My research is in the area of elliptic curve cryptography and related finite field arithmetic. I am interested in new cryptographic primitives, new algorithms in computational number theory, new protocols, efficient hardware and software implementations, and side-channel attacks and countermeasures.

**Post-Quantum Cryptography**

Presence of quantum computers is a real threat against the security of currently used public key cryptographic algorithms such as RSA and Elliptic curve cryptography. Post-quantum cryptography refers to research on cryptographic primitives (usually public-key cryptosystems) that are not efficiently breakable using quantum computers. This research investigates design, analysis, and implementation of quantum-safe cryptographic algorithms. For more information refer to PQCryptARM.

**Finite Field Arithmetic**

The arithmetic operations in the finite fields over prime fields and binary extension fields are largely utilized for cryptographic algorithms such as point multiplication in elliptic curve cryptography, exponentiation-based cryptosystems, and coding. This research investigates efficient algorithms and efficient architectures for the computation of finite field operations.

**Efficient Implementations of Cryptographic Primitives**

Providing security for the emerging deeply-embedded systems utilized in sensitive applications is a problem whose practical mechanisms have not received sufficient attention by the research community and industry alike. This research investigates efficient implementations of elliptic curve cryptography on embedded devices with extremely-constrained environments.

**Machine-Level Optimization for the Computation of Cryptographic Pairings**

High-speed computations of pairing-based cryptography is crucial for both desktop computers and embedded hand-held devices. This research investigates the machine-level and assembly optimizations for the computation of lower level finite field arithmetic used in pairings.

**Highly-parallel scalable architectures for Cryptography Computations**

Highly-parallel and fast computations of the widely-used cryptographic algorithm is required for high-performance applications. However, a challenge to cope with is that most applications for which parallelism is essential, have significantly large scale that is not commonly supported by today’s algorithms. Therefore, new algorithms are required to investigate parallelization.

The prospect of quantum computers is a threat against the security of currently used public key cryptographic algorithms. It has been widely accepted that, both public key cryptosystems including RSA and ECC will be broken by quantum computers employing certain algorithms. Although large-scale quantum computers do not yet exist, but the goal is to develop** quantum-resistant cryptosystems** in anticipation of quantum computers as most of the public key cryptography that is used on the Internet today is based on algorithms that are vulnerable to quantum attacks.

This project will explore isogenies on elliptic curves as a foundation for quantum-resistant cryptography. **Isogeny computation** is known to be difficult. This project will analyze newer and faster families of isogenies, which yield a faster solution to the problem of finding isogenies. It will exploit state-of-the-art techniques and employ new optimizations to speed up the computation in isogeny-based cryptography, including tower field and curve arithmetic. The performance of field arithmetic computation is strongly influenced by the processor micro-architecture features, the size of the operands, the algorithms, and programming techniques associated to them. This research will provide preliminary results on developing fast algorithms and architectures for** post-quantum cryptographic** computations suitable for emerging embedded systems.

For more information click HERE.

**Publications**

- R. Azarderakhsh, D. Jao, K. Kalach, B. Koziel and Ch. Leonardi, “Key compression for isogeny-based cryptosystems”, in Proc.
**AsiaPKC 2016**, pp. 1-10, ACM, Jun. 2016. - B. Koziel, R. Azarderakhsh, A. Jalali, D. Jao, and M. Mozaffari Kermani, “NEON-SIDH: Efficient implementation of supersingular isogeny Diffie-Hellman key exchange protocol on ARM”, in Proc. Conf. Cryptology and Network Security,
**CANS 2016**, to appear in 2016. - B. Koziel, R. Azarderakhsh, D. Jao and M. Mozaffari Kermani, “On Fast Calculation of Addition Chains for Isogeny-Based Cryptography”, in Proc.
**Inscrypt 2016**, pp.334-347, 2016. - R. Azarderakhsh and K. Karabina, “Efficient Algorithms and Architectures for the Computation of Double Point Multiplication on Elliptic Curves”, in Proc. Third ACM workshop on Cryptography and Security in Computing Systems,
**CS2@HiPEAC 2016**, ACM, pp.25-30, Jan. 2016.

