technology (MIT), where he delved into cryptography and decoding theory.

In traditional encryption methods, a certain key is required both to encrypt a message and to read it. The main weakness in these secure encryption methods is the need to distribute the key. Scientists tried to find an encryption method where anyone could encrypt a message without needing a key but only the owner of the key would be able to decrypt it. Together with his partners at MIT - Ron Rivest and Leonard Edelman, they reached a breakthrough and found a public key encryption method - they identified a one-way mathematical function - a function whose starting point cannot be recovered after its solution, based on the multiplication of two prime numbers.

The new method was given the name RSA after the initials of Rivest, Shamir and Edelman. Due to its enormous importance, it also aroused the interest of mathematicians, companies, governments and intelligence organizations. With the rise in importance of computer communication and internet hacking, it is applied in almost all online transactions to protect confidential information such as credit card numbers. To protect the information, the method uses two different keys that are mathematically linked - a public key that is used to encrypt the message and a completely different private key that is used for decryption.

Among his many other contributions to information security, Shamir introduced the groundbreaking "secret sharing" method. This method turns secrets into a collection of random numbers, which requires a specific combination to recover the original secret, and is the basis for secure calculations. In collaboration with colleagues, he promoted authentication and signature methods based on zero-information proofs and devised the "ring signature" to encrypt and decrypt information within a defined group of participants. Shamir's ingenuity extended to encrypting television broadcasts, allowing encrypted broadcasts only for those who paid for them. In recent years, his research has delved into the functions T, which are complex mathematical functions for encrypting information.

Shamir's influence also extends to exposing weak points in encryption systems, developing general mathematical methods that are used for direct attacks on encryption systems as well as for indirect attacks on hardware and software applications of ciphers. Beyond information security, his contributions resonate in many core topics in computer science, and in particular in computational complexity theory.

## Noga Alon

The 2024 Wolf Prize in Mathematics is awarded to Professor Noga Alon

"For his fundamental contributions to combinatorics and the theory of computer science."

Alon Noga (born in Israel, 1956) is a professor of mathematics at Princeton University and professor emeritus of mathematics and computer science at Tel Aviv University, one of the world's foremost researchers in the field of combinatorics. His research and developments changed the face of the field, created new concepts and original methods, and contributed greatly to the development of theoretical research and their applications in mathematics In isolation, in the theory of graphs, and in their use in the theory of computer science. He is one of the most prolific mathematicians in the world, and has published hundreds of articles in mathematics and computer science. His book "The Probabilistic Method" (in collaboration with Joel Spencer) appeared in 4 editions. 2016) contains 50 percent more material than the first (1992), and all editions have been very successful among researchers in discrete mathematics, with thousands of citations.

Alon showed a deep interest in mathematics and solving mathematical puzzles from a young age, he was attracted to its objectivity and the pursuit of absolute truth; To the magic of mathematics expressed in unexpected connections between different fields, in short and elegant proofs, in the absolute certainty that comes from the correctness of a proof and in the intellectual challenge of finding it. He realized his love for mathematics with the encouragement of his parents and his math teacher during high school, participating and winning many competitions.

Alon graduated with honors from his undergraduate studies in mathematics at the Technion, and went on to graduate studies in graph theory and developed a formula for the approximate calculation of the maximum number of copies of any graph in a graph with a given number of arcs. In his doctoral thesis at the Hebrew University in Jerusalem (1983), Alon continued to deal with extreme combinatorial problems that have applications in many areas such as engineering, computer science and computer communication. After his doctorate, Alon went to study at the Massachusetts Institute of Technology, MIT, in the USA. In his research, he continued to engage mainly in combinatorics, and collaborated with the renowned Hungarian mathematician Paul Ardes, who greatly influenced his research directions and produced several joint articles over the years. Alon was involved in many studies in the most important research laboratories in the world, including Harvard, the Institute for Advanced Studies in Princeton, the Almaden Research Center, IBM, Bell Laboratories, Belcor and research at Microsoft (in Redmond and Israel). In 1985, he joined Tel Aviv University, where he served as head of the School of Mathematics. In 2018, he moved to Princeton University where he continues to work to this day. Alon guided dozens of PhD students, he serves in the systems of more than a dozen international journals. Professor Alon gave hundreds of invited lectures and plenary lectures at conferences around the world, was the head of the scientific committee of the World Congress of Mathematicians (Madrid, 2006) and a member of prestigious award committees in the world. He published more than six hundred research articles and one book.

