Modular exponentiation java Take a look at the multiple module types out there, how module descriptors work, and tips on using them. More than 100 million people use GitHub to discover, fork, and contribute to over 330 million projects. Jul 14, 2025 · The idea of binary exponentiation is to reduce the exponent by half at each step, using squaring, which lowers the time complexity from O (n) to O (log n). One of the most effective methods to compute large powers efficiently is Fast Exponentiation, also known […] GitHub is where people build software. Double Modular Exponentiation in Python, Java, C++ and more. -> xn = (xn/2)2 if n is even. In this article, we will dive deep into the concept of modular exponentiation and explore its step-by-step implementation. May 5, 2024 · Introduction Exponentiation is a mathematical operation written as ab, which means the value when a is multiplied by itself, b times. Modular Exponentiation for Large Numbers | GFG POTD | C++ | Java | Code Kar Lo CODE KAR LO 3. Montgomery representation However the Montgomery multiplication doesn't come for free. Modular Exponentiation Java method. Exponentiation refers to the process of raising a number to a power. Use an online compiler. In-depth solution and explanation for LeetCode 2961. 模幂 （英語： modular exponentiation）是一种对 模 进行的 冪 运算，在 计算机科学，尤其是 公开密钥加密 方面有一定用途。 模幂运算是指求整数 的 次方 被 正整数 所除得到的余数 的过程，可用数学符号表示为 。由 的定义可得 。 例如，给定 ， 和 ， 被13除得的余数 。 指数 为负数时可使用 扩展 Learn about fast exponentiation algorithms including the brute force approach, exponentiation by squaring, modular exponentiation along with the Montgomery ladder technique. Right after that lesson there is a calculator for modular exponents, so you can check your calculations. Create an auxiliary method to do the recursion. org/wiki/Modular_exponentiation In this video, you will be learning about modular exponentiation which is a very common topic while solving DSA problems. For example, 5 10 510 = 5 1010 2 510102 = 5 8 5 2 58 ⋅52. Modular exponentiation (Recursive) Given three numbers a, b and c, we need to find (ab) % c Now why do “% c” after exponentiation, because ab will be really large even for relatively small values of a, b and that is a problem because the data type … Programs written in Java using BigIntegers. Pepcoding 211K subscribers 152 6K views 3 years ago #competitiveprogramming #engineering #java Jun 5, 2015 · Modular Exponentiation overflow Asked 10 years, 2 months ago Modified 9 years, 9 months ago Viewed 570 times Hey guys, In this video We'll learn about some of the most common Algorithms and concepts used in Competitive Programming. Programs written in Java using BigIntegers. BigInteger, using modular exponentiation techniques. You may use commas or spaces. Link to all codes:Brute Force Solut Sep 3, 2025 · Modular Exponentiation Finding a^b mod m is the Modular Exponentiation. All inputs are nonnegative integers, x has about 256 bits, and p is a prime numbe Jul 23, 2025 · Matrix Exponentiation is a technique used to calculate a matrix raised to a power efficiently, that is in logN time. And another large number X. gcd rabin rsa-cryptography elgamal modular-exponentiation euclidean-algorithm miller-rabin chinese-remainder-theorem modular-inverse Updated Jan 10, 2021 Java khanacademy_algorithms / fast_modular_exponentiation. java Cannot retrieve latest commit at this time. My problem is to compute (g^x) mod p quickly in JavaScript, where ^ is exponentiation, mod is the modulo operation. The modular exponentiation is useful before the size of the result is bounded. Modular Exponentiation Modular exponentiation aims to calculate ab mod (m). wikipedia. One can use modular multiplication to calculate this and multiply a to itself b times. So, something like the following should work (although I haven't tested it): Tool to compute any modulo operation. In this article, we will explore the basics of modular arithmetic and delve into some popular number theory algorithms used in competitive programming, using Java as our chosen programming language. Intuitions, example walk through, and complexity analysis. out. In other words, you hav Dec 24, 2024 · Problem: Currently, the Java algorithm template does not include an efficient implementation of the fast exponentiation algorithm (also known as exponentiation by squaring). In this guide, we will Feb 15, 2022 · I have this function to calculate modular exponentiation in Java, but due to an excessive recursion for BigIntegers with 2048 and 4096 bits, I have a StackOverflowError. Feel free to visit the 2000+ Algorithm Examples in