Fast Software Implementation of Binary Elliptic Curve Cryptography

This paper presents an efficient and side channel protected software implementation of point multiplication for the standard NIST and SECG binary elliptic curves. The enhanced performance is achieved by improving the Lòpez-Dahab/Montgomery method at the algorithmic level, and by leveraging Intel\u27s AVX architecture and the pclmulqdq processor instruction at the coding level. The fast carry-less multiplication is further used to speed up the reduction on the newest Haswell platforms. For the five NIST curves over $GF(2^m)$ with $m$ $\in$ $\{163,233,283,409,571\}$, the resulting point multiplication implementation is about 6 to 12 times faster than that of OpenSSL-1.0.1e, enhancing the ECDHE and ECDSA algorithms significantly

Analysis of Parallel Montgomery Multiplication in CUDA

For a given level of security, elliptic curve cryptography (ECC) offers improved efficiency over classic public key implementations. Point multiplication is the most common operation in ECC and, consequently, any significant improvement in perfor- mance will likely require accelerating point multiplication. In ECC, the Montgomery algorithm is widely used for point multiplication. The primary purpose of this project is to implement and analyze a parallel implementation of the Montgomery algorithm as it is used in ECC. Specifically, the performance of CPU-based Montgomery multiplication and a GPU-based implementation in CUDA are compared

Enhancing an Embedded Processor Core with a Cryptographic Unit for Performance and Security

We present a set of low-cost architectural enhancements to accelerate the execution of certain arithmetic operations common in cryptographic applications on an extensible embedded processor core. The proposed enhancements are generic in the sense that they can be beneficially applied in almost any RISC processor. We implemented the enhancements in form of a cryptographic unit (CU) that offers the programmer an extended instruction set. The CU features a 128-bit wide register file and datapath, which enables it to process 128-bit words and perform 128-bit loads/stores. We analyze the speed-up factors for some arithmetic operations and public-key cryptographic algorithms obtained through these enhancements. In addition, we evaluate the hardware overhead (i.e. silicon area) of integrating the CU into an embedded RISC processor. Our experimental results show that the proposed architectural enhancements allow for a significant performance gain for both RSA and ECC at the expense of an acceptable increase in silicon area. We also demonstrate that the proposed enhancements facilitate the protection of cryptographic algorithms against certain types of side-channel attacks and present an AES implementation hardened against cache-based attacks as a case study

I2PA, U-prove, and Idemix: An Evaluation of Memory Usage and Computing Time Efficiency in an IoT Context

The Internet of Things (IoT), in spite of its innumerable advantages, brings many challenges namely issues about users' privacy preservation and constraints about lightweight cryptography. Lightweight cryptography is of capital importance since IoT devices are qualified to be resource-constrained. To address these challenges, several Attribute-Based Credentials (ABC) schemes have been designed including I2PA, U-prove, and Idemix. Even though these schemes have very strong cryptographic bases, their performance in resource-constrained devices is a question that deserves special attention. This paper aims to conduct a performance evaluation of these schemes on issuance and verification protocols regarding memory usage and computing time. Recorded results show that both I2PA and U-prove present very interesting results regarding memory usage and computing time while Idemix presents very low performance with regard to computing time

Efficient Unified Arithmetic for Hardware Cryptography

The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF(q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1], the US federal Digital Signature Standard [2], elliptic curve cryptography [3, 4], and also recently identity based cryptography [5, 6]. Most popular finite fields that are heavily used in cryptographic applications due to elliptic curve based schemes are prime fields GF(p) and binary extension fields GF(2n). Recently, identity based cryptography based on pairing operations defined over elliptic curve points has stimulated a significant level of interest in the arithmetic of ternary extension fields, GF(3^n)