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Cryptography General Interview Questions

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Blind signature schemes, first introduced by Chaum, allow a person to get a message signed by another party without revealing any information about the message to the other party.

Chaum demonstrated the implementation of this concept using RSA signatures as follows: Suppose Alice has a message m that she wishes to have signed by Bob, and she does not want Bob to learn anything about m. Let (n,e) be Bob's public key and (n,d) be his private key. Alice generates a random value r such that gcd(r, n) = 1 and sends to Bob. The value m' is "blinded" by the random value r, and hence Bob can derive no useful information from it. Bob returns the signed value to Alice. Since s'=rmd mod n, Alice can obtain the true signature s of m by computing. Now Alice's message has a signature she could not have obtained on her own. This signature scheme is secure provided that factoring and root extraction remain difficult. However, regardless of the status of these problems the signature scheme is unconditionally "blind" since r is random. The random r does not allow the signer to learn about the message even if the signer can solve the underlying hard problems. 

A designated confirmer signature [Cha94] strikes a balance between self-authenticating digital signatures and zero-knowledge proofs. While the former allows anybody to verify a signature, the latter can only convince one recipient at a time of the authenticity of a given document, and only through interaction with the signer. A designated confirmer signature allows certain designated parties to confirm the authenticity of a document without the need for the signer's input. At the same time, without the aid of either the signer or the designated parties, it is not possible to verify the authenticity of a given document. Chaum developed implementations of designated confirmer signatures with one or more confirmers using RSA digital signatures. 

A fail-stop signature scheme is a type of signature devised by van Heyst and Pederson [VP92] to protect against the possibility that an enemy may be able to forge a person's signature. It is a variation of the one-time signature scheme, in which only a single message can be signed and protected by a given key at a time. The scheme is based on the discrete logarithm problem. In particular, if an enemy can forge a signature, then the actual signer can prove that forgery has taken place by demonstrating the solution of a supposedly hard problem. Thus the forger's ability to solve that problem is transferred to the actual signer. (The term "fail-stop" refers to the fact that a signer can detect and stop failures, i.e., forgeries. Note that if the enemy obtains an actual copy of the signer's private key, forgery cannot be detected. What the scheme detects are forgeries based on cryptanalysis.) 

A group signature, introduced by Chaum and van Heijst, allows any member of a group to digitally sign a document in a manner such that a verifier can confirm that it came from the group, but does not know which individual in the group signed the document. The protocol allows for the identity of the signer to be discovered, in case of disputes, by a designated group authority who has some auxiliary information. Unfortunately, each time a member of the group signs a document, a new key pair has to be generated for the signer. The generation of new key pairs causes the length of both the group members' secret keys and the designated authority's auxiliary information to grow. This tends to cause the scheme to become unwieldy when used by a group to sign numerous messages or when used for an extended period of time. Some improvements have been made in the efficiency of this scheme. 

Blowfish is a 64-bit block cipher developed by Schneier. It is a Feistel cipher and each round consists of a key-dependent permutation and a key-and-data-dependent substitution. All operations are based on exclusive-ors and additions on 32-bit words. The key has a variable length (with a maximum length of 448 bits) and is used to generate several subkey arrays. This cipher was designed specifically for 32-bit machines and is significantly faster than DES. There was an open competition for the cryptanalysis of Blowfish supported by Dr. Dobb's Journal with a $1000 prize. This contest ended in April 1995 and among the results were the discoveries of existence of certain weak keys , an attack against a three-round version of Blowfish, and a differential attack against certain variants of Blowfish. However, Blowfish can still be considered secure, and Schneier has invited cryptanalysts to continue investigating his cipher.

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