Python, Java, Javascript, C, C++, Go, Matlab, Kotlin, Ruby, R and ScalaThe binary exponentiation algorithm, also known as exponentiation by squaring, is an efficient method for computing large powers of a number, particularly in modular arithmetic. As a result, multiplication is replaced with O(log(n)) additions and 'multiplying by 2' operations. Dec 24, 2011 · The BigInteger class in Java 7 has a modPow method, which handles modular exponentiation. Nov 10, 2025 · This article explains LeetCode Problem 372: Super Pow. Oct 3, 2023 · The answer is we can try exponentiation by squaring which is a fast method for calculating exponentiation of a number. This method is, however, slow. Whether it’s calculating large powers for cryptographic algorithms or scientific computations, the efficiency of exponentiation plays a critical role in various applications. On the other hand, computing the modular discrete logarithm – that is, finding the exponent e when given b, c, and m – is believed to be difficult. Oct 15, 2024 · For exponentiation, the modular exponential leverages a logarithmic time complexity technique called “exponentiation by squaring,” which enables fast and efficient computation of large powers. pow(X). Tool to compute modular power. Sep 9, 2014 · Exponentiation by squaring still "works" for modulo exponentiation. So, (2 ^ 3) % 6 is 8 % 6 is 2. println(b); int c = 1; Binary exponentiation can be used to efficiently compute x n m o d m xn mod m. It leverages recursion to break down the problem into smaller subproblems. For simplicity, basically I have two very large prime numbers P and G. Here, a is called the base, and b is called the exponent or the power. It is mostly used for solving problems related to linear recurrences. Hi, Today we will learn how to evaluate Modular Exponentiation in java. Jul 1, 2022 · I am working on this code challenge: Problem Description Given 2 integers x and n, you have to calculate x to the power of n, modulo 10^9+7 i. Other structures which can use this basic algorithm include matrix exponentiation with floating 模冪 （英語： modular exponentiation）是一種對 模 進行的 冪 運算，在 電腦科學，尤其是 公開金鑰加密 方面有一定用途。 模冪運算是指求整數 的 次方 被 正整數 所除得到的餘數 的過程，可用數學符號表示為 。由 的定義可得 。 例如，給定 ， 和 ， 被13除得的餘數 。 指數 為負數時可使用 擴充 Network Security: Modular Exponentiation (Part 1) Topics discussed: 1) Explanation of modular exponentiation with examples. Modular exponentiation is efficient to compute, even for very large integers. Learn how to efficiently implement modular exponentiation in Java with step-by-step instructions and code snippets for better performance. Our results look like: [2, 4, 16, 256, 65536, 4294967296, 73709551616, 431768211456 Jul 15, 2017 · This can be fixed by several approaches: (a*b) % M operation can be done with the algorithm that is similar to your "exponentiation by squaring" implementation. GCD of two numbers is the greatest common divisor of the two numbers. Modular exponentiation is exponentiation performed over a modulus. Idea behind Matrix Exponentiation: Similar to Binary Exponentiation which is used to calculate a number raised to a power, Matrix Exponentiation is used to calculate a matrix raised to a power efficiently. It uses mathematical techniques and recursion to solve the problem step-by-step, expands on the fast exponentiation algorithm, and provides code implementations in Java, Python, Go, JavaScript, and C++. In the fast exponentiation strategy developed in this section we write any powers such that it can be computed as a product of powers obtained with repeated squaring. gcd rabin rsa-cryptography elgamal modular-exponentiation euclidean-algorithm miller-rabin chinese-remainder-theorem modular-inverse How to calculate modulus of 5^55 modulus 221 without much use of calculator? I guess there are some simple principles in number theory in cryptography to calculate such things. This will help you to learn some built-in methods that we will use here. (You can also use exponent == 1 as a base case, in which case it should return the base. Mar 27, 2024 · The algorithm generally used to calculate the modular inverse is the extended-euclidean algorithm. This repository contains all the example code from the Java 9 Modularity book. All of these numbers are well above 512 bits. This is the last part of these thr Java 9 Modularity The Java module system offers new ways of creating modular and maintainable applications. I have to perform the following operation G X (mod) P. Apr 25, 2013 · Yes, there are a number of well-documented ways to do this without involving big integers at any stage. This