Advanced Secure Networks and the Security Landscape

Entanglement-based Quantum Networks and the Security Landscape

A security strategy that includes Quantum Networking ensures resilience in the face of an ever-evolving threat landscape today and into the future.

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Introduction

Organizations must continually navigate the protection of digital assets in an ever-evolving threat landscape. Classical encryption algorithms such as symmetric and asymmetric encryption form the cornerstone of cybersecurity, safeguarding everything from individual privacy to global financial transactions. Symmetric encryption relies on a single key for both encryption and decryption, making it fast and efficient for securing large volumes of data. Asymmetric encryption, on the other hand, uses a pair of keys — one public and one private — to facilitate secure data exchange over unsecured channels. While effective against classical computing threats, quantum computation is more powerful. Quantum computers, with their ability to solve complex mathematical problems at unprecedented speeds, will be able to break these cryptographic systems. Development and adoption of quantum-safe methods that can withstand the sophisticated computational capabilities of quantum technology are needed in order to ensure the continued protection of sensitive information.

Classical security today

Today’s security is underpinned by symmetric and asymmetric encryption algorithms.

Symmetric encryption

In symmetric encryption, a sender will encrypt information with a single pre-shared secret key that the receiver then uses to decrypt the message. This key must be kept secret between sender and receiver, or the information encrypted with the key could be compromised. Symmetric encryption is very efficient: it uses just one key and can encrypt large amounts of data quickly, and the resulting ciphertext is relatively small. Symmetric key schemes include AES, TDEA, and hash-based password systems.

AES (Advanced Encryption Standard) is a symmetric block cipher that encrypts data in fixed-size blocks. It's widely used to secure sensitive data due to its efficiency and strong security characteristics. AES is one of the most popular symmetric encryption algorithm in use today.

Here’s how AES encryption works[AES]:

  1. Key Generation

    • Key Selection: Start by choosing a key of appropriate length, typically 128, 192, or 256 bits.
    • Key Expansion: Expand the initial key into multiple sets of round keys using the Rijndael key schedule.

  2. Encryption

    • Initial Setup: Divide the plaintext into blocks of 128 bits each, as AES processes 128 bits (16 bytes) at a time in a 4x4 column-major order matrix called the state.
    • Round Process: Perform the following steps for each block of plaintext:
      • SubBytes, ShiftRows, MixColumns (omitted in the final round), AddRoundKey.

  3. Decryption

    • Use the same key and perform the inverse of each encryption step in reverse order to decrypt.

The challenge with symmetric encryption algorithms like AES is sharing the key in a secure manner, so that the information it protects won’t be compromised. For this reason, symmetric encryption is often used in combination with asymmetric encryption.

Asymmetric encryption

In asymmetric encryption, two keys are used to encrypt and decrypt information. One key is publicly available, and one key is private and known only to the receiver. In this scheme, the sender encrypts data with the public key of the receiver, and the receiver decrypts the message with the private key. Asymmetric encryption schemes include RSA, Elliptical Curve Cryptography, and Diffie-Hellman.

Asymmetric encryption, such as RSA, is commonly used along with a symmetric encryption algorithm, such as AES. An AES symmetric key is encrypted using an asymmetric RSA algorithm, and sent to the receiver. Subsequent secret data transmissions are then encrypted using the AES symmetric key.

The underlying security of RSA is based on the computational hardness of factoring a large composite number into its prime factors.

RSA relies on the practical difficulty of factoring the product of two large prime numbers, making it computationally infeasible to derive p and q from N. This ensures that while the public key ( N, e) can be widely distributed and used for encrypting messages, the private key ( N, d) remains secure and confidential.

Vulnerabilities of today’s encryption algorithms

Both symmetric and asymmetric algorithms are vulnerable to quantum attacks. Shor's algorithm enables quantum computers to factor large integers and compute discrete logarithms very quickly. Similarly, Grover's algorithm can significantly reduce the time required to brute-force symmetric keys, effectively halving the bit strength of algorithms like AES.

RSA and Shor’s Algorithm

RSA encryption is based on the principle that it is easy to multiply large numbers together but difficult to factorize the product back into its original prime factors. The security of RSA depends on the computational difficulty of the integer factorization problem. Any cryptographic algorithm that relies on integer factorization for security is vulnerable to Shor’s algorithm.

The integer factorization problem, discrete logarithm, period-finding problem, and hidden-subgroup problem are all vulnerable to Shor’s algorithm.

At the heart of Shor’s algorithm lies the order-finding problem, which fundamentally transforms the approach to integer factorization.

Shor’s algorithm uses properties of modular arithmetic, focusing on finding the period or order of a number. The task is to find the smallest positive integer r such that a r = 1(mod N) , where N is the RSA modulus (product of two primes p and q), and a is a randomly chosen integer less than N .

