Current RSA public-key (asymmetric) encryption systems and other versions rely on trapdoor mathematical functions, which make it simple to compute a public key from a private key but computationally impossible to compute the converse, a private key from a public key.
The difficulties of integer factorization and elliptic curve variations of the discrete logarithm issue, both of which have no known solution for computing an inverse in polynomial time, are exploited to create frequently used trapdoor functions (that is, on a finite timescale).
In a nutshell, this so-called "computational hardness" provides safety.
In 1994, however, Peter Shor proposed a quantum method that may be employed on a sufficiently large-scale quantum computer to perform integer factorization in polynomial time.
The now-famous quantum technique has now been proved to solve the discrete logarithm and elliptic-curve logarithm problems in polynomial time as well.
As a result of the creation of an FTQC in conjunction with this quantum algorithm, the security of present asymmetric public-key cryptography is jeopardized.
Furthermore, Shor's method exemplifies how advances in the mathematics and physical sciences have the potential to jeopardize secure communications in general.
In addition to Defense Department and critical cyber infrastructure systems, the world's digital revolution, which includes 4 billion internet users, 2 billion websites, and over $3 trillion in retail transactions, is backed at multiple tiers by existing public-key cryptography.
While the creation of an FTQC is estimated to be at least a decade or two away, there is still a pressing need to solve this issue because of the ‘record now, exploit later' danger, in which encrypted data is collected and kept for subsequent decryption by an FTQC when one becomes available.
As a result, the US National Institute of Standards and Technology's Post Quantum Cryptography Project, which includes worldwide partners—a security "patch" for the internet—is prioritizing the development of new "quantum hard" public-key algorithms.