general algorithm may also be used for other algebraic structures which have multiplication and exponentiation and is efficient when the size of values has an upper bound - the modulus. The modulo calculator returns the rest of the integer division. In the context of Java, the modPow() method in the BigInteger class allows you to perform this operation with arbitrarily large integers. Modular Exponentiation (or power modulo) is the result of the calculus a^b mod n. Write a program (Java) to compute modular exponentiation: take g (base), e (exponent), and, N (modulas) as input from the user and output the result. Jul 11, 2025 · Now why do “% c” after exponentiation, because a b will be really large even for relatively small values of a, b and that is a problem because the data type of the language that we try to code the problem, will most probably not let us store such a large number. 2) Solving 23 power 3 mod 30 with clear steps and shortcuts. - c-vargas/modular-exponentiation Oct 14, 2024 · Binary exponentiation, also known as exponentiation by squaring, is a powerful algorithm used to efficiently calculate large powers of numbers. Modular Exponentiation Calculator (Java) Some Java code to calculate a^j mod n where a, j and n must be Long values and the inputs can be as large as (2^63)-1 (the limits of Long) Dec 24, 2024 · Problem: Currently, the Java algorithm template does not include an efficient implementation of the fast exponentiation algorithm (also known as exponentiation by squaring). mod(P) is painfully slow and oftentimes yeilds Write a program (Java) to compute modular exponentiation: take g (base), e (exponent), and N (modulus) as input from the user and output the result. Examples: Input : a = 2312 b = 3434 c = 6789 Output : 6343 Input : a = -3 b = 5 Nov 7, 2025 · Modular exponentiation You are encouraged to solve this task according to the task description, using any language you may know. It should have two arguments: the base and the exponent. Using naive approach of first raiseing G to the power of X and then applying mod P ie. With this hands-on book, Java developers will learn not only about the joys of modularity, but also about the patterns needed to create truly modular and reliable applications. It is often used in informatics and cryptography. One of the most effective methods to compute large powers efficiently is Fast Exponentiation, also known […] Mar 27, 2024 · The algorithm generally used to calculate the modular inverse is the extended-euclidean algorithm. Nov 8, 2012 · Edit - clarified I'm trying to implement modular exponentiation in Java using lagrange and the chinese remainder theorem. G. Feb 10, 2019 · Modular exponentiation is the normal exponentiation that you’re used to (2 ^ 3 = 2 * 2 * 2 = 8) modulo some number. For example, if N is 55, having been given the prime factors 5 and 11, ph Fast Modular Power The modular exponentiation of a number is the result of computing an exponent followed by getting the remainder from division. This algorithm plays a crucial role in various cryptographic systems and mathematical calculations. Idea behind Modular Arithmetic: The concept of modular arithmetic is to find the remainder of a number upon division by another number. Code to solve a^j mod n in Java. Binary exponentiation (also known as exponentiation by squaring) is a trick which allows to calculate a n using only O (log n) multiplications (instead of O (n) multiplications required by the naive approach). Oct 25, 2015 · DSA involves one modular exponentiation for signing and two for decrypting, while DH requires one modular exponentiation by each participant in a key exchange. See: en. Modular exponentiation is a mathematical operation that calculates the remainder when a number is raised to a certain power and then divided by a modulus. Instead of dividing the product and subtracting n multiple times, it adds multiples of n to cancel out the lower bits and then just discards the lower bits. in); // Reading the base,power,modulo values from the user. Programs I wrote that helped me understand encryption, decryption and signing functions along with security protocols. This algorithm is Verificatum Multiplicative Groups Library for Java (VMGJ) Overview This package allows invoking GMP's modular exponentiation, including the extension provided by the GMP Modular Exponentiation Extension package (GMPMEE) for simultaneous or fixed base modular exponentiation and primality testing, from within a Java application. public static int modExp(int b, int e, int m){ System. Then, if we know x y xy for all y y which are powers of two (x 1 x1, x 2 x2, x 4 x4, … , x 2 ⌊ log 2 n ⌋ x2⌊log2n⌋, we can compute x n xn in O (log n) O(logn). This is a common requirement in cryptography problems. HP Forums / HP Calculators (and very old HP Computers) / General Forum « Previous 1 127 128 129 130 131 235 Next » Aug 1, 2024 · Exponentiation, or raising a number to a power, is a fundamental operation in mathematics and computer science. 