Hikaru Morita

A Switching Closure Test to Analyze Cryptosystems

The closure test MCT (meet-in-the-middle closure test) was introduced to analyze the algebraic properties of cryptosystems [KaRiSh]. Since MCT needs a large amount of memory, it is hard to implement with an ordinary meet-in-the-middle method. As a feasible version of MCT, this paper presents a switching closure test SCT which based on a new memoryless meet-in-the-middle method. To achieve the memoryless method, appropriate techniques, such as expansion of cycling detection methods for one function into a method for two functions and an efficient intersection search method that uses only a small amount of memory, are used in an extremely effective manner.

A Fast Modular-multiplication Algorithm based on a Higher Radix

This paper presents a new fast compact modular-multiplication algorithm, which will multiply modulo N in log(N)/log(r) clock pulses when the algorithm is based on radix r (r ? 4).

A Fast Modular-multiplication Module for Smart Cards

A new compact modular multiplication algorithm based on a higher radix can reduce the amount of processing to half or less that of conventional algorithms. When applied to smart cards, the new division method can reduce the number of memory access events. Consequently, a module containing 3 Kbits of RAM and a 3-Kgate operation unit will calculate a 512-bit modular exponentiation in under two seconds at a 4-MHz clock.

Higher Radix Nonrestoring Modular Multiplication Algorithm and Public-key LSI Architecture with Limited Hardware Resources

Security applications to be installed in small size hardware such as cellular phones and smart cards need a small and practical LSI for key distribution or authentication. This paper describes an improved modular multiplication algorithm and LSI architecture for public-key schemes with the goal of limiting hardware resources. The algorithm, which employs higher radix arithmetic, eliminates the slow restoring which occurs in modular multiplication. The proposed architecture is based on the use of RAM and low operation frequency. The LSI is designed to calculate 512 bit modular exponentiation within 0.1 seconds at the frequency of 17 MHz. This requires only 13 Kgates and six 512bit RAMs.

Results of switching-closure-test on FEAL

The closure tests, CCT and MCT, were introduced to analyze the algebraic properties of cryptosystems by Kaliski et al. [KaRiSh]. If a cryptosystem is closed, the tests give the same results “Fail” and the cryptosystem might be breakable. Though CCT requires much less memory and time than MCT, we cannot apply CCT to check cryptosystems having the same data and key block lengths such as FEAL with non-parity mode. Because CCT utilizes the differences in data and key block lengths.