# New Speed Records for Montgomery Modular Multiplication on 8-Bit AVR Microcontrollers

@inproceedings{Liu2014NewSR, title={New Speed Records for Montgomery Modular Multiplication on 8-Bit AVR Microcontrollers}, author={Zhe Liu and Johann Gro{\ss}sch{\"a}dl}, booktitle={International Conference on Cryptology in Africa}, year={2014} }

Modular multiplication of large integers is a performance-critical arithmetic operation of many public-key cryptosystems such as RSA, DSA, Diffie-Hellman (DH) and their elliptic curve-based variants ECDSA and ECDH. The computational cost of modular multiplication and related operations (e.g. exponentiation) poses a practical challenge to the widespread deployment of public-key cryptography, especially on embedded devices equipped with 8-bit processors (smart cards, wireless sensor nodes, etc…

## 33 Citations

### Efficient Ring-LWE Encryption on 8-Bit AVR Processors

- Computer Science, MathematicsCHES
- 2015

A carefully-optimized implementation of a ring-LWE encryption scheme for 8-bit AVR processors like the ATxmega128 and outperform related RSA and ECC implementations by an order of magnitude.

### Reverse Product-Scanning Multiplication and Squaring on 8-Bit AVR Processors

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High performance, small code size, and good scalability are important requirements for software implementations of multi-precision arithmetic algorithms to fit resource-limited embedded systems. In…

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A novel Double Operand Scanning (DOS) method to speed-up multi-precision squaring with non-redundant representations on SIMD architecture, compatible with separated Montgomery algorithms and highly efficient for RSA crypto system is introduced.

### Efficient modular exponential algorithms compatible with hardware implementation of public-key cryptography

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The bit forwarding BFW techniques to reduce the count of modular multiplications for hardware implementation of modular exponentiation are presented and will result in increased throughput and decreased power consumption.

### Multiprecision multiplication on AVR revisited

- Computer Science, MathematicsJournal of Cryptographic Engineering
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This paper presents new speed records for multiprecision multiplication on the AVR ATmega family of 8-bit microcontrollers and shows that subquadratic-complexity Karatsuba multiplication is in fact faster than fully unrolled product-scanning multiplication already for surprisingly small inputs, starting at 48 bits.

### A Synthesis of Multi-Precision Multiplication and Squaring Techniques for 8-Bit Sensor Nodes: State-of-the-Art Research and Future Challenges

- Computer Science, MathematicsJournal of Computer Science and Technology
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A survey on the multi-precision multiplication and squaring techniques, and makes special focus on the comparison of their performance and memory footprint on sensor nodes using 8-bit processors.

### Study of Modular Multiplication Methods for Embedded Processors

- Computer Science, MathematicsJ. Inform. and Commun. Convergence Engineering
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This study investigated Montgomery multiplication for public key cryptography on embedded microprocessors and the results reported will become part of a reference book for advanced Montgomery multiplication methods for future researchers.

### Bit Forwarding 3-Bits Technique for Efficient Modular Exponentiation

- Computer Science, MathematicsInt. J. Inf. Secur. Priv.
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The Bit Forwarding 3-bitsBFW3 technique for efficient implementation of modular exponentiation is presented and shows that the B FW3 technique is able to reduce the frequency of multiplications by 18.20% for 1024-bit exponent, resulting in increased throughput and reduced power consumption.

### Low-Weight Primes for Lightweight Elliptic Curve Cryptography on 8-bit AVR Processors

- Computer Science, MathematicsInscrypt
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A special variant of Montgomery multiplication for OPFs that does not execute any input-dependent conditional statements and is, hence, resistant against certain side-channel attacks is described, improving the state-of-the-art in lightweight ECC on 8-bit processors.

### Area-Time Efficient Hardware Implementation of Modular Multiplication for Elliptic Curve Cryptography

- Computer ScienceIEEE Access
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In this paper, an area-time efficient hardware implementation of modular multiplication over five National Institute of Standard and Technology (NIST)-recommended prime fields is proposed for…

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