Quantum-Safe Cryptography: Preparing for Post-Quantum Security

 


As quantum computing advances at an unprecedented pace, it threatens traditional cryptographic methods that software creators currently rely on for security. The power of quantum computers has the potential to break widely used encryption algorithms, leaving sensitive data vulnerable to decryption. 

For software providers, this means one thing: preparation is essential. When post-quantum cryptography (PQC) becomes standardized, software vendors must be ready to seamlessly integrate these new algorithms. This demands a shift towards crypto-agile architectures — flexible software systems that can quickly adopt new encryption methods and security practices.

What is post-quantum cryptography:

 Post-Quantum Cryptography also called quantum-safe or quantum-resistant cryptography, is the development of algorithms designed to secure data against both classical and quantum computing attacks. 

Today, digital security heavily relies on cryptographic algorithms such as Rivest-Shamir-Adleman (RSA) and Elliptic Curve Cryptography (ECC). These algorithms secure communications, financial transactions, and data across industries. 

Traditional cryptographic algorithms depend on the inability of classic computers to perform certain mathematical calculations, such as factoring large numbers and solving discrete logarithms. On the other hand, quantum computers can potentially solve these problems — for example, Shor’s algorithm can theoretically crack RSA and ECC. This becomes possible due to quantum computers using quantum bits (qubits) instead of classical bits. They exploit quantum phenomena such as superposition and entanglement to perform certain types of computations exponentially faster than traditional computers.

Basic principles of quantum-safe cryptography:

  • Computational complexity: In cryptography, the computational complexity class 

     plays an important role. This class consists of decision problems for which proposed solutions can be verified in polynomial time using a  (DTM). The importance of NP stems from the fact that it is conjectured to consist of many computational problems that cannot be solved efficiently by both classical and quantum computers.

    The first generation of successful asymmetric key cryptosystems developed in the 1970s based their security on mathematical problems such as prime factorization and discrete logarithms that are now conjectured to belong to the NP-intermediate subclass of NP. This subclass consists of problems that are believed not to have polynomial-time solutions on DTMs but at the same time are also not as hard as the hardest problems in NP.
  • Average vs worst-case hardness: While there are many known NP-hard problems, not every such problem is suitable as a basis for cryptographic security. In this context, the notion of  is useful for cryptography. A problem is average-case hard if most instances of the problem drawn randomly from some distribution are hard, whereas a problem is worst-case hard if it is hard only on some isolated worst-case instances. Quantum-safe cryptologists therefore search for mathematical problems that satisfy the assumption of average-case hardness and employ theoretical tools such as worst-case to average-case to identify suitable protocols whose security and efficiency can be guaranteed.

Summary:

The migration to quantum-safe cryptography (QSC) of asymmetric key cryptosystems is necessitated by the expected advent of quantum computers that can break traditional asymmetric key algorithms predicated on the classical hardness of NP-intermediate problems. QSC is conjectured to be robust to quantum attacks because its security is based on NP-hard problems, which generally cannot be efficiently solved even with quantum computers.
In this context, hard problems rooted in the theory of mathematical lattices such as the learning with errors (LWE) problem have emerged as leading contenders for QSC standardization. In particular, the CRYSTALS-Kyber and CRYSTALS-Dilithium algorithms, based on modular lattices, are well positioned as near-term alternatives to popular asymmetric key protocols like RSA, Elliptic Curve, Diffie-Hellman, and DSA.


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