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Putting it all together: using multiple primitives together

Putting it all together: using multiple primitives together. Exercise 1. Say you have a signature scheme. SScheme = ( KGen , Sign, Vf ). Say this scheme is unforgeable against CMA. Modify the signature algorithm:. iff . & = 1. Is this still unforgeable against CMA?. Exercise 2.

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Putting it all together: using multiple primitives together

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  1. Putting it all together: using multiple primitives together

  2. Exercise 1 • Say you have a signature scheme SScheme = (KGen, Sign, Vf) • Say this scheme is unforgeable against CMA • Modify the signature algorithm: iff. & = 1 • Is this still unforgeable against CMA?

  3. Exercise 2 • We have an arbitrary unforgeable signature scheme: SScheme = (KGen, Sign, Vf) • And we also have any IND-CCA encryption scheme EScheme = (KGen, Enc, Dec) • Say we want to ensure that a confidentialmessage comes from a given party. Can we send: • ? • ? • ?

  4. Interlude • What would we use in order to: • Send a confidential message • Encrypt a large document • Send a confidential AND authenticated message • Authenticate a message with non-repudiation • Authenticate a message without non-repudiation • Find correspondences • Confidentiality • Hash function • Collision-resistance • MAC code • Authenticity • Symmetric encryption • Non-repudiation • PK Encryption • Integrity • Digital Signatures

  5. Exercise 3 • The Hash paradigm for signatures : • Improves the security of signature schemes • Improves efficiency for signatures, making their size the same, irrespective of the message length • Can we do the same for encryption schemes, i.e. use instead of • Can we send just instead of

  6. Exercise 4 • Symmetric encryption is faster than PK encryption • Suppose Amélie generates a symmetric encryption key (e.g. for AES 128) and encrypts a message for Baptiste withthis key. • Baptiste does not know the secret key. • By using one (or more) of the following mechanisms, show how Amélie can ensure that Baptiste can decrypt. • A public key encryption scheme • A symmetric encryption scheme • A signature scheme • A MAC scheme • A hash scheme

  7. Exercise 5 • Amélie and Baptiste share a secret key for a MAC scheme ……… Amélie Baptiste • They exchange some messages, without signing each one, but at the end, each party will send a MAC of the message: {<Name> || || || || … || } • How does CBC-mode symmetric encryption work? Why would this method be indicated for long conversations?

  8. Exercise 6 • Consider the DSA signature scheme • Say Amélie signs two different messages with the sameephemeral value (and obviously the sameprivate key ) • How would an attacker know from the signatures that the same ephemeral value was used for both signatures? • Show how to retrieve given the two signatures for and

  9. Exercise 7 • Amélie wants to do online shopping, say on Ebay • She needs to establish a secure channel with an Ebay server, i.e. be able to exchange message confidentially and integrally/authentically with its server • This is actually done by sharing one MAC key and one symmetric encryption key between them • The server has a certified RSA public encryption key, but Amélie does not • How can Amélie make sure they share the two secret keys? • How can they check that they are sharing the same keys?

  10. Exercise 8 • List the properties of a hash function. Think of: input size, output size, who can compute it etc. • Imagine we have a public key encryption scheme. We generate and , but throw away and publish • We implement a hash scheme by using the PKE scheme, by using • Should the PKE scheme be deterministic or probabilistic? • Analyse the case of Textbook RSA as the encryption scheme. Which properties of the hash function are guaranteed? • Assume the generic PKE scheme ensures that a plaintext cannot be recovered from the ciphertext. Which properties of the hash scheme does the PKE scheme guarantee?

  11. Exercise 9 • A pseudo-random generator is a deterministic function thattakes as input a fixed-length string (a seed) and which outputs a much longer string , suchthat looks random to anyadversary • Assume Amélie and Baptiste share a seed • Consider symmetric encryption with key , whereencryptionisdone as , for messages of lengthequal to that of (and paddedotherwise) • Is this scheme deterministic or probabilistic? • Show that this scheme is insecure if the adversary can request the decryption of even a single ciphertext. • How can we make it secure even if the adversary can decrypt arbitrary ciphertexts?

  12. Thanks!

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