Cs290g — Introduction to Modern Cryptography Task 1 — Modular Arithmetic
نویسنده
چکیده
(i) Since 32 = 9 = 7 · 1 + 2, then we clearly have 32 mod 7 = 9 mod 7 = 2. (ii) The solution is easy found by inspection: We have 4 · 4 mod 15 = 16 mod 15 = 1, and thus 4−1 mod 15 = 4. (iii) I have seen many complicated solutions here, but the solution is very simple, and uses the fact that 32 mod 8 = 9 mod 8 = 1. Then, we use the fact (discussed in class) that a · b mod n = (a mod n) · (b mod n) mod n. 3 mod 8 = 32·15668+1 mod 8 = (3) · 3 mod 8 = ((3 mod 8) mod 8) · 3 mod 8 = (1 mod 8) · 3 mod 8 = 1 · 3 = 3 .
منابع مشابه
Introduction to the RSA algorithm and modular arithmetic
These notes are an introduction to the RSA algorithm, and to the mathematics needed to understand it. The RSA algorithm — the name comes from the initials of its inventors, Rivest, Shamir, and Adleman — is the foundation of modern public key cryptography. It is used for electronic commerce and many other types of secure communication over the Internet. The RSA algorithm is based on a type of ma...
متن کاملCs290g — Introduction to Modern Cryptography Task 1 — Pseudorandom Functions and Macs
Note that F ′ cannot be a MAC in the strict sense as defined in the lecture, as it does not take inputs of arbitrary length. (My bad!) But still, the notion of UF-CMA makes sense for finite domains – and it is easy to see that F ′ is not UF-CMA secure even in this case: Indeed, we can consider the adversary that makes no queries to Eval, and then makes on query to Vrfy with input (02n, 0n). Cle...
متن کاملBabaï round-off CVP method in RNS: Application to lattice based cryptographic protocols
Lattice based cryptography is claimed as a serious candidate for post quantum cryptography, it recently became an essential tool of modern cryptography. Nevertheless, if lattice based cryptography has made theoretical progresses, its chances to be adopted in practice are still low due to the cost of the computation. If some approaches like RSA and ECC have been strongly optimized in particular ...
متن کاملPartially Interleaved Modular Karatsuba-Ofman Multiplication
We describe a method of performing modular multiplication that has various applications in the field of modern cryptography and coding theory. The proposed algorithm, which combines the Karatsuba-Ofman multiplier and bipartite modular reduction, presents an interleaved processing on the upper most level of Karatsuba-Ofman's recursion. The method provides an efficient and highly parallel modular...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014