A Lightweight Implementation of NTRU Prime for the Post-Quantum Internet of Things

The dawning era of quantum computing has initiated various initiatives for the standardization of post-quantum cryptosystems with the goal of (eventually) replacing RSA and ECC. NTRU Prime is a variant of the classical NTRU cryptosystem that comes with a couple of tweaks to minimize the attack surface; most notably, it avoids rings with "worrisome" structure. This paper presents, to our knowledge, the first assembler-optimized implementation of Streamlined NTRU Prime for an 8-bit AVR microcontroller and shows that high-security lattice-based cryptography is feasible for small IoT devices. An encapsulation operation using parameters for 128-bit post-quantum security requires 8.2 million clock cycles when executed on an 8-bit ATmega1284 microcontroller. The decapsulation is approximately twice as costly and has an execution time of 15.6 million cycles. We achieved this performance through (i) new low-level software optimization techniques to accelerate Karatsuba-based polynomial multiplication on the 8-bit AVR platform and (ii) an efficient implementation of the coefficient modular reduction written in assembly language. The execution time of encapsulation and decapsulation is independent of secret data, which makes our software resistant against timing attacks. Finally, we assess the performance one could theoretically gain by using a so-called product-form polynomial as part of the secret key and discuss potential security implications

Acceleration strategies for post-quantum cryptographic schemes

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Xavier Guitart Morales i Oriol Farràs Ventura[en] The aim of project is to study the quantum-resistant cryptosystems Classic McEliece and NTRU, revising some of their previous literature and proving some of the main results upon which these cryptosystems are built. We also study the implementation strategies for the acceleration of these schemes. Finally, we make a comparative study of the reference implementations, considering metrics such as performance and key size

Performance and Efficiency Exploration of Hardware Polynomial Multipliers for Post-Quantum Lattice-Based Cryptosystems

The significant effort in the research and design of large-scale quantum computers has spurred a transition to post-quantum cryptographic primitives worldwide. The post-quantum cryptographic primitive standardization effort led by the US NIST has recently selected the asymmetric encryption primitive Kyber as its candidate for standardization and indicated NTRU, as a valid alternative if intellectual property issues are not solved. Finally, a more conservative alternative to NTRU, NTRUPrime was also considered as an alternate candidate, due to its design choices that remove the possibility for a large set of attacks preemptively. All the aforementioned asymmetric primitives provide good performances, and are prime choices to provide IoT devices with post-quantum confidentiality services. In this work, we present a comprehensive exploration of hardware designs for the computation of polynomial multiplications, the workhorse operation in all the aforementioned cryptosystems, with a thorough analysis of performance, compactness and efficiency. The presented designs cope with the differences in the arithmetics of polynomial rings employed by distinct cryptosystems, benefiting from configurations and optimizations that are applicable at synthesis time and/or run time. In this context, we target a use case scenario where long-term key pairs are used, such as the ones for VPNs (e.g., over IPSec), secure shell protocols and instant messaging applications. Our high-performance design variants exhibit figures of latency comparable to the ones needed for the execution of the symmetric cryptographic primitives also included in the Post-Quantum schemes. Notably, the performance figures of the designs proposed for NTRU and NTRU Prime surpass the ones described in the related literature

CRYSTALS - Kyber: A CCA-secure Module-Lattice-Based KEM

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digital-signature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of post-quantum security

Multi-Unit Serial Polynomial Multiplier to Accelerate NTRU-Based Cryptographic Schemes in IoT Embedded Systems

Concern for the security of embedded systems that implement IoT devices has become a crucial issue, as these devices today support an increasing number of applications and services that store and exchange information whose integrity, privacy, and authenticity must be adequately guaranteed. Modern lattice-based cryptographic schemes have proven to be a good alternative, both to face the security threats that arise as a consequence of the development of quantum computing and to allow efficient implementations of cryptographic primitives in resource-limited embedded systems, such as those used in consumer and industrial applications of the IoT. This article describes the hardware implementation of parameterized multi-unit serial polynomial multipliers to speed up time-consuming operations in NTRU-based cryptographic schemes. The flexibility in selecting the design parameters and the interconnection protocol with a general-purpose processor allow them to be applied both to the standardized variants of NTRU and to the new proposals that are being considered in the post-quantum contest currently held by the National Institute of Standards and Technology, as well as to obtain an adequate cost/performance/security-level trade-off for a target application. The designs are provided as AXI4 bus-compliant intellectual property modules that can be easily incorporated into embedded systems developed with the Vivado design tools. The work provides an extensive set of implementation and characterization results in devices of the Xilinx Zynq-7000 and Zynq UltraScale+ families for the different sets of parameters defined in the NTRUEncrypt standard. It also includes details of their plug and play inclusion as hardware accelerators in the C implementation of this public-key encryption scheme codified in the LibNTRU library, showing that acceleration factors of up to 3.1 are achieved when compared to pure software implementations running on the processing systems included in the programmable devices.European Union 952622Ministerio de Ciencia e Innovación PID2020-116664RB100, 10.13039/50110001103

CRYSTALS - Kyber: A CCA-secure Module-Lattice-Based KEM

Rapid advances in quantum computing, together with the announcement by the National Institute of Standards and Technology (NIST) to define new standards for digitalsignature, encryption, and key-establishment protocols, have created significant interest in post-quantum cryptographic schemes. This paper introduces Kyber (part of CRYSTALS - Cryptographic Suite for Algebraic Lattices - a package submitted to NIST post-quantum standardization effort in November 2017), a portfolio of post-quantum cryptographic primitives built around a key-encapsulation mechanism (KEM), based on hardness assumptions over module lattices. Our KEM is most naturally seen as a successor to the NEWHOPE KEM (Usenix 2016). In particular, the key and ciphertext sizes of our new construction are about half the size, the KEM offers CCA instead of only passive security, the security is based on a more general (and flexible) lattice problem, and our optimized implementation results in essentially the same running time as the aforementioned scheme. We first introduce a CPA-secure public-key encryption scheme, apply a variant of the Fujisaki-Okamoto transform to create a CCA-secure KEM, and eventually construct, in a black-box manner, CCA-secure encryption, key exchange, and authenticated-key-exchange schemes. The security of our primitives is based on the hardness of Module-LWE in the classical and quantum random oracle models, and our concrete parameters conservatively target more than 128 bits of postquantum security