Protocol Failures for RSA-Like Functions Using Lucas Sequences and Elliptic Curves
نویسندگان
چکیده
We show that the cryptosystems based on Lucas sequences and on elliptic curves over a ring are insecure when a linear relation is known between two plaintexts that are encrypted with a “small” public exponent. This attack is already known for the classical RSA system, but the proofs and the results here are different.
منابع مشابه
Cryptanalysis of RSA-type cryptosystems: A visit
This paper surveys RSA-type implementations based on Lucas sequences and on elliptic curves. The main focus is the way how some known attacks on RSA were extended to LUC, KMOV and Demytko’s system. It also gives some directions for the choice of the most appropriate RSA-type system for a given application.
متن کاملGeneralised Cycling Attacks on RSA
Given an RSA modulus n, a ciphertext c and the encryption exponent e, one can construct the sequence x 0 = c mod n; x i+1 = x e i mod n; i = 0; 1; : : : until gcd(x i+1 ? x 0 ; n) 6 = 1 or i > B, B a given boundary. If i B, there are two cases. Case 1: gcd(x i+1 ? x 0 ; n) = n. In this case x i = m and the secret message m can be recovered. Case 2: 1 6 = gcd(x i+1 ? x 0 ; n) 6 = n. In this case...
متن کاملECDSA - Application and Implementation Failures
Elliptic Curve Cryptography (ECC) is the newest member of public-key algorithms with practical relevance. It is based on the algebraic structure of elliptic curves over finite fields. Compared to RSA and Discrete Logarithm (DL) schemes, in many cases ECC has performance advantages with respect to fewer computations, and bandwidth advantages due to shorter signatures and keys. In addition, ECC p...
متن کاملA Comparative S-Index in Factoring RSA Modulus via Lucas Sequences
General Lucas sequences are practically useful in cryptography. In the past quarter century, factoring large RSA modulo into its primes is one of the most important and most challenging problems in computational number theory. A factoring technique on RSA modulo is mainly hindered by the strong prime properties. The success of factoring few large RSA modulo within the last few decades has been ...
متن کاملInformation Security on Elliptic Curves
The aim of this paper is to provide an overview for the research that has been done so far on elliptic curves cryptography role in information security area. The elliptic curves cryptosystem is the newest public-key cryptographic system and represents a mathematically richer procedure then the traditional cryptosystem based on public-key, like RSA, Diffie-Hellman, ElGamal and Digital Signature ...
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 1996