Modular multiplication is the most dominant arithmetic operation in elliptic curve cryptography (ECC), that is a type of public-key cryptography. Montgomery multiplier is commonly used to compute the modular multiplications and requires scalability because the bit length of operands varies depending on its security level. In addition, ECC is performed in GF(P) or GF(2n), and unified architecture for multipliers in GF(P) and GF(2n) is required. However, in previous works, changing frequency is necessary to deal with delay-time difference between GF(P) and GF(2n) multipliers because the critical path of the GF(P) multiplier is longer. This paper proposes unified dual-radix architecture for scalable Montgomery multiplications in GF(P) and GF(2n). This proposed architecture unifies four parallel radix-216 multipliers in GF(P) and a radix-264 multiplier in GF(2n) into a single unit. Applying lower radix to GF(P) multiplier shortens its critical path and makes it possible to compute the operands in the two fields using the same multiplier at the same frequency so that clock dividers to deal with the delay-time difference are not required. Moreover, parallel architecture in GF(P) reduces the clock cycles increased by dual-radix approach. Consequently, the proposed architecture achieves to compute a GF(P) 256-bit Montgomery multiplication in 0.28 µs. The implementation result shows that the area of the proposal is almost the same as that of previous works: 39 kgates.

A scan chain is one of the most important testing techniques, but it can be used as side-channel attacks against a cryptography LSI. We focus on scan-based attacks, in which scan chains are targeted for side-channel attacks. The conventional scan-based attacks only consider the scan chain composed of only the registers in a cryptography circuit. However, a cryptography LSI usually uses many circuits such as memories, micro processors and other circuits. This means that the conventional attacks cannot be applied to the practical scan chain composed of various types of registers. In this paper, a scan-based attack which enables to decipher the secret key in an AES cryptography LSI composed of an AES circuit and other circuits is proposed. By focusing on bit pattern of the specific register and monitoring its change, our scan-based attack eliminates the influence of registers included in other circuits than AES. Our attack does not depend on scan chain architecture, and it can decipher practical AES cryptography LSIs.

Scan-based side-channel attacks retrieve a secret key in a cryptography circuit by analyzing scanned data. Since they must be considerable threats to a cryptosystem LSI, we have to protect cryptography circuits from them. RSA is one of the most important cryptography algorithms because it effectively realizes a public-key cryptography system. RSA is extensively used but conventional scan-based side-channel attacks cannot be applied to it because it has a complicated algorithm. This paper proposes a scan-based side-channel attack which enables us to retrieve a secret key in an RSA circuit. The proposed method is based on detecting intermediate values calculated in an RSA circuit. We focus on a 1-bit time-sequence which is specific to some intermediate values. By monitoring the 1-bit time-sequence in the scan path, we can find out the register position specific to the intermediate value and we can know whether this intermediate value is calculated or not in the target RSA circuit. We can retrieve a secret key one-bit by one-bit from MSB to LSB. The experimental results demonstrate that a 1,024-bit secret key used in the target RSA circuit can be retrieved using 30.2 input messages within 98.3 seconds and its 2,048-bit secret key can be retrieved using 34.4 input within 634.0 seconds.