DESIGN AND IMPLEMENTATION OF DUAL-FIELD MODULAR INVERSION ALGORITHM

Modular inverse arithmetic plays an important role in elliptic curve cryptography. Based on the analysis of Montgomery modular inversion algorithm, this paper presents a new dual-field modular inversion algorithm, and a novel scalable and unified architecture for Montgomery inverse hardware in finite fields GF(p) and GF(2n) is proposed. Furthermore, this architecture based on the new modular inversion algorithm has been verified by modeling it in Verilog-HDL, and accomplished it under 0.18 μm CMOS technology. The result indicates that our work has better performance and flexibility than other works.

Fast VLSI Implementation of Modular Inversion in Galois Field GF(p)

Modular inversion is one of the key arithmetic operations in public key cryptosystems, so low-cost, high-speed hardware implementation is absolutely necessary. This paper presents an algorithm for prime fields for hardware implementation. The algorithm involves only ordinary addition/subtraction and does not need any modular operations, multiplications or divisions. All of the arithmetic operations in the algorithm can be accomplished by only one adder, so it is very suitable for fast very large scale integration (VLSI) implementation. The VLSI implementation of the algorithm is also given with good performance and low silicon penalty.

To Construct High Level Secure Communication System： CTMI Is Not Enough

Public key cryptographic （PKC） algorithms, such as the RSA, elliptic curve digital signature algorithm （ECDSA） etc., are widely used in the secure communication sys- tems, such as OpenSSL, and a variety of in- formation security systems. If designer do not securely implement them, the secret key will be easily extracted by side-channel attacks （SCAs） or combinational SCA thus mitigat- ing the security of the entire communication system. Previous countermeasures of PKC im- plementations focused on the core part of the algorithms and ignored the modular inversion which is widely used in various PKC schemes. Many researchers believe that instead of straightforward implementation, constant time modular inversion （CTMI） is enough to resist the attack of simple power analysis combined with lattice analysis. However, we find that the CTMI security can be reduced to a hidden t-bit multiplier problem. Based on this feature, we firstly obtain Hamming weight of interme- diate data through side-channel leakage. Then, we propose a heuristic algorithm to solve the problem by revealing the secret （partial and full） base of CTMI. Comparing previous nec-essary input message for masking filtering, our procedure need not any information about the secret base of the inversion. To our knowl- edge, this is the first time for evaluating the practical security of CTM! and experimental results show the fact that CTMI is not enough for high-level secure communication systems.