Parametric, Secure and Compact Implementation of RSA on FPGA

We present a fast, efficient, and parameterized modular multiplier and a secure exponentiation circuit especially intended for FPGAs on the low end of the price range. The design utilizes dedicated block multipliers as the main functional unit and Block-RAM as storage unit for the operands. The adopted design methodology allows adjusting the number of multipliers, the radix used in the multipliers, and number of words to meet the system requirements such as available resources, precision and timing constraints. The architecture, based on the Montgomery modular multiplication algorithm, utilizes a pipelining technique that allows concurrent operation of hardwired multipliers. Our design completes 1020-bit and 2040-bit modular multiplications in 7.62 μs and 27.0 μs, respectively. The multiplier uses a moderate amount of system resources while achieving the best area-time product in literature. 2040-bit modular exponentiation engine can easily fit into Xilinx Spartan-3E 500; moreover the exponentiation circuit withstands known side channel attacks

Secure and Efficient RNS Approach for Elliptic Curve Cryptography

Scalar multiplication, the main operation in elliptic curve cryptographic protocols, is vulnerable to side-channel (SCA) and fault injection (FA) attacks. An efficient countermeasure for scalar multiplication can be provided by using alternative number systems like the Residue Number System (RNS). In RNS, a number is represented as a set of smaller numbers, where each one is the result of the modular reduction with a given moduli basis. Under certain requirements, a number can be uniquely transformed from the integers to the RNS domain (and vice versa) and all arithmetic operations can be performed in RNS. This representation provides an inherent SCA and FA resistance to many attacks and can be further enhanced by RNS arithmetic manipulation or more traditional algorithmic countermeasures. In this paper, extending our previous work, we explore the potentials of RNS as an SCA and FA countermeasure and provide an description of RNS based SCA and FA resistance means. We propose a secure and efficient Montgomery Power Ladder based scalar multiplication algorithm on RNS and discuss its SCAFA resistance. The proposed algorithm is implemented on an ARM Cortex A7 processor and its SCA-FA resistance is evaluated by collecting preliminary leakage trace results that validate our initial assumptions

Residue Number System Hardware Emulator and Instructions Generator

Residue Number System (RNS) is an alternative form of representing integers on which a large value gets represented by a set of smaller and independent integers. Cryptographic and signal filtering algorithms benefit from the use of RNS, due to its capabilities to increase performance and security. Herein, a simulation tool is presented which emulates the hardware implementation of an actual RNS co-processor. An “high-level to assembly” instructions generator is also built into this tool. The programmability and scalable architecture of the considered processor along with the high level description of the algorithm allows researchers and developers to easily evaluate and test their RNS algorithms on an actual architecture, using Java

Efficient scalar multiplication against side channel attacks using new number representation

Elliptic curve cryptography (ECC) is probably the most popular public key systems nowadays. The classic algorithm for computation of elliptic curve scalar multiplication is Doubling-and-Add. However, it has been shown vulnerable to simple power analysis, which is a type of side channel attacks (SCAs). Among different types of attacks, SCAs are becoming the most important and practical threat to elliptic curve computation. Although Montgomery power ladder (MPL) has shown to be a good choice for scalar multiplication against simple power analysis, it is still subject to some advanced SCAs such like differential power analysis. In this thesis, a new number representation is firstly proposed, then several scalar multiplication algorithms using this new number system are presented. It has also been shown that the proposed algorithms outperform or comparable to the best of existing similar algorithms in terms of against side channel attacks and computational efficiency. Finally we extend both the new number system and the corresponding scalar multiplication algorithms to high radix cases

RSA Power Analysis Obfuscation: A Dynamic FPGA Architecture

The modular exponentiation operation used in popular public key encryption schemes, such as RSA, has been the focus of many side channel analysis (SCA) attacks in recent years. Current SCA attack countermeasures are largely static. Given sufficient signal-to-noise ratio and a number of power traces, static countermeasures can be defeated, as they merely attempt to hide the power consumption of the system under attack. This research develops a dynamic countermeasure which constantly varies the timing and power consumption of each operation, making correlation between traces more difficult than for static countermeasures. By randomizing the radix of encoding for Booth multiplication and randomizing the window size in exponentiation, this research produces a SCA countermeasure capable of increasing RSA SCA attack protection

Combined small subgroups and side-channel attack on elliptic curves with cofactor divisible by 2m2^m

Nowadays, alternative models of elliptic curves like Montgomery, Edwards, twisted Edwards, Hessian, twisted Hessian, Huff's curves and many others are very popular and many people use them in cryptosystems which are based on elliptic curve cryptography. Most of these models allow to use fast and complete arithmetic which is especially convenient in fast implementations that are side-channel attacks resistant. Montgomery, Edwards and twisted Edwards curves have always order of group of rational points divisible by 4. Huff's curves have always order of rational points divisible by 8. Moreover, sometimes to get fast and efficient implementations one can choose elliptic curve with even bigger cofactor, for example 16. Of course the bigger cofactor is, the smaller is the security of cryptosystem which uses such elliptic curve. In this article will be checked what influence on the security has form of cofactor of elliptic curve and will be showed that in some situations elliptic curves with cofactor divisible by $2^m$ are vulnerable for combined small subgroups and side-channel attacks