On the Design of Hardware Building Blocks for Modern Lattice-Based Encryption Schemes

Göttert, Norman; Feller, Thomas; Schneider, Michael; Buchmann, Johannes; Huss, Sorin A.

doi:10.1007/978-3-642-33027-8_30

Cited by 95 publications

(100 citation statements)

References 25 publications

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“…In order to achieve quasi-linear speed in O(n log n) when performing the essential polynomial-multiplication operation we use the Fast Fourier Transform (FFT) or more specifically the Number Theoretic Transform (NTT) [21]. The advantages offered by the NTT have recently been shown by a hard-and software implementation of an ideal lattice-based public key cryptosystem [12]. The NTT is defined in a finite field or ring for a given primitive n-th root of unity ω.…”

Section: High-level Optimizationmentioning

confidence: 99%

“…Another target for comparison is a recently reported implementation of an ideal lattice-based encryption system in soft-and hardware [12]. In software, the necessary polynomial arithmetic relies on Shoup's NTL library [22].…”

Section: Performance Analysis and Benchmarksmentioning

confidence: 99%

“…The speed advantage of ideal lattices over standard lattice constructions usually stems from the applicability of the Number Theoretic Transform (NTT), which allows operations in quasi-linear runtime of O(n log n) instead of quadratic complexity. In particular, two implementations of promising lattice-based constructions for encryption [12] and digital signatures [14] were recently presented and demonstrate that such constructions can be efficient in reconfigurable hardware. However, as the proof-of-concept implementation in [12] is based on the generic NTL library [22], it remains still somewhat unclear how these promising schemes perform on high-performance processors that include modern SIMD multimedia extensions such as SSE and AVX.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Software Speed Records for Lattice-Based Signatures

Güneysu

Oder

Pöppelmann

et al. 2013

Post-Quantum Cryptography

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Abstract. Novel public-key cryptosystems beyond RSA and ECC are urgently required to ensure long-term security in the era of quantum computing. The most critical issue on the construction of such cryptosystems is to achieve security and practicability at the same time. Recently, lattice-based constructions were proposed that combine both properties, such as the lattice-based digital signature scheme presented at CHES 2012. In this work, we present a first highly-optimized SIMD-based software implementation of that signature scheme targeting Intel's Sandy Bridge and Ivy Bridge microarchitectures. This software computes a signature in only 634988 cycles on average on an Intel Core i5-3210M (Ivy Bridge) processor. Signature verification takes only 45036 cycles. This performance is achieved with full protection against timing attacks.

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Section: High-level Optimizationmentioning

confidence: 99%

Section: Performance Analysis and Benchmarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Software Speed Records for Lattice-Based Signatures

Güneysu

Oder

Pöppelmann

et al. 2013

Post-Quantum Cryptography

View full text Add to dashboard Cite

show abstract

“…After the proposal of the encryption scheme, several implementations of the encryption scheme followed [12,25,29,7,3,18,27]. The basic arithmetic operations are polynomial multiplication, addition, subtraction, and generation of error polynomials from a discrete Gaussian distribution.…”

Section: Public-key Encryption Schemesmentioning

confidence: 99%

Ring-LWE: Applications to Cryptography and Their Efficient Realization

Roy

Karmakar

Verbauwhede

2016

Security, Privacy, and Applied Cryptography Engineering

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Abstract. The persistent progress of quantum computing with algorithms of Shor and Proos and Zalka has put our present RSA and ECC based public key cryptosystems at peril. There is a flurry of activity in cryptographic research community to replace classical cryptography schemes with their post-quantum counterparts. The learning with errors problem introduced by Oded Regev offers a way to design secure cryptography schemes in the post-quantum world. Later for efficiency LWE was adapted for ring polynomials known as Ring-LWE. In this paper we discuss some of these ring-LWE based schemes that have been designed. We have also drawn comparisons of different implementations of those schemes to illustrate their evolution from theoretical proposals to practically feasible schemes.

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“…There has also been research in similar areas, for example [14] discusses the practicality of existing applications of homomorphic encryption by an empirical evaluation based on the lattice-based scheme by Smart and Vercauteren [15], and highlights implementation issues such as memory access. Another related publication [16] considers the hardware building blocks for the LWE cryptosystem and uses Fast Fourier Transform (FFT) multiplication in polynomial rings. Although it is stated that there may be more suitable multiplication algorithms for this purpose, it is shown that this hardware implementation of LWE still outperforms the software implementation.…”

Section: Introductionmentioning

confidence: 99%

Targeting FPGA DSP Slices for a Large Integer Multiplier for Integer Based FHE

Moore¹,

Hanley²,

McAllister³

et al. 2013

Financial Cryptography and Data Security

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Abstract. Homomorphic encryption offers potential for secure cloud computing. However due to the complexity of homomorphic encryption schemes, performance of implemented schemes to date have been unpractical. This work investigates the use of hardware, specifically Field Programmable Gate Array (FPGA) technology, for implementing the building blocks involved in somewhat and fully homomorphic encryption schemes in order to assess the practicality of such schemes. We concentrate on the selection of a suitable multiplication algorithm and hardware architecture for large integer multiplication, one of the main bottlenecks in many homomorphic encryption schemes. We focus on the encryption step of an integer-based fully homomorphic encryption (FHE) scheme. We target the DSP48E1 slices available on Xilinx Virtex 7 FPGAs to ascertain whether the large integer multiplier within the encryption step of a FHE scheme could fit on a single FPGA device. We find that, for toy size parameters for the FHE encryption step, the large integer multiplier fits comfortably within the DSP48E1 slices, greatly improving the practicality of the encryption step compared to a software implementation. As multiplication is an important operation in other FHE schemes, a hardware implementation using this multiplier could also be used to improve performance of these schemes.

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On the Design of Hardware Building Blocks for Modern Lattice-Based Encryption Schemes

Cited by 95 publications

References 25 publications

Software Speed Records for Lattice-Based Signatures

Software Speed Records for Lattice-Based Signatures

Ring-LWE: Applications to Cryptography and Their Efficient Realization

Targeting FPGA DSP Slices for a Large Integer Multiplier for Integer Based FHE

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