Background

The Quantum Threat

Modern digital security relies heavily on Public Key Infrastructure (PKI), which derives its security from mathematical problems that are computationally infeasible for classical computers to solve. However, a powerful fault-tolerant quantum computer could:

  • Use Shor's Algorithm to factorize large prime numbers efficiently
  • Break RSA and elliptic curve cryptography
  • Compromise banking networks, government communications, military systems, and internet infrastructure

India's Response

The Department of Science & Technology (DST) constituted a task force that has recommended:

  • 2027: CII sectors to begin PQC transition
  • 2028: Migrate priority systems
  • 2029: Achieve full PQC adoption

What is Post-Quantum Cryptography (PQC)?

Definition: PQC refers to cryptographic algorithms designed to remain secure against attacks from both classical and quantum computers. Also known as quantum-resistant cryptography.

Key Difference: Unlike Quantum Cryptography (like Quantum Key Distribution), PQC does not rely on quantum physics. Instead, it uses mathematical problems believed to be computationally infeasible even for quantum machines.

Major Mathematical Foundations of PQC

1. Lattice-Based Cryptography

  • Based on difficulty of solving problems in high-dimensional lattices (shortest vector problem)
  • Most promising and widely adopted PQC approach
  • Offers flexibility for encryption, digital signatures, and key exchange
  • NIST has standardized algorithms like CRYSTALS-Kyber and CRYSTALS-Dilithium under this category

2. Code-Based Cryptography

  • Relies on difficulty of decoding random linear error-correcting codes
  • Known for strong security guarantees
  • Main limitation: requires large key sizes
  • Example: Classic McEliece algorithm

3. Multivariate Polynomial Cryptography

  • Based on solving systems of multivariate polynomial equations over finite fields
  • Primarily explored for digital signature schemes
  • Provides alternative security assumptions

4. Hash-Based Cryptography

  • Uses security properties of cryptographic hash functions
  • Mainly applied for digital signatures
  • Considered highly secure and mathematically well-understood
  • Example: SPHINCS+ algorithm

Significance for India

  1. National Security: Protects sensitive government, military, and intelligence communications
  2. Financial Sector: Secures banking networks and digital transactions
  3. Critical Infrastructure: Protects power grids, telecom, transportation systems
  4. Strategic Independence: Reduces reliance on foreign cryptographic standards
  5. Compliance Requirements: Aligns with global security standards as major economies transition to PQC

Global Context

  • NIST finalized PQC standards in 2024 (FIPS 203, 204, 205)
  • USA: Executive Order on Promoting Leadership in Quantum Computing
  • EU: Quantum加密战略 and post-quantum migration initiatives
  • China: Significant investment in quantum computing and corresponding countermeasures

Key Terminology

  • PKI (Public Key Infrastructure): Framework enabling secure electronic transfer of information
  • Shor's Algorithm: Quantum algorithm for integer factorization
  • Quantum Supremacy: Point where quantum computers outperform classical ones
  • Cryptographic Agility: Ability to swap cryptographic algorithms without major system redesign