Introduction to Cryptography: Principles and Applications by Prof. Dr. Hans Delfs, Prof. Dr. Helmut Knebl (auth.)

By Prof. Dr. Hans Delfs, Prof. Dr. Helmut Knebl (auth.)

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Additional info for Introduction to Cryptography: Principles and Applications

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She computes G(w) = (G 1(W),G 2 (w)) and y:= wll(G1(w) EB rHG 2 (w). (If y f/. ) 3. The signature of m is 0' := j-l(y). As usual, II denotes the concatenation of strings and EB the bitwise XOR operator. If Alice wants to sign message m, she concatenates a random seed r to the message and applies the hash function h to mllr. Then Alice applies the generator G to the hash value w. 4 Hash Functions 45 to mask rj the second part of G(w), G2 (w), is appended to wIG 1 (w) EB r to obtain a bit string y of appropriate length.

If F(a) =/; y and F(b) =/; y, we call FInvers(y, a, b). 4. 3 RSA 31 F is efficiently computable. The repeat-until loop terminates after O(log2(lb - aD) steps. Hence, Flnvers is also efficiently computable, and we see that F considered as a function from Z to Z can easily be inverted in an efficient way. Now consider the same maps modulo n. 26). The algorithm Flnvers, however, does not work in modular arithmetic. The reason is that in modular arithmetic, it does not make sense to ask in line 3 whether F(c) < y.

Using OAEP with RSA encryption no longer preserves the multiplicative structure of numbers, and it is probabilistic. 4 Hash Functions 39 discussed small-message-space attack. The low encryption exponent attack against RSA is also prevented, provided that the plaintext is individually re-encoded by OAEP for each recipient before it is encrypted with RSA. 4 Hash Functions A hash function takes a message as input and produces an output referred to as hash code or hash value. A hash function maps an arbitrary bit string to a bit string of length n: h: {O,l}* -t {o,l}n, m t----t h(m).

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