**isogeny-based cryptosystems**are required for high-performance applications. However, a challenge to tackle is that most applications that lend themselves to being parallelized, a key attribute for high-performance computing, have very significant scale that is rarely seen in the original algorithms proposed. Therefore, new algorithms and techniques are required to investigate parallelization and scalability in all levels of computations for isogeny-based cryptography over supersingular elliptic curves.

The goal of this project is,

*through building on our preliminary work,*to design a highly parallel and fast architecture for

**post-quantum cryptosystem**in anticipation of the future construction of quantum computers. In particular, we aim to construct more efficient hardware architectures for finite field arithmetic and post-quantum protocols based on supersingular elliptic curve isogenies, which we believe offer several advantages compared to the other approaches for

**post-quantum cryptography**.

**Publications**

- B. Koziel, R. Azarderakhsh, and M. Mozaffari Kermani, D. Jao, “Post-quantum cryptography on FPGA based on Isogenies on elliptic curves”,
**IEEE Transactions on Circuits and Systems (TCAS-I)**, vol. 64, no. 1, pp. 86-99, Jan. 2017. - B. Koziel, R. Azarderakhsh, D. Jao and M. Mozaffari Kermani, “On Fast Calculation of Addition Chains for Isogeny-Based Cryptography”, in Proc.
**Inscrypt 2016**, pp.334-347, 2016. - B. Koziel, R. Azarderakhsh, D. Jao, “On Secure Implementations of Quantum-Resistant Supersingular Isogeny Diffie-Hellman”, poster, in Proc.
**HOST 2017,**to appear 2017.

**implantable**and

**wearable**medical devices, Internet of nano-Things, and extremely-constrained smart cards, call for new and practical security mechanisms. Unfortunately, adopting the traditional security and cryptographic solutions often either fails in providing the required security properties or exhibits sub-optimal efficiency. In fact, in addition to exhibiting security, crypto-systems need to be feasible to utilize as well for applications in which performance and implementation metrics are bottleneck, without jeopardizing the security properties needed. Due to this order change in constraints, new cryptographic algorithms and architectures (and not those providing

**incremental performance**and

**battery-life alleviations**) are needed. The aforementioned is the motivation in this proposal whose outcome is envisioned enabling security for emerging usage models which outperforms current solutions.

In this project, the we provide coherent crypto-solutions feasibly applicable in practice through identifying three main levels of computations: finite field arithmetic, group operations, and point multiplication. The PIs also propose new approaches for computing point multiplication on binary elliptic curves using

**endomorphisms**and differential addition chains. The outcome of this proposal is envisioned to protect emerging, sensitive infrastructures, for both resource-constrained and high-performance applications. The goal of this proposal is to establish a paradigm shift in security, reliability, and energy-efficacy of sensitive embedded systems.

**Publications**

- K. Järvinen; A. Miele, R. Azarderakhsh, P. Longa, “FourQ on FPGA: New Hardware Speed Records for Elliptic Curve Cryptography over Prime Fields”, in Proc.
**CHES 2016**, pp. 517-537, LNCS, vol. 9813, Aug. 2016. - R. Azarderakhsh and K. Karabina, “Efficient Algorithms and Architectures for the Computation of Double Point Multiplication on Elliptic Curves”, in Proc. Third ACM workshop on Cryptography and Security in Computing Systems,
**CS2@HiPEAC 2016**, ACM, pp.25-30, Jan. 2016. - B. Koziel, R. Azarderakhsh, and M. Mozaffari Kermani, “Low-resource and fast binary Edwards curves cryptography using Gaussian normal basis” in Proc.
**IndoCrypt 2015**, pp. 347-369, Dec. 2015. - R. Azarderakhsh and K. Karabina, “A New Double Point Multiplication Algorithm and its Application to Binary Elliptic Curves with Endomorphisms“, I
**EEE Transactions on Computers**, vol. 63, no. 10, pp. 2614-2619, 2014.