<h2>組合語言與微處理機實驗</h2> --- <h1>NTRU</h1> 楊志璿、許家愷、涂哲誠 --- <h1>Outline</h1> <font color=verdana>What</font> is this issue? <font color=yellow>Why</font> is this issue? <font color=red>How</font> is this issue? --- <h1><font color=verdana>What</font> is this issue?</h1> ---- A post-quantum cryptography. Open source. Can be optimized by hardware. (known as hardware acceleration) ---- * $\mathbb{N}, p$ are primes, $q \gt p$, and $gcd(p,q)=1$ * Polynomials $\mathbb{f}$ and $\mathbb{g}$ are degree at most $\mathbb{N}-1$ * $\mathbb{f}$ is invertable in $\mathbb{Z}[\mathbb{X}]\over{\mathbb{x}^{\mathbb{N}}-1}$ * $\mathbb{r}$ is a random polynomial * $\mathbb{m}$ is a message polynomial ---- <font color=verdana>Public</font> key: $\mathbb{h} \equiv \mathbb{f}_q * \mathbb{g}(mod\ q)$ <font color=red>Private</font> key: $\{\mathbb{f}, \mathbb{f}_p\}$ ---- $\mathbb{E} \equiv p \cdot \mathbb{r} * \mathbb{h} + \mathbb{m}(mod\ q)$ ---- $\mathbb{a} = \mathbb{f}*\mathbb{E}(mod\ q)$ $\mathbb{m}'=\mathbb{f}_p*\mathbb{a}(mod\ p)$ $\mathbb{m}' \equiv \mathbb{f}_p*(p \cdot \mathbb{r} * \mathbb{g} + \mathbb{f} * \mathbb{m})(mod\ p) \equiv \mathbb{m} (mod\ p)$ ---- Polynomial multiplication..... Yeah, <font color=yellow>FFT</font> comes back! Yeah, <font color=verdana>extended Euclidean</font> algorithm comes back! --- <h1><font color=yellow>Why</font> is this issue?</h1> ---- 楊志璿：資安專長 許家愷：實做專長 涂哲誠：程式專長 ---- We want to do something interesting. --- <h1><font color=red>How</font> is this issue?</h1> ---- <div style="text-align: left"> <h3>Where is hardware acceleration?</h3> <font color=#FFD43B>"polynomial multiplication"</font> <font size=6> In normal way , it takes too many time for multiply and add one by one. So, the solution nowadays change domain and using prebuild Adder and Multiplier parallelly to accelerate the computation. </font> </div> ---- Implement most of the NTRU by <font color=#1589FF>C</font> in Xilinx SDK , and polynomial multiplication will implement in <font color=#BCE954>verilog </font>accessed by AXI interface ---- <h2>Feasibility</h2>  ---- Thanks --- [Spec.](https://ntru.org/f/ntru-20190330.pdf)