up:: [[Post-Quantum Cryptography (PQC)]], [[Lattice-based cryptography]] # Nth Degree Truncated Polynomial Ring Units (NTRU) NTRU (Nth Degree Truncated Polynomial Ring Units) is a [[Lattice-based cryptography|lattice-based cryptographic algorithm]] that is primarily used for key [[encryption]] and [[Digital Signature|digital signatures]]. It was developed in 1996 and is known for its security strength against [[Quantum Computing|quantum computer]] attacks, which makes it a candidate for [[Post-Quantum Cryptography (PQC)|post-quantum cryptography]]. ## How It Works NTRU operates in a polynomial ring, which involves operations on polynomials with coefficients that are reduced modulo a fixed integer. The [[algorithm]] uses three main polynomials: a [[private key]] �f, a [[public key]] ℎh, and a message representative polynomial �m. [[Encryption]] involves multiplying the message polynomial by the [[public key]] in the ring, and decryption involves using the [[private key]] to recover the original message. This process relies on the mathematical hardness of finding short, nonzero vectors in high-dimensional lattices (the "[[Shortest Vector Problem (SVP)|shortest vector problem]]"), which is believed to be difficult for both classical and [[Quantum Computing|quantum computers]]. ## Key Features - **Resistance to Quantum Attacks:** Based on mathematical problems that are currently not solvable by [[Quantum Computing|quantum computers]]. - **Efficient Performance:** Tends to be faster and requires less computational power compared to other [[Asymmetric Encryption|public-key algorithms]] like [[RSA]] and [[Elliptic Curve Cryptography|ECC]]. - **Scalability:** Suitable for environments with limited computational resources, such as mobile devices and embedded systems. ## Advantages - **[[Quantum-Resistant|Quantum Resistance]]:** Offers protection against potential future threats from [[quantum computing]], making it suitable for long-term security planning. - **Speed:** Generally provides faster operations than many traditional [[Asymmetric Encryption|public-key cryptography]] systems, particularly in decryption. - **Low Power Requirements:** Efficient in terms of energy consumption, which is beneficial for use in mobile and IoT devices. ## Exploitable Mechanisms/Weaknesses While NTRU is considered secure against many types of attacks, it has a higher susceptibility to certain side-channel attacks if not properly implemented. Additionally, as a relatively newer cryptographic scheme, it may require further vetting and standardization in diverse real-world applications. ## Common Tools/Software - **libntru:** An open-source C library implementing NTRU [[encryption]], which is widely used for experimental and educational purposes. - **Bouncy Castle:** Provides support for NTRU in its cryptographic library, available for Java and C# platforms. - **NTRU-OpenSSL:** A fork of OpenSSL that includes support for NTRU, though it is primarily used for research and development. ## Related Cybersecurity Policies - **[[NIST Post-Quantum Cryptography Standardization]] Process:** NTRU has been submitted for consideration in the ongoing effort by NIST to standardize [[Post-Quantum Cryptography (PQC)|post-quantum cryptographic algorithms]]. This process aims to find and standardize cryptographic methods that are secure against both classical and [[Quantum Computing|quantum computers]]. - **[[ISOIEC 29192-3]]:** International standard covering lightweight [[cryptography]], under which NTRU is categorized due to its efficiency and suitability for constrained environments. ## Current Status NTRU is part of the broader exploration and experimentation within the field of [[Post-Quantum Cryptography (PQC)|post-quantum cryptography]]. It is being evaluated for standardization by bodies like NIST and is gaining attention as the need for [[quantum-resistant]] cryptographic solutions becomes more pressing. ## Revision History - **2024-04-19:** Entry created.