Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping...
Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being per...
RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers. It is also the most popular and widely-used cryptographic system in today's digital world, for which its three inventors Rivest, Shamir and Adleman received the year 2002 Turing Award, the equivalent Nobel Prize in Computer Science.
Cryptanalytic Attacks on RSA covers almost all major known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. Since RSA depends heavily on computational complexity theory and number...
RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers. It is also the most popular and...
The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm, whereas the Integer Factorization Problem (IFP) still remains unsolvable in (P). There is still no polynomial-time algorithm for IFP. Many practical public-key cryptosystems and protocols such as RSA (Rivest-Shamir-Adleman) rely their security on computational intractability of IFP.
Primality Testing and Integer Factorization in Public Key Cryptography, Second Edition, provides a survey of recent progress in primality testing and integer...
The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm,...
The cryptosystems based on the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP) and the Elliptic Curve Discrete Logarithm Problem (ECDLP) are essentially the only three types of practical public-key cryptosystems in use. The security of these cryptosystems relies heavily on these three infeasible problems, as no polynomial-time algorithms exist for them so far. However, polynomial-time quantum algorithms for IFP, DLP and ECDLP do exist, provided that a practical quantum computer exists.
Quantum Attacks on Public-Key Cryptosystems presemts almost all...
The cryptosystems based on the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP) and the Elliptic Curve Discrete Logarithm ...
Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject areas. Since my own graduate study had empha sized probability theory, statistics, and real analysis, when I started work ing in cryptography around 1970, I found myself swimming in an unknown, murky sea. I thus know from personal experience how inaccessible number theory can be to the uninitiated. Thank you for your efforts to case the transition for a new generation of cryptographers. Thank you also for helping...
Modern cryptography depends heavily on number theory, with primality test ing, factoring, discrete logarithms (indices), and elliptic curves being per...
RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers. It is also the most popular and widely-used cryptographic system in today's digital world, for which its three inventors Rivest, Shamir and Adleman received the year 2002 Turing Award, the equivalent Nobel Prize in Computer Science.
Cryptanalytic Attacks on RSA covers almost all major known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. Since RSA depends heavily on computational complexity theory and number...
RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers. It is also the most popular and...
The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm, whereas the Integer Factorization Problem (IFP) still remains unsolvable in (P). There is still no polynomial-time algorithm for IFP. Many practical public-key cryptosystems and protocols such as RSA (Rivest-Shamir-Adleman) rely their security on computational intractability of IFP.
Primality Testing and Integer Factorization in Public Key Cryptography, Second Edition, provides a survey of recent progress in primality testing and integer...
The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm,...
"Principles of Compilers: A New Approach to Compilers Including the Algebraic Method" introduces the ideas of the compilation from the natural intelligence of human beings by comparing similarities and differences between the compilations of natural languages and programming languages. The notation is created to list the source language, target languages, and compiler language, vividly illustrating the multilevel procedure of the compilation in the process. The book thoroughly explains the LL(1) and LR(1) parsing methods to help readers to understand the how and why. It not only covers...
"Principles of Compilers: A New Approach to Compilers Including the Algebraic Method" introduces the ideas of the compilation from the natural inte...
The only book to provide a unified view of the interplay between computationalnumber theory and cryptography
Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical...
The only book to provide a unified view of the interplay between computationalnumber theory and cryptography
This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on applications in cryptography. Readers will learn to develop fast algorithms, including quantum algorithms, to solve various classic and modern number theoretic problems. Key problems include prime number generation, primality testing, integer factorization, discrete logarithms, elliptic curve arithmetic, conjecture and numerical verification.
The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the...
This book provides a comprehensive introduction to advanced topics in the computational and algorithmic aspects of number theory, focusing on appli...
