Brian Koziel

Brian Koziel

MS Computer Engineering

About

19
Publications
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Publications

Publications (19)
Chapter
In the third round of the NIST PQC standardization process, the only isogeny-based candidate, SIKE, suffers from slow performance when compared to other contenders. The large-degree isogeny computation performs a series of isogenous mappings between curves, to account for about 80% of SIKE’s latency. Here, we propose, implement, and evaluate a new...
Chapter
In this work, we present a small architecture for quantum-safe hybrid key exchange targeting ECDH and SIKE. This is the first known hardware implementation of ECDH/SIKE-based hybrid key exchange in the literature. We propose new ECDH and EdDSA parameter sets defined over the SIKE primes. As a proof-of-concept, we evaluate SIKEX434, a hybrid PQC sch...
Chapter
When evaluating different cryptosystems, one primary metric is the cost to deploy the scheme in today’s software or hardware platforms. Given the option, hardware acceleration is typically preferred as optimizing a cryptosystem’s computations in logical gates leads to improvements in performance, power, and energy. Here, we survey the progress on a...
Chapter
CSIDH is a recent post-quantum key establishment protocol based on constructing isogenies between supersingular elliptic curves. Several recent works give constant-time implementations of CSIDH along with some optimizations of the ideal class group action evaluation algorithm, including the SIMBA technique of Meyer et al. and the “two-point method”...
Chapter
Isogeny-based key establishment protocols are believed to be resistant to quantum cryptanalysis. Two such protocols—supersingular isogeny Diffie-Hellman (SIDH) and commutative supersingular isogeny Diffie-Hellman (CSIDH)—are of particular interest because of their extremely small public key sizes compared with other post-quantum candidates. Althoug...
Article
In this work, we present a fast parallel architecture to perform supersingular isogeny key encapsulation (SIKE). We propose and implement a fast isogeny accelerator architecture that uses fast and parallelized isogeny formulas. On top of our isogeny accelerator, we build a novel architecture for the SIKE primitive, which provides both quantum and I...
Technical Report
Full-text available
This manuscript describes SIKE, the isogeny-based key encapsulation candidate, submitted to the second round of the NIST standardization process.
Chapter
Problems relating to the computation of isogenies between elliptic curves defined over finite fields have been studied for a long time. Isogenies on supersingular elliptic curves are a candidate for quantum-safe key exchange protocols because the best known classical and quantum algorithms for solving well-formed instances of the isogeny problem ar...
Article
In this work, we present a high-performance and scalable architecture for isogeny-based cryptosystems. In particular, we use the architecture in a fast, constant-time FPGA implementation of the quantum-resistant supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol. On a Virtex-7 FPGA, we show that our architecture is scalable by implem...
Conference Paper
Addition chain calculations play a critical role in determining the efficiency of cryptosystems based on isogenies on elliptic curves. However, finding a minimal length addition chain is not easy; a generalized version of the problem, in which one must find a chain that simultaneously forms each of a sequence of values, is NP-complete. For the spec...
Conference Paper
In this paper, we present a constant-time hardware implementation that achieves new speed records for the supersingular isogeny Diffie-Hellman (SIDH), even when compared to highly optimized Haswell computer architectures. We employ inversion-free projective isogeny formulas presented by Costello et al. at CRYPTO 2016 on an FPGA. Modern FPGA’s can t...
Conference Paper
We investigate the efficiency of implementing the Jao and De Feo isogeny-based post-quantum key exchange protocol (from PQCrypto 2011) on ARM-powered embedded platforms. In this work we propose new primes to speed up constant-time finite field arithmetic and perform isogenies quickly. Montgomery multiplication and reduction are employed to produce...
Article
To the best of our knowledge, we present the first hardware implementation of isogeny-based cryptography available in the literature. Particularly, we present the first implementation of the supersingular isogeny Diffie-Hellman (SIDH) key exchange, which features quantum-resistance. We optimize this design for speed by creating a high throughput mu...
Conference Paper
Full-text available
We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the...
Conference Paper
Elliptic curve cryptography (ECC) is an ideal choice for low-resource applications because it provides the same level of security with smaller key sizes than other existing public key encryption schemes. For low-resource applications, designing efficient functional units for elliptic curve computations over binary fields results in an effective pla...