Public key cryptography, also known as asymmetric cryptography, is a cryptographic method that uses a pair of mathematically related keys: a public key and a private key. The public key is widely distributed and can be freely shared with others, while the private key is kept secret by the owner. The keys are generated in such a way that data encrypted with the public key can only be decrypted using the corresponding private key, and vice versa.
In public key cryptography, one common application is secure communication over an insecure channel. For example, if Alice wants to send a confidential message to Bob, she can encrypt the message using Bob's public key, which only Bob can decrypt using his private key. This ensures that even if the encrypted message is intercepted during transmission, it remains unreadable without the private key.
As for quantum computers, they have the potential to break certain commonly used public key cryptography algorithms. Traditional public key algorithms, such as RSA and Elliptic Curve Cryptography (ECC), rely on the difficulty of certain mathematical problems for their security. Quantum computers, with their ability to perform quantum computations, could potentially solve these mathematical problems much faster than classical computers.
One such problem that is vulnerable to quantum attacks is integer factorization, which forms the basis of RSA. Shor's algorithm, a quantum algorithm developed by Peter Shor in 1994, can efficiently factor large integers using a quantum computer, thereby breaking RSA. Similarly, quantum computers can also break the elliptic curve discrete logarithm problem, which is the basis of ECC.
To address the threat of quantum computers to public key cryptography, there is ongoing research and development of quantum-resistant cryptographic algorithms, often referred to as post-quantum cryptography (PQC). These algorithms are designed to be secure against attacks from both classical and quantum computers. Organizations and researchers are actively working on standardizing and implementing PQC algorithms to ensure the long-term security of cryptographic systems in a post-quantum world.