Modern Cryptography and the Future

Cryptography continues to evolve in response to new threats, new computing paradigms, and new use cases. This lesson explores the cutting-edge developments in cryptographic research and the challenges that lie ahead — including the looming threat of quantum computing.

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The Quantum Computing Threat

Quantum computers use qubits that can exist in superposition (0 and 1 simultaneously), enabling certain computations to be performed exponentially faster than on classical computers.

Impact on Current Cryptography

Algorithm	Quantum Threat	Attack
RSA	Broken	Shor's algorithm factors large numbers efficiently
ECC / ECDSA / ECDH	Broken	Shor's algorithm solves the discrete logarithm problem
Diffie-Hellman	Broken	Shor's algorithm
AES-128	Weakened	Grover's algorithm reduces effective security to 64 bits
AES-256	Secure	Grover's algorithm reduces to 128-bit security — still infeasible
SHA-256	Secure	Grover's provides only a quadratic speedup for pre-image attacks

Key insight: Quantum computing breaks asymmetric cryptography (RSA, ECC, DH) but only weakens symmetric cryptography and hash functions. Doubling the key size (AES-256) provides quantum resilience.

Timeline

• Current quantum computers (2024–2026) have hundreds to thousands of noisy qubits — insufficient to break cryptography
• Cryptographically relevant quantum computers (CRQCs) are estimated to require millions of stable qubits
• Estimates vary widely: 10–30 years, but the exact timeline is uncertain
• The threat is real enough that migration must begin now — "harvest now, decrypt later" attacks mean encrypted data captured today could be decrypted when quantum computers arrive

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Post-Quantum Cryptography (PQC)

Post-quantum cryptography (PQC) refers to algorithms designed to resist attacks from both classical and quantum computers.

NIST Post-Quantum Standards

In 2024, NIST published the first post-quantum cryptographic standards after an 8-year competition:

Standard	Algorithm	Type	Use Case
FIPS 203 (ML-KEM)	CRYSTALS-Kyber	Lattice-based	Key encapsulation (key exchange)
FIPS 204 (ML-DSA)	CRYSTALS-Dilithium	Lattice-based	Digital signatures
FIPS 205 (SLH-DSA)	SPHINCS+	Hash-based	Digital signatures (stateless)

Mathematical Foundations

Approach	Hard Problem	Example
Lattice-based	Learning with Errors (LWE), Shortest Vector Problem (SVP)	CRYSTALS-Kyber, CRYSTALS-Dilithium
Hash-based	Security of hash functions	SPHINCS+, XMSS
Code-based	Decoding random linear codes	Classic McEliece
Isogeny-based	Relationships between elliptic curves	SIKE (broken in 2022)
Multivariate	Solving systems of multivariate polynomial equations	Rainbow (broken in 2022)

Note: Some promising PQC candidates (SIKE, Rainbow) were broken during the competition — demonstrating the importance of rigorous analysis before standardisation.

Hybrid Approach

During the transition, a hybrid approach combines classical and post-quantum algorithms:

Hybrid key exchange:  ECDHE + ML-KEM (Kyber)
Hybrid signature:     ECDSA + ML-DSA (Dilithium)

If either algorithm is broken, the other still provides security. Chrome and other browsers already support hybrid key exchange (X25519Kyber768).

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Homomorphic Encryption

Homomorphic encryption allows computations to be performed on encrypted data without decrypting it:

Encrypt(a) + Encrypt(b) = Encrypt(a + b)
Encrypt(a) × Encrypt(b) = Encrypt(a × b)

Types

Type	Operations	Performance
Partially Homomorphic (PHE)	Addition OR multiplication	Fast
Somewhat Homomorphic (SHE)	Limited number of both	Moderate
Fully Homomorphic (FHE)	Unlimited additions and multiplications	Slow (but improving rapidly)

Use Cases

• Cloud computing — process sensitive data without the cloud provider seeing it
• Healthcare — analyse patient data without exposing personal information
• Financial analysis — compute on encrypted financial records
• Machine learning — train models on encrypted training data

Current State

• FHE has historically been 10,000–1,000,000× slower than plaintext computation
• Recent advances (2020–2026) have reduced the overhead to 100–1,000× for practical workloads
• Hardware acceleration (Intel HEXL, GPU implementations) is narrowing the gap
• Libraries: Microsoft SEAL, IBM HElib, Google FHE, Zama TFHE

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Zero-Knowledge Proofs (ZKPs)

A zero-knowledge proof allows one party to prove they know a secret without revealing the secret itself.

Properties