Today's digital infrastructure relies heavily on encryption and authentication mechanisms that are based on mathematical problems currently solvable by classical computers. However, these are becoming increasingly vulnerable to quantum computing advances.

The primary challenges include:

Current Challenges

P1 Prime Number Factorization:

Used in asymmetric key encryption.

P2 Discrete Logarithm Problem (DLP):

Another foundation for asymmetric key systems.

P3 Hash Functions:

Employed for data integrity and compression.

Quantum computers, through algorithms like Shor’s and the most recent Chinese proposal based on a modified version of Babai's reduction and elliptical quantum algorithms, threaten to solve these problems, potentially compromising existing security measures.

Additionally, brute force attacks on hash functions pose a significant risk as quantum computing power increases.