Integer factorization is the mathematical process of decomposing a composite number into a product of smaller integers, specifically prime numbers. This problem is computationally challenging and forms the basis of the security of many cryptographic systems, such as RSA encryption, due to the difficulty of factoring large numbers efficiently.

Integer Factorization

Integer factorization

mathematical process

A composite number is a positive integer greater than one that has at least one positive divisor other than one and itself, meaning it can be divided evenly by numbers other than one and itself. Unlike prime numbers, which have exactly two distinct positive divisors, composite numbers have more than two divisors, indicating their non-prime nature.

composite number

product of smaller integers

Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves, serving as the building blocks of number theory. They play a crucial role in various fields, including cryptography, due to their properties and distribution patterns.

prime numbers

computationally challenging

Security of cryptographic systems

RSA encryption is a widely used public-key cryptographic system that enables secure data transmission by leveraging the mathematical properties of large prime numbers. It ensures confidentiality and authenticity by using a pair of keys: a public key for encryption and a private key for decryption, making it foundational for secure communications over the internet.

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