In this paper we propose an efficient and compact processor for a ring-LWE based encryption scheme. We present three optimizations for the Number Theoretic Transform (NTT) used for polynomial multiplication: we avoid preprocessing in the negative wrapped convolution by merging it with the main algorithm, we reduce the fixed computation cost of the twiddle factors and propose an advanced memory access scheme. These optimization techniques reduce both the cycle and memory requirements. Finally, we also propose an optimization of the ring-LWE encryption system that reduces the number of NTT operations from five to four resulting in a 20% speed-up. We use these computational optimizations along with several architectural optimizations to design an instruction-set ring-LWE cryptoprocessor. For dimension 256, our processor performs encryption/decryption operations in 20/9 µs on a Virtex 6 FPGA and only requires 1349 LUTs, 860 FFs, 1 DSP-MULT and 2 BRAMs. Similarly for dimension 512, the processor takes 48/21 µs for performing encryption/decryption operations and only requires 1536 LUTs, 953 FFs, 1 DSP-MULT and 3 BRAMs. Our processors are therefore more than three times smaller than the current state of the art hardware implementations, whilst running somewhat faster.

This work describes a low-cost Public-Key Cryptography (PKC) based solution for security services such as key-distribution and authentication as required for wireless sensor networks. We propose a custom hardware assisted approach to implement Elliptic Curve Cryptography (ECC) in order to obtain stronger cryptography as well as to minimize the power. Our compact and low-power ECC processor contains a Modular Arithmetic Logic Unit (MALU) for ECC field arithmetic. The best solution features 6718 gates for the MALU and control unit (data memory not included) in 0.13 μm CMOS technology over the field F 2 131 , which provides a reasonable level of security for the time being. In this case the consumed power is less than 30 μW when operating frequency is 500 kHz.

RFID-tags are a new generation of bar-codes with added functionality. An emerging application is the use of RFIDtags for anti-counterfeiting by embedding them into a product. Public-key cryptography (PKC) offers an attractive solution to the counterfeiting problem but whether a publickey cryptosystem can be implemented on an RFID tag or not remains unclear. In this paper, we investigate which PKCbased identification protocols are useful for these anticounterfeiting applications. We also discuss the feasibility of identification protocols based on Elliptic Curve Cryptography (ECC)

Abstract. This work proposes a compact implementation of the AES S-box using composite field arithmetic in GF(((2 2 ) 2 )2 ). It describes a systematic exploration of different choices for the irreducible polynomials that generate the extension fields. It also examines all possible transformation matrices that map one field representation to another. We show that the area of Satoh's S-box, which is the most compact to our knowledge, is at least 5% away from an optimal solution. We implemented this optimal solution and Satoh's design using a 0.18 µm standard cell library.