Recent Advances in RSA Cryptography by Stefan Katzenbeisser (auth.)

By Stefan Katzenbeisser (auth.)

Recent Advances in RSA Cryptography surveys an important achievements of the final 22 years of analysis in RSA cryptography. targeted emphasis is laid at the description and research of proposed assaults opposed to the RSA cryptosystem. the 1st chapters introduce the mandatory heritage details on quantity idea, complexity and public key cryptography. next chapters overview factorization algorithms and particular houses that make RSA beautiful for cryptographers. latest assaults opposed to RSA are mentioned within the 3rd a part of the ebook (among them assaults opposed to low-exponent RSA, Hastad's broadcast assault, and Franklin-Reiter attacks). ultimately, the final bankruptcy reports using the RSA functionality in signature schemes.
Recent Advances in RSA Cryptography is of curiosity to graduate point scholars and researchers who will achieve an perception into present learn themes within the box and an outline of modern ends up in a unified approach.
Recent Advances in RSA Cryptography is acceptable as a secondary textual content for a graduate point direction, and as a reference for researchers and practitioners in industry.

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Extra resources for Recent Advances in RSA Cryptography

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I is restricted to the domain Di). Algorithm I chooses on input In one arbitrary element i E {O, I} n , whereas algorithm D unifonnly chooses, on input i, one element x E Di = {O,l}n. Finally, algorithm F, on input i and x, computes Ji(x) = I(x). Then, the collection (Ji) is a one-way collection, as the last condition in the definition of a one-way collection follows from the similar condition in the definition of a strong one-way function. To show the opposite, suppose that F' = {Ji : Di I---t {a, l}*LEI is a oneway collection.

However, the machine can simply multiply all numbers and reject if the sequence of numbers guessed does not equal n. If the product of the generated numbers is 44 RECENT ADVANCES IN RSA CRYPTOGRAPHY n, the machine guarantees in a second step that all numbers are indeed prime by applying the technique indicated in Pratt's theorem: the machine checks whether the guessed certificates are valid for the sequence of numbers. If so, the machine accepts. Since a prime factorization exists for every integer n and a valid certificate of primality exists for each prime, the machine will eventually guess the right prime factorization and correct certificates, so there exists at least one computation path which accepts (however, the clear majority of all paths will reject) [19].

It is also possible to construct a randomized polynomial time algorithm that accepts primes in random polynomial time [1], which establishes the more general result PRIMALITY E RP n co-RP and thus PRIMALITY E ZPP. 4. One-way functions In this section, one-way filnctions and generalizations will be introduced formally; the material in this section is based on [43] and [44]. 1, we say that a function I is a one-way function, if I can be efficiently computed and if I is "hard" to invert. g. [83]).

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