模冪 （英語： modular exponentiation）是一種對 模 進行的 冪 運算，在 計算機科學，尤其是 公開密鑰加密 方面有一定用途。 模冪運算是指求整數 的 次方 被 正整數 所除得到的餘數 的過程，可用數學符號表示為 。由 的定義可得 。 例如，給定 ， 和 ， 被13除得的餘數 。 指數 為負數時可使用 擴展 Modular exponentiation is a powerful technique that can help you design efficient and secure algorithms. It is a fundamental operation in number theory, cryptography, and computer science, as it is used in many applications such as the RSA cryptosystem Fast modular exponentiation in Java Script. Example: a = 5, b = 2, m = 7 (5 ^ 2) % 7 = 25 % 7 = 4 There is often a need to efficiently calculate the value of xn mod m. It is used to compute the remainder of a number raised to a certain power, modulo another number (A^B mod C). Call it with a value of 10 for the exponent and have it recurse with (exponent-1). The examples are grouped by chapter in the book: Modules and Modular JDK Working with Modules Services Modularity Patterns Advanced Modularity Patterns Migration Without Modules Migration to Modules Migration Case Study: Spring and Hibernate Library Migration Build Tools and IDEs Testing Modules Most examples May 18, 2025 · 模幂 （英语： modular exponentiation）是一种对 模 进行的 幂 运算，在 计算机科学，尤其是 公开密钥加密 方面有一定用途。 模幂运算是指求整数 的 次方 被 正整数 所除得到的余数 的过程，可用数学符号表示为 。由 的定义可得 。 例如，给定 ， 和 ， 被13除得的余数 。 指数 为负数时可使用 扩展欧 Closed aashutoshrathi opened this issue Apr 12, 2017 · 0 comments · Fixed by #136 Closed aashutoshrathi opened this issue Apr 12, 2017 · 0 comments · Fixed by #136 Assignees Labels Algorithmdifficulty-easylang-java Member This repository contains all the example code from the Java 9 Modularity book. Understanding Modular Jul 15, 2025 · Another efficient approach : Recursive exponentiation Recursive exponentiation is a method used to efficiently compute AN, where A & N are integers. Whether you want to compute the power of a number, work with fractional exponents, or explore applications such as financial calculations or cryptography, understanding exponentiation in Java is essential. Scanner; // Importing scanner class to get input public class ModularExponentiation { public static void main (String [] args) { // Initializing the scanner class Scanner sc = new Scanner (System. Modular Exponentiation: Finding a^b mod m is the modular exponentiation. An exploration of cryptographic concepts, including modular exponentiation, RSA algorithm analysis, and brute-force password cracking techniques. gcd rabin rsa-cryptography elgamal modular-exponentiation euclidean-algorithm miller-rabin chinese-remainder-theorem modular-inverse Contribute to tejartr7/Strivers-SDE-Sheet-Challenge development by creating an account on GitHub. 71K subscribers Subscribe As part of an assignment in Cryptography I've been asked to write code that involves calculating modular exponentiation. 2000+ Algorithm Examples in Python, Java, Javascript, C, C++, Go, Matlab, Kotlin, Ruby, R and ScalaThe modular exponential algorithm, also known as “modular exponentiation” or "fast exponentiation," is a fundamental algorithm in computer science and cryptography. gcd rabin rsa-cryptography elgamal modular-exponentiation euclidean-algorithm miller-rabin chinese-remainder-theorem modular-inverse So I was trying Diffie Hellman Key Exchange in java. The base case is exponent == 0, in which case it should return 1. Contribute to Mostafijur28/Code-and-Notes development by creating an account on GitHub. The examples are grouped by chapter in the book: Modules and Modular JDK Working with Modules Services Modularity Patterns Advanced Modularity Patterns Migration Without Modules Migration to Modules Migration Case Study: Spring and Hibernate Library Migration Build Tools and IDEs Testing Modules Most examples May 18, 2025 · 模幂 （英语： modular exponentiation）是一种对 模 进行的 幂 运算，在 计算机科学，尤其是 公开密钥加密 方面有一定用途。 模幂运算是指求整数 的 次方 被 正整数 所除得到的余数 的过程，可用数学符号表示为 。由 的定义可得 。 例如，给定 ， 和 ， 被13除得的余数 。 