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Up to $8k$ 8 k -bit Modular Montgomery Multiplication in Residue Number Systems With Fast 16-bit Residue Channels.
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- Author(s): Ahmadpour, Zabihollah; Jaberipur, Ghassem
- Source:
IEEE Transactions on Computers; Jun2022, Vol. 71 Issue 6, p1399-1410, 12p- Subject Terms:
- Source:
- Additional Information
- Abstract: Hardware realization of public-key cryptosystems often entails Montgomery modular multiplication (MMM), which is more efficient in residue number systems (RNS). A large pool of co-prime moduli allows for higher number of dynamically changeable moduli-set pairs for the required base extension, leading to ultra-wide key-lengths to accommodate the indispensable resistance to differential power-analysis (DPA) attacks. The moduli are often of the form ${2^r} - {{\delta }}$ 2 r - δ , where $r$ r denotes the width of residue channels. In a previous relevant RNS MMM design, with $r\ = \ 64$ r = 64 , probability of a successful DPA attack is less than ${2^{ - 66}}$ 2 - 66 , where efficient arithmetic is obtained only for a limited set of moduli that are insufficient for key-lengths over 1024 bits. Here we propose a free- ${{\delta }}$ δ RNS MMM scheme, for up-to 8192-bit key-lengths and fast 16-bit residue channels, based on the proposed ${{\delta }}$ δ -independent modulo-(${2^r} - {{\delta }}$ 2 r - δ ) adders and multipliers. Moreover, we propose an especial method for moduli selection that is required for base extension, leading to the same aforementioned DPA-resistance measure and much lower measures for key-lengths over 1024. The implementation results show $82,69,44\ percent$ 82 , 69 , 44 p e r c e n t less RSA delay, for key-lengths $512,1024,2048$ 512 , 1024 , 2048 , respectively of the home designs versus the 512-bit main reference design, and more than $5,100\ percent$ 5 , 100 p e r c e n t for $4096,8192$ 4096 , 8192 key-lengths, respectively, all per 512-bit encrypted messages. [ABSTRACT FROM AUTHOR]
- Abstract: Copyright of IEEE Transactions on Computers is the property of IEEE and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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