By Boris Ryabko
The purpose of this publication is to supply a accomplished creation to cryptography with no utilizing complicated mathematical structures. the topics are conveyed in a kind that merely calls for a easy wisdom of arithmetic, however the tools are defined in adequate aspect to allow their laptop implementation.
The ebook describes the most ideas and amenities of up to date cryptography, proving key effects alongside the way in which. The contents of the 1st 5 chapters can be utilized for one-semester direction.
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Additional info for Basics of Contemporary Cryptography for IT Practitioners
The ElGamal cipher allows to solve the same problem in only one pass, but also has a disadvantage of expanding the message: the ciphertext is twice as long as the plaintext. The RSA encryption is free of such disadvantages. It is interesting that this system is based on other one-way function different from discrete logarithm. Moreover, we meet here one more invention of contemporary cryptography - trapdoor function. g. [Menezes et al. e. finding p and q given n, is very hard (or computationally infeasible) when p and q are sufficiently large (see also [Menezes et al.
4) In signature verification at Step 8, u1 and u2 are computed by the formulas u1= s . h- 1 mod q, 2 ~ 2= --T. h-l mod q. + Taking into account these differences one can easily rewrite the whole scheme in “Russian” style. The proof of correctness is quite similar. Problems and Exercises Assume in all tasks that h(m)= m for all m. 1 Generate RSA signature on m given the following parameters: (a) (b) (c) (d) (e) P = 5, Q = 11, c = 27, m = 7; P = 5, Q = 13, c = 29, m = 10; P = 7, Q = 11, c = 43, m = 5; P = 7, Q = 13, c = 29, m = 15; P = 3, Q = 11, c = 7, m = 24.
Then A sends B the encrypted message as a pair of numbers (17,12). 17’ mod 23 = 1 2 . 7 m o d 23 = 1 5 . We can see that B has been able to decrypt the message transmitted. It is clear that the same scheme may be used by all the users in a network. Note that any user who knows the public key of user B ( d g ) can send B messages encrypted using dg. But it is only user B , and nobody else, who is able to decrypt those messages since decryption is done by utilising the private key cg which is known only to B.
Basics of Contemporary Cryptography for IT Practitioners by Boris Ryabko