Efficient and Secure Algorithms for GLV-Based Scalar Multiplication and their Implementation on GLV-GLS Curves (Extended Version)

We propose efficient algorithms and formulas that improve the performance of side-channel protected elliptic curve computations with special focus on scalar multiplication exploiting the Gallant-Lambert-Vanstone (CRYPTO 2001) and Galbraith-Lin-Scott (EUROCRYPT 2009) methods. Firstly, by adapting Feng et al.\u27s recoding to the GLV setting, we derive new regular algorithms for variable-base scalar multiplication that offer protection against simple side-channel and timing attacks. Secondly, we propose an efficient, side-channel protected algorithm for fixed-base scalar multiplication which combines Feng et al.\u27s recoding with Lim-Lee\u27s comb method. Thirdly, we propose an efficient technique that interleaves ARM and NEON-based multiprecision operations over an extension field to improve performance of GLS curves on modern ARM processors. Finally, we showcase the efficiency of the proposed techniques by implementing a state-of-the-art GLV-GLS curve in twisted Edwards form defined over GF(p^2), which supports a four dimensional decomposition of the scalar and is fully protected against timing attacks. Analysis and performance results are reported for modern x64 and ARM processors. For instance, we compute a variable-base scalar multiplication in 89,000 and 244,000 cycles on an Intel Ivy Bridge and an ARM Cortex-A15 processor (respect.); using a precomputed table of 6KB, we compute a fixed-base scalar multiplication in 49,000 and 116,000 cycles (respect.); and using a precomputed table of 3KB, we compute a double scalar multiplication in 115,000 and 285,000 cycles (respect.). The proposed techniques represent an important improvement of the state-of-the-art performance of elliptic curve computations, and allow us to set new speed records in several modern processors. The techniques also reduce the cost of adding protection against timing attacks in the computation of GLV-based variable-base scalar multiplication to below 10%

Portunus: Re-imagining access control in distributed systems

TLS termination, which is essential to network and security infrastructure providers, is an extremely latency sensitive operation that benefits from access to sensitive key material close to the edge. However, increasing regulatory concerns prompt customers to demand sophisticated controls on where their keys may be accessed. While traditional access-control solutions rely on a highly available centralized process to enforce access, the round-trip latency and decreased fault tolerance make this approach unappealing. Furthermore, the desired level of customer control is at odds with customizing the distribution process for each key. To solve this dilemma, we have designed and implemented Portunus, a cryptographic storage and access control system built using a variant of public-key cryptography called attribute-based encryption (ABE). Using Portunus, TLS keys are protected using ABE under a policy chosen by the customer. Each server is issued unique ABE keys based on its attributes, allowing it to decrypt only the TLS keys for which it satisfies the policy. Thus, the encrypted keys can be stored at the edge, with access control enforced passively through ABE. If a server receives a TLS connection but is not authorized to decrypt the necessary TLS key, the request is forwarded directly to the nearest authorized server, further avoiding the need for a centralized coordinator. In comparison, a trivial instantiation of this system using standard public-key cryptography might wrap each TLS key with the key of every authorized data center. This strategy, however, multiplies the storage overhead by the number of data centers. We have deployed Portunus on Cloudflare\u27s global network of over 400 data centers. Our measurements indicate that we can handle millions of requests per second globally, making it one of the largest deployments of ABE

High-performance implementation of elliptic curve cryptography using vector instructions

Elliptic curve cryptosystems are considered an efficient alternative to conventional systems such as DSA and RSA. Recently, Montgomery and Edwards elliptic curves have been used to implement cryptosystems. In particular, the elliptic curves Curve25519 and Curve448 were used for instantiating Diffie-Hellman protocols named X25519 and X448. Mapping these curves to twisted Edwards curves allowed deriving two new signature instances, called Ed25519 and Ed448, of the Edwards Digital Signature Algorithm. In this work, we focus on the secure and efficient software implementation of these algorithms using SIMD parallel processing. We present software techniques that target the Intel AVX2 vector instruction set for accelerating prime field arithmetic and elliptic curve operations. Our contributions result in a high-performance software library for AVX2-ready processors. For example, our library computes digital signatures 19% (for Ed25519) and 29% (for Ed448) faster than previous optimized implementations. Also, our library improves by 10% and 20% the execution time of X25519 and X448, respectively453FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP14/50704-

A Faster Software Implementation of the Supersingular Isogeny Diffie-Hellman Key Exchange Protocol

Since its introduction by Jao and De Feo in 2011, the supersingular isogeny Diffie-Hellman (SIDH) key exchange protocol has positioned itself as a promising candidate for post-quantum cryptography. One salient feature of the SIDH protocol is that it requires exceptionally short key sizes. However, the latency associated to SIDH is higher than the ones reported for other post-quantum cryptosystem proposals. Aiming to accelerate the SIDH runtime performance, we present in this work several algorithmic optimizations targeting both elliptic-curve and field arithmetic operations. We introduce in the context of the SIDH protocol a more efficient approach for calculating the elliptic curve operation P + [k]Q. Our strategy achieves a factor 1.4 speedup compared with the popular variable-three-point ladder algorithm regularly used in the SIDH shared secret phase. Moreover, profiting from pre-computation techniques our algorithm yields a factor 1.7 acceleration for the computation of this operation in the SIDH key generation phase. We also present an optimized evaluation of the point tripling formula, and discuss several algorithmic and implementation techniques that lead to faster field arithmetic computations. A software implementation of the above improvements on an Intel Skylake Core i7-6700 processor gives a factor 1.33 speedup against the state-of-the-art software implementation of the SIDH protocol reported by Costello-Longa-Naehrig in CRYPTO 2016