PDF-Secure arithmetic modulo some integer M can be seen as secure integer computation

21TheArithmeticBlackboxThearithmeticblackboxallowsnpartiesP1PntosecurelystoreandretrieveelementsofaringZMHereMwillbeeitheraprimeoranRSAmodulusietheproductoftwooddprimesThesecurestorag. But actual computation with real numbers is not very practical because it involves limits and in64257 n i t i e s Instead M A T L A B and most other technical computing environments use o a t i n g p o i n t arithmetic which involves a 64257nite s CS1313 Spring 2016. 1. Arithmetic Expressions Lesson #2 Outline. Arithmetic Expressions Lesson #2 Outline. Named Constant & Variable Operands #1. Named Constant & Variable Operands #2. Named Constant & Variable Operands #2. Chapter 4. With Question/Answer Animations. Chapter Motivation. Number theory . is the part of mathematics devoted to the study of the integers and their properties. . Key ideas in number theory include divisibility and the . Ranjit . Kumaresan. (MIT). Based on joint works with . Iddo. . Bentov. (. Technion. ), Tal Moran (IDC), Guy . Zyskind. (MIT). x. f. . (. x,y. ). y. f. . (. x,y. ). Secure Computation. Most general problem in cryptography. 4. 3. 2. 1. 0. In addition to level 3.0 and above and beyond what was taught in class,  the student may:. · Make connection with other concepts in math. · Make connection with other content areas.. Arithmetic Sequences. An arithmetic sequence is a sequence in which each term after the first differs from the preceding term by a constant amount.. The difference between consecutive terms is called the . th. term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion . of “I have…who has…”.. 12. 1 Arithmetic Sequences and Series. Arithmetic Sequences. Tore Frederiksen. , . Thomas . Jakobsen. , . Jesper. Nielsen, Peter . Nordholt. , Claudio . Orlandi. 27-08-2016. The LEGO Approach for. Maliciously Secure Two-Party Computation. 1. What we will present. 2, 4, 6, 8, . …. The . first term in a sequence is denoted as . a. 1. , . the second term is . a. 2. , . and so on up to the nth term . a. n. .. Each number in the list called a . term. .. a. 1. , a. Lesson 3.13 Applications of Arithmetic Sequences Concept: Arithmetic Sequences EQ: How do we use arithmetic sequences to solve real world problems? F.LE.2 Vocabulary: Arithmetic sequence, Common difference B. 50. 4. /. I. 538. :. . Introduction to. Cryptography. (2017—03—02). Tuesday’s lecture:. One-way permutations (OWPs). PRGs from OWPs. Today’s lecture:. Basic number theory. So far:. “secret key”. Chongwon Cho. . (HRL Laboratories). Sanjam. . Garg. (IBM T.J. Watson). . Rafail. . Ostrovsky. (UCLA). 2. Secure . Computation [Yao, GMW]. Alice and Bob. Alice holds input . x. .. Bob holds input . Compute a. b. ?. ǁa. b. ǁ. = O(b · . ǁaǁ. ). Just writing down the answer takes . exponential. time!. Instead, look at . modular. exponentiation. I.e., . c. ompute [a. b. mod N]. Size of the answer < . & Series. Story Time…. When another famous mathematician was in first grade, his teacher asked the class to add up the numbers one through a hundred (1+2+3 etc., all the way up to 100). . Write out the teacher’s request in summation notation, then find the answer (no calculators!) Try to figure out an efficient way!.