Introduction to Cryptography: Principles and Applications by Hans Delfs, Helmut Knebl

By Hans Delfs, Helmut Knebl

Due to the swift progress of electronic verbal exchange and digital facts trade, details defense has develop into a very important factor in undefined, enterprise, and management. sleek cryptography offers crucial ideas for securing info and preserving data.

In the 1st half, this publication covers the major techniques of cryptography on an undergraduate point, from encryption and electronic signatures to cryptographic protocols. crucial options are verified in protocols for key alternate, person identity, digital elections and electronic money. within the moment half, extra complex themes are addressed, equivalent to the bit defense of one-way capabilities and computationally excellent pseudorandom bit turbines. the safety of cryptographic schemes is a relevant subject. commonplace examples of provably safe encryption and signature schemes and their protection proofs are given. even though specific awareness is given to the mathematical foundations, no targeted history in arithmetic is presumed. the mandatory algebra, quantity thought and likelihood concept are incorporated within the appendix. each one bankruptcy closes with a suite of workouts.

The moment version comprises corrections, revisions and new fabric, together with an entire description of the AES, a longer part on cryptographic hash services, a brand new part on random oracle proofs, and a brand new part on public-key encryption schemes which are provably safe opposed to adaptively-chosen-ciphertext attacks.

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Extra resources for Introduction to Cryptography: Principles and Applications (Information Security and Cryptography)

Example text

The algorithm uses the continued fraction expansion of e/n. 44 3. Public-Key Cryptography Efficient factoring algorithms are known for special types of primes p and q. To give these algorithms no chance, we have to avoid such primes. First we require that the absolute value |p − q| is large. This prevents the following 2 2 2 attack: We have (p + q) /4 − n = (p + q) /4 − pq = (p − q) /4. If |p − q| is small, 2 2 (p + q) /4 is slightly larger than n. then (p − q) /4 is also small and therefore √ p + q /2 is slightly larger than n and the following factoring method Thus could be successful: √ 1.

N, for all possible k ∈ {0, 1}56 . If such a k is found, the probability that k is really the key is very high. Special computers were proposed to perform an exhaustive key search (see [DifHel77]). Recently a specially designed supercomputer and a worldwide network of nearly 100 000 PCs on the Internet were able to find out the key after 22 hours and 15 minutes (see [RSALabs]). This effort recovered one key. This work would need to be repeated for each additional key to be recovered. The key size and the block size of DES have become too small to resist the progress in computer technology.

In the case x ∈ Z∗n , p or q is a factor of x. If both divide x, we have x = 0 and xed = 0. Thus the equalities hold. 30). If p divides x and q does not divide x, then (xe )d mod p = 0, x mod p = 0 and (xe )d ≡ xed mod (q−1) ≡ x mod q, because ed ≡ 1 mod (q − 1). This shows that (xe )d ≡ x mod n. The case where p does not divide x and q divides x 40 3. Public-Key Cryptography follows analogously. Thereby (xe )d = xed = x for all x ∈ Zn , and we have proven our assertion. ✷ We see that RSAe is an (easily computable) permutation of Zn .

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