Combinatorics is the mathematical study of discrete structures, and is of paramount importance in many areas of mathematics and computer science. Most of the algorithms used in computer programming, computer communication and even biological information processing are based on combinatorial methods. Prof. Alon deals with discrete mathematics and computer science focusing on combinatorics and graph theory and their uses in the theory of computer science. His many works in the field changed the face of modern combinatorics and introduced important concepts, structures and methods to the field. He proved the Nullstellensatz- Combinatorial, a powerful algebraic technique that yielded highly significant applications in graph theory and combinatorics, including an extension of the four-color theorem, and generalizations of the Kushi-Davenport theorem in additive number theory.

Prof. Alon is the leading scientist in the probabilistic method in discrete mathematics. His book written with Joel Spencer is unquestionably the leading text in this key area. In the probabilistic method, randomness - randomization - is used as a tool to investigate even problems that do not have a probabilistic component, and Prof. Alon found complex and surprising uses for this method. For example, working with Matias and Segdi, the researchers found a way to efficiently handle huge amounts of information that cannot be stored. The other side of the coin in the probabilistic method is derandomization: the theory that tries to provide explicit structures that will replace probabilistic methods in mathematics and computer science. Prof. Alon made important contributions to explicit constructions and the field of derandomization; Among other things, he developed methods for building small sample spaces that support almost independent variables. The examples he found to solve various problems are surprising in their beauty and depth.

Alon developed the "polynomial method" - a powerful algebraic tool, with many uses in combinatorics, graph theory, additive number theory and information theory. For this method based on understanding combinatorial structures using spaces of polynomials corresponding to them, Alon found surprising uses in graph coloring problems, in extremal problems concerning graphs and hypergraphs, and problems in associative number theory. Alon used this tool to solve a problem raised by Claude Shannon, the father of information theory, that has troubled scientists for more than fifty years. Contrary to Shannon's hypothesis, Alon showed that the capacity of combining two channels can be much greater than the sum of the capacities of each channel separately. Working together with Kleitman, Alon solved the problem of Hedwiger and Debroner in combinatorial geometry that had been open for about fifty years, which proved a far-reaching generalization of Heli's theorem. Prof. Alon cracked open important problems that had been open for decades in graph theory and Ramsey theory as well.

The color coding method he developed together with Yoster Wotzwick has found applications in several other fields, including the theory of Fixed Parameter Tractability and bioinformatics. His joint work with Matias and Szegedi initiated the study of streaming algorithms that test which statistical properties of streaming data can be sampled and evaluated in motion.This research formed the basis of the groundbreaking field of streaming algorithms and drawing algorithms and has many practical theoretical and applied applications.

Alon's research contributed significantly to the understanding of spectral properties and expansion properties of graphs and the uses of expansion graphs in mathematics and computer science. Alon Halutz was a pioneer in the application of spectral methods in the study of algorithmic problems and the relationship he found, in collaboration with Vitali Milman, between separation properties and spectral properties of graphs stimulated much research and are cited in all the extensive work that followed in the field.

Together with his partners, Alon developed an algorithmic version of Szemerédi's regularity lemma, Szemerédi discovered its connection to Grothendieck's classical inequality, and used it to solve basically all the main open problems in the theory of property testing for dense graphs. This work opened up extensive research and played an important role in the subsequent development of the theory of convergent graph sequences by Lubasz and his collaborators.

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Why is no prize given to a Mizrachi or an Arab?