指数 为负数时可使用 扩展欧 Closed aashutoshrathi opened this issue Apr 12, 2017 · 0 comments · Fixed by #136 Closed aashutoshrathi opened this issue Apr 12, 2017 · 0 comments · Fixed by #136 Assignees Labels Algorithmdifficulty-easylang-java Member Modular exponentiation - using Recursion mycodeschool 797K subscribers Subscribe An application of all of this modular arithmetic Amazon chooses random 512-bit (or 1024-bit) prime numbers an exponent (often about 60,000). Let Here we show the modular exponentiation algorithm for integers - a way to efficiently compute ae (mod n). This can be done in O (logn) time using the following recursion: Using the repeated squaring algorithm to calculate 2^300 mod 50. This algorithm takes advantage of the binary representation of the exponent to reduce the number of multiplications Modular exponentiation is the remainder when an integer (the base) is raised to the power (the exponent), and divided by a positive integer (the modulus); that is, . This technique is particularly useful in various fields of computer science, including cryptography, compe We can compute \ (a^n x_0 \text { mod } m\) quickly using the well-known modular exponentiation algorithm, which is exponentiation by squaring with a reduction of each intermediate result modulo \ (m\). You just need to replace all multiplications with additions. Square and Multiply algorithm for fast modular exponentiation - SquareAndMultiply. To do this, let's break down x n xn into binary components. Modulo is the name of the calculation of the remainder in the Euclidean division. java Last 12 digit means take the mod 10^12 of the result 2^34 = 17179869184 Which is a power of two so the binary representation only has the 34th bit set. This algorithm is important for efficiently calculating large powers in algorithms related to number theory, cryptography, and Jun 8, 2022 · The Montgomery (modular) multiplication is a method that allows computing such multiplications faster. Better than official and forum solutions. This repository contains Python implementations, performance evaluations, and visualizations as part of the MATH 359 project for the 2024/25 academic year. Aug 1, 2024 · Exponentiation, or raising a number to a power, is a fundamental operation in mathematics and computer science. That way the co-processor - which is generally present on high end Java Card implementations - can be used directly. It involves computing the remainder of a large exponentiation operation by using a modular Programs written in Java using BigIntegers. A Java program to demonstrate the working of Modular Exponentiation. Read more about it here. Modular Exponentiation Java method GitHub - Gist Quick tutorial on doing modular exponentiation in Java in O (log (b)) time Rate Like Subscribe Modular exponentiation - formulasearchengine The modular exponentiation of a number is the result of computing an exponent followed by getting the remainder from division. Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus Aug 4, 2015 · The formula given for modular exponentiation is: (A^B)%M I tried my best to implement this formula into my code, but the answers I have been getting are incorrect. This method returns a BigInteger whose value is (thisexponent mod par Quick tutorial on doing modular exponentiation in Java in O(log(b)) time Rate Like Subscribe Use fast modular exponentiation as described in the next lesson. calculate (x^n) % (10^9+7). 2000+ Algorithm Examples in Python, Java, Javascript, C, C++, Go, Matlab, Kotlin, Ruby, R and ScalaModular exponentiation is an algorithm that efficiently computes the result of an exponentiation operation followed by a modular reduction. You can calculate the modular. Jul 5, 2017 · Learn the basics of Java modularity via Project Jigsaw. e. In those modular exponentiations g and m are L bits long, while x is N bits long. 模幂 （英语： modular exponentiation）是一种对 模 进行的 幂 运算，在 计算机科学，尤其是 公开密钥加密 方面有一定用途。 模幂运算是指求整数 的 次方 被 正整数 所除得到的余数 的过程，可用数学符号表示为 。由 的定义可得 。 例如，给定 ， 和 ， 被13除得的余数 。 指数 为负数时可使用 扩展欧 In the field of number theory, modular exponentiation is a fundamental algorithm used to efficiently calculate large exponents modulo a given number. In this article, we will see how to calcular (a ^ b) % m in O(log2(b)) complexity. It is useful in computer science, especially in the field of public-key cryptography, where it is used in both Diffie–Hellman key exchange and RSA public/private keys. To deal with m m, observe Modular-Exponentiation A Java program to demonstrate the working of Modular Exponentiation, a type of exponentiation performed over a modulus. 模冪 （英語： modular exponentiation）是一種對 模 進行的 冪 運算，在 電腦科學，尤其是 公開金鑰加密 方面有一定用途。 模冪運算是指求整數 的 次方 被 正整數 所除得到的餘數 的過程，可用數學符號表示為 。由 的定義可得 。 例如，給定 ， 和 ， 被13除得的餘數 。 