Foundations of Computer SecurityLecture 44: Symmetric vs. Asymmetric EncryptionDr. Bill YoungDepartment of Computer SciencesUniversity of Texas at AustinLecture 44: 1 Symmetric vs. Asymmetric EncryptionSymmetric vs. Asymmetric SystemsRecall that there are two basic types of encryption:symmetric algorithms: (also called “secret key”) use the same keyfor both encryption and decryption;asymmetric algorithms: (also called “public key”) use differentkeys for encryption and decryption.For any encryption approach, there are two major challenges:Key distribution: how do we convey keys to those who need themto establish secure communication.Key management: given a large number of keys, how do wepreserve their safety and make them available asneeded.Lecture 44: 2 Symmetric vs. Asymmetric EncryptionAsymmetric Encryption PrimerIn asymmetric or public key encryption, different keys are used forencryption and decryption.Each subject S has a publicly disclosed key KS(“S’s public key”)that anyone can use to encrypt, and a privately held key K−1S(“S’sprivate key”). The relationship is:M = {{M}KS}K−1S.Anyone wishing to send a message M confidentially to S sends{M}Ks. Only the holder of K−1Scan decrypt this message.Asymmetric encryption largely solves the key distribution problem.Why?Lecture 44: 3 Symmetric vs. Asymmetric EncryptionHow Many Keys: Symmetric EncryptionGiven a symmetric system with n users, how many keys are neededfor pairwise secure communication?S1S5S2S3S4Each time a new user is added to the system, it needs to share anew key with each previous user. Thus, for n users, we have1 + 2 + . . . + (n − 1) = n(n − 1)/2 keys.This is O(n2) keys.Lecture 44: 4 Symmetric vs. Asymmetric EncryptionHow Many Keys: Asymmetric EncryptionGiven an asymmetric system of n users, how many keys are neededfor pairwise secure communication?Each time a new user is added to the system, it needs only a publickey and a private key.Thus, for n users, we have 2n keys, which is O(n).Depending on the algorithm, each user may need separate pairs forconfidentiality and signing, i.e., 4n keys, which is still O(n).Lecture 44: 5 Symmetric vs. Asymmetric EncryptionCharacteristics of KeysTypically, in a symmetric encryption system keys are:1randomly generated k-bit strings,2simple to generate,3have no special properties.In a public key system, keys:1have special structure (e.g., are large primes), and2are expensive to generate.Key sizes are not comparable between the two approaches. A128-bit symmetric key may be equivalent in strength to a 3000-bitpublic key.Lecture 44: 6 Symmetric vs. Asymmetric EncryptionLessonsUsing symmetric encryption, security requires that each pairof users share a secret key.In an asymmetric system, each user has a public/private keypair.Keys in the two approaches have very different characteristicsand are not directly comparable.Next lecture: Stream and Block EncryptionLecture 44: 7 Symmetric vs. Asymmetric
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