1 Security quizz [5 points]
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1 Université de Nice-Sophia Antipolis M1 Info Cryptography & security Nom : Pr enom : Examen de december 2017 Durée : 1h30 Note : The exam contains independant parts. Please answer directely on the answer sheet, clearly and briefly. 1 Security quizz [5 points] 1. Explain what is a digital enveloppe and its use(s)? 2. What are the main reasons to prefer signing a fingerprint rather than the message itself? 3. Explain the cases when a trapdoor is not required together with a one-way function? 4. Why don t we use Vernam-like ciphers more often? 5. Why is it preferable to use real certificates rather than self-signed ones? 1
2 2 Hash function [7 points] Dan Bernstein created this hashing algorithm. It is known by many as the Chris Torek hash. Remember that an unsigned int is one byte sized, that the integer overflow can be viewed as the mathematical modulo and that the input parameter len denotes the length of the input. unsigned djb_hash(void *input, int len){ unsigned char *p = input; unsigned h = 0; int i; for (i = 0; i < len; i++) { h = 27 * h + p[i]; } return h;} 1. By using djb hash, compute the decimal fingerprint value of ATB whose ASCII encoding is (65, 84, 66). Detail the operations. 2. Apply the birthday paradox attack on djb hash to find how many pairs of values are necessary to haveaprobablilitygreaterthan 3/4to find a collision. (Recall that ln(4) = 1.4 and ln(3) = 1.1). 2
3 Thedjb hashfunction will be used in the sequelas aone-wayfunction tosecurelystorepasswords. 3. Describe the operation mode to store passwords on a remote server and next the way to authenticate remotely (there are two protocols to describe). 4. Show that fu = (102,117) collides with ATB. Since ATB and fu collide, we have the following two questions: 5. Can we use equivalently ATB or fu as an encryption (or decryption) key? Please detail your answer. 6. Can we use equivalently ATB or fu as an authentication credential? Please detail your answer. 3
4 3 Variations around EL Gamal Signature [5 points] We study some properties of the El Gamal s signature scheme whose operation mode follows: we randomly choose k Z p 1 invertible in Z p 1 and keep it secret. The signature of a message M is: with sig SK (M,k) = (γ,δ) γ = α k mod p, and δ = (M aγ)k 1 mod (p 1). There are many variations around El Gamal s signing algorithm obtained by modifying the traditionnal signing equation δ = (M aγ)k 1 mod (p 1). 1. We consider the new signing equation δ = aγ + km mod (p 1) where γ s value remains unchanged. Show the validity of the predicate Ver(M,γ,δ) = True α δ = β γ γ M mod p with β = α a mod p. We assume that the signer s random number generator library fails and uses the private parameter a instead of k. The next two questions use the new signing scheme δ = aγ +km mod (p 1). 2. Explain how an eavesdropper who intercepts (M,γ,δ) can be aware of this failure: 3. How does the eavesdropper use this knowledge to recover the value of the private parameter a and thus break the signature scheme? 4
5 4 Putting things together [3 points] We would like to combine the hash function from exercise 2 with the signature scheme from exercise What are the parameters that need to be public and private for this new signature scheme with hashing? 2. If we denote by H to shorten the djb hash function, please detail the new signature scheme with hashing and its verification predicate. 3. Would you trust this signature scheme with hashing? (Detail your answer). 5
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