The use of quantum Fourier transform to efficiently compute the period r is a key component of Shor’s algorithm. This quantum approach provides a significant speed advantage over classical methods.

Above is an example of a circuit for implementing Shor's algorithm.[QUANTUMCIRCUIT]

Shor’s Algorithm leverages quantum phase estimation.

Here is an overview of how this works[SHOR]:

  1. Define the Unitary Operator:

    • Select a specific unitary operator U such that when it operates on the quantum state ∣k⟩ by multiplying it by a k mod N.

  2. Setting Up the Quantum Circuit:

    • The quantum circuit involves two registers:
      • Index Register: This is the top register, initialized in a state of superposition.
      • Target Register: This is the lower register where the actual computation of U2j ∣k⟩ occurs.

  3. Controlled Unitary Operations:

    • The algorithm leverages the index register to control the application of the unitary operations U2j on the target register.

  4. Quantum Fourier Transform:

    • After processing through the unitary operations, an inverse Quantum Fourier Transform is performed on the index register.

  5. Measurement and Phase Estimation:

    • The state of the index register is measured, providing an output from which the phase θ can be deduced.

  6. Interpreting the Output:

    • The output from the measurement is used to estimate the order r of a modulo N.

  7. Factorization of N:

    • With r known, Shor’s algorithm proceeds to calculate a r/2 ±1 and uses the greatest common divisor (gcd) method to find the factors of N.

AES and Grover’s Algorithm

Grover's algorithm is a method used in quantum computing to efficiently find a specific input for a function when only the output is known. This is a critical vulnerability because a lot of cryptographic functions are one-way functions. Grover's algorithm significantly impacts symmetric encryption algorithms like AES (Advanced Encryption Standard). Here's a brief explanation of how Grover's algorithm functions and its implications for AES[GROVER]:

  1. Key Generation

    • Quantum Oracle Creation: The first step involves defining a "quantum oracle."

  2. Encryption (Grover's Search Mechanism)

    • Iteration Process: Each iteration of Grover's search begins with the oracle function evaluating whether a given key in superposition correctly decrypts the ciphertext.

  3. Decryption (Finding the AES Key)

    • Measurement: After sufficient iterations, measuring the quantum state collapses it to a state that corresponds to the correct key with a high probability.

Grover’s algorithm greatly reduces the effective security of AES. For example, AES-128, which classically would require 2^{128} operations to break, would need only about 2^{64} quantum operations[GROVER2].

Post Quantum Cryptography

Post Quantum Cryptography (PQC) is an evolving field of classical cryptographic methods designed to secure communication against the potential threat posed by quantum computation. PQC protocols have been developed and continue to evolve in order to withstand attacks from quantum algorithms.

Lattice-Based Cryptography

Lattice-based cryptography is the cornerstone of many PQC methods due to its resistance to known quantum attacks. Some underlying mathematical challenges used in lattice-based cryptography include:

Information-theoretic Security

Information-theoretic security refers to a standard of cryptography that is impossible to break, even with unlimited computational power and time. One foundational principle is that the encryption process introduces randomness, making the output appear completely random to anybody without the decryption key.

The One Time Pad (OTP)

The One Time Pad (OTP) is recognized as the only perfectly secure classical encryption method when applied correctly. The encryption process combines the plaintext message with a key using the XOR operation. This method ensures no information is revealed about the plaintext.

However, OTP's requirement for key uniqueness and length equal to the message makes practical application challenging.

Quantum Communication Protocols

Communication protocols such as teleportation and quantum secure direct communication (QSDC) provide information-theoretic security due to fundamental scientific principles:

Entanglement. Entanglement connects quantum systems, making it a resource for secure data transmission.

No-cloning Theorem. It is impossible to create an exact copy of an unknown quantum state, ensuring security.

State distinguishability. Determining if quantum states can be distinguished without prior knowledge is limited by their orthogonality.

The Evolving Security Landscape

Quantum Networking technologies signify a transformative shift in security. Classical networks, while offering high data rates, are increasingly susceptible to attacks by quantum computers. These vulnerabilities can be addressed by entanglement-based Quantum Networks, which promise high-security standards through information-theoretic security.

Integrating Entanglement-based Quantum Networks

It is evident that the landscape of security is rapidly evolving. Classical cryptographic techniques are giving way to more robust protocols enabled by Quantum Networks. Preparing your cybersecurity infrastructure for the future involves proactive adaptation and thoughtful integration of these technologies into your existing frameworks.

Building entanglement-based quantum networks requires:

This process can be facilitated by solutions like AliroNet™, which ensure customers meet secure networking goals and leverage the capabilities of entanglement-based quantum networking.