指數 為負數時可使用 擴充 Learn how to efficiently compute the modulo of high powers in Java without Math. From the definition of division, it follows that . The BigInteger modPow is not allowed in this case, we have to implement it Learn Modular Exponentiation and Fast Power Algorithm with clear explanations, step-by-step breakdowns, Python examples, and visual diagrams for competitive programming and cryptography. While vanilla binary exponentiation with a compiler-generated fast modulo trick requires ~170ns per inverse call, this implementation takes ~166ns, going down to ~158ns we omit transform and reduce (a reasonable use case is for inverse to be used as a subprocedure in a bigger modular computation). Jul 23, 2025 · Binary Exponentiation or Exponentiation by squaring is the process of calculating a number raised to the power another number (AB) in Logarithmic time of the exponent or power, which speeds up the execution time of the program. Your problem isn't that 2 ^ 168277 is an exceptionally large number, it's that one of your intermediate results is a fairly large number (bigger than 2^32), because 673109 is bigger than 2^16. util. There are two approaches for this - recursive and iterative. This one-way function behavior makes modular exponentiation a candidate for use in cryptographic algorithms. Aug 14, 2019 · A Java program to find the result of raising a large number to a power over a modulus does not appear to work when the base of the exponent is 8 digits or greater. Sample implementation Network Security: Modular Exponentiation (Part 1) Topics discussed: 1) Explanation of modular exponentiation with examples. Jul 23, 2025 · The modular inverse of a mod m exists only if a and m are relatively prime i. Problem Statement Given three integers x,y, and m Jul 15, 2024 · Learn how to perform modulo-arithmetic operations in Java with 10^9 + 7 as an example format for the modulus. Here we will be discussing two most common/important methods: Mar 14, 2014 · Modular Exponentiation in java (the algorithm gives a wrong answer) Asked 11 years, 8 months ago Modified 11 years, 8 months ago Viewed 3k times Mar 20, 2025 · The modPow() method of Java BigInteger class is used to perform modular exponentiation. , gcd (a, m) = 1. Follow the steps below : If N = 0, the result is always 1 because any non zero number raised to the power of 0 is 1. Modular Exponentiation works when calculating a pow b mod m. It will never produce a number larger than the modulus. We treat the modular exponent as a three input function Fast Modular Exponentiation | প্রত্রিক্ষার মুড়লার ইংলারিক্ষ It is one of the most important tools in Competitive Programming and Introduction In the world of Java programming, mastering exponentiation is a crucial skill. Unlike pow, this method permits negative exponents. So in this simple case we can do fast modular exponentiation by simply squaring the previous value and taking the mod 10^12 to increase our result by one bit. ) Because modular exponentiation is an important operation in computer science, and there are efficient algorithms (see above) that are much faster than simply exponentiating and then taking the remainder, many programming languages and arbitrary-precision integer libraries have a dedicated function to perform modular exponentiation: Apr 12, 2025 · HP Forums › HP Calculators (and very old HP Computers) › General Forum « Previous 1 … 140 141 142 143 144 … 248 Next » Nov 7, 2024 · Learn how to leverage the modular capabilities of Java 9+ to design packages and create modules and discover how the JPMS affects access to APIs while building your own modular app. Sep 10, 2017 · Modular exponentiation in general can be used through raw RSA (RSA without padding) or Diffie-Hellman calculations on a Java Card. Bases that have 8 or more digits do not work (checked against online modular exponentiation calculator). Use 18-digit or smaller integers. Codeforces Solution-Modular Exponentiation-Solution in C, C++, Java, Python gcd rabin rsa-cryptography elgamal modular-exponentiation euclidean-algorithm miller-rabin chinese-remainder-theorem modular-inverse Updated on Jan 10, 2021 Java import java. Contribute to FrogletApps/Modular_Exponentiation_Calculator development by creating an account on GitHub. This algorithm is important for efficiently calculating large powers in algorithms related to number theory, cryptography, and HP Forums / HP Calculators (and very old HP Computers) / General Forum « Previous 1 103 104 105 106 107 212 Next » CSE 311: Foundations of Computing Lecture 13: Modular Inverse, Exponentiation. In this article, we will solve the problem of modular exponentiation. GitHub Gist: instantly share code, notes, and snippets.