# Questions tagged [montgomery-multiplication]

A modular multiplication algorithm invented by Peter Montgomery that allows modular arithmetic to be performed efficiently when the modulus is large (typically several hundred bits).

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### Which one is fastest? Karatsuba or Montgomery multiplication?

Is there any complexity analysis between Karatsuba and Montgomery multiplication algorithms? It seems that Karatsuba is more general in the sense that is not modulo tuned while Montgomery it is. Does ...
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### RSA Timing Attack on "Extra" Montgomery Reduction

In "A practical implementation of the timing attack", the authors take advantage of a timing difference that stems from "extra reductions" that occur when multiplying numbers in the Montgomery form. ...
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### How does Montgomery reduction work?

I want to reduce a multi-precision integer $x$ modulo a prime $p$, very fast. Performing the traditional Euclidean division for only calculating the modulo, is inefficient and modular reduction is at ...
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### Reverse engineering hardware crypto processor for modular multiplication

I'm currently working with an undocumented crypto offload processor that is capable of accelerating modular multiplication in some fashion. I need to figure out what operation it is implementing ...
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### Efficient setup for a Montgomery multiplication

Montgomery described an efficient method to compute a modular multiplication. This works by using a special constant $R$ and assumes the inputs $a$ and $b$ have been made into a special representation ...
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### Blockwise Montgomery multiplication

I have to implement a 256*256 bit Montgomery multiplier for pairing computations. The straightforward approach is to use a bit-serial version, but I would like to utilize the built-in 64*64 bits ...
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### How to use Montgomery arithmetic for elliptic curves (FIAT cryptography)

Let us consider the source code for curve P-256 from BoringSSL. This source code can be found here. This source code uses the FIAT generated implementation for field arithmetic. This implementation ...
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### Montgomery Multiplication in FPGA explanation

I'm trying to implement an RSA module in a FPGA. I choose to use Montgomery multiplication. I've found a document where the Montgomery Multiplication is pretty clear. I don't understand only a step. ...
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