Basics of Contemporary Cryptography for IT Practitioners by Boris Ryabko

By Boris Ryabko

The purpose of this publication is to supply a complete advent to cryptography with no utilizing complicated mathematical structures. the topics are conveyed in a kind that simply calls for a easy wisdom of arithmetic, however the equipment are defined in adequate element to permit their computing device implementation.The publication describes the most suggestions and amenities of latest 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 resources for Basics of Contemporary Cryptography for IT Practitioners (Series on Coding Theory and Cryptology, 1)

Example text

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. Note also that the length of the ciphertext is twice the length of the plaintext but only one pass in needed (provided the table with public keys was delivered to all users in advance). 6 27 RSA Encryption and Trapdoor Functions Named after its developers Ron Rivest, Adi Shamir, and Leonard Adleman, this cipher proposed in [Rivest et al.

2 35 The Baby-step Giant-step Algorithm In the unclassified literature this method was first described by Daniel Shanks (see [Knuth (1973)l); references thereto have been known since 1973. It was one of the first methods to show that the discrete logarithm problem can be solved much faster than by the exhaustive search. The algorithm is as follows. Step 1 Take two integers m and k such that mk>p. 3) Step 2 Compute two number series Y, ay, aml a2Yl ' * e l urn-ly (mod p ) ; a2m, . . 5) (all computations are carried out modulo p ) .

Let d = 3. Such a choice of d is valid since gcd(40,3) = 1. Compute the private key c = 3-1 mod 40 with the extended Euclidean algorithm (see Sec. 3), c = 27. Assume that Alice wishes to sign the message ? =ii abbbaa, the value of hash function being, say, 13: h = h(abbbaa) = 13. 2) s = 1327mod 55 = 7 and obtains the signed message (abbbaa, 7 ) . Now the one who knows Alice’s public key N = 55, d = 3 can verify the signature. 4) w = 73 mod 55 = 13. The values of w and the hash function are equal, hence, the signature is valid.

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