Causes of the N2 Problem

• Pairwise Operations: Cryptographic algorithms frequently require pairwise comparisons or operations between elements. As the number of elements increases, the range of pairwise operations grows exponentially. This includes tasks like comparing hash values and encrypting data values integrated with multiple keys. It also leads to computational complexity.

• Complexity of Operations: Cryptographic operations consisting of modular exponentiation or elliptic curve mathematics involve complex mathematical computations. Performing these operations on a large scale such as modular multiplications, reductions, and exponentials intensifies computational overhead as the size of keys increases.

• Data Size: In cryptographic applications, the size of the dataset or the input has a direct impact on computational complexity. Processing large volumes of data requires more time and operational resources which gives an increase to the N2 problem. Data size scenarios include digital signature and data encryption operations where cryptographic algorithms are operated on entire data sets and messages.

• Resource Constraints: Limited computational resources, which include processing power and memory, increase the N2 problem, especially in resource-restrained environments including embedded systems, mobile platforms, and IoT devices. These have low-power processors generally with limited access to computational resources. As resource constraints also include the integration of storage and memory, cryptographic algorithms often require a good amount of storage for storing values, data structures, and keys. Moreover, memory constraints may necessitate frequent data transfers between different memory storage units, further increasing computational overhead.

The N2 problem emerges as a significant challenge in cryptography, protecting and safeguarding the information is most important. This problem is related to the issues of scalability and it arises when handling large volumes of data and also when processing numerous cryptographic operations at the same time. In this article, we will understand the N2 problem because it is very crucial for having efficient cryptographic systems and ensuring the security of digital assets.