Security of Identity-Based Encryption Algorithms

The concept of Identity Based Cryptography was proposed in (Shamir,A., 1984) which introduced the idea of using arbitrary strings such as e-mail addresses and IP Addresses to form public keys with the corresponding private keys being created by the Trusted Authority(TA) who is in possession of a system-wide master secret (Srinivasan,S.,2010). Then a party, Alice who wants to send encrypted communication to Bob need only Bob’s identifier and the system-wide public parameters. Thus the receiver is able to choose and manipulate the public key of the intended recipient which has a number of advantages. While Identity Based Cryptography (IBC) removes the problem of trust in the public key, it introduces trust in the TA. As the TA uses the system-wide master secret to compute private keys for users in the system, it can effectively recompute a private key for any arbitrary string without having to archive private keys. This greatly simplifies key management as the TA simply needs to protect its master secret. Some of the earlier Identity Based Cryptosystems proposed such as the one by Cocks (Cocks, C., 2010) and Boneh (Boneh, et.al.,2007) were not based on mathematics of pairings. The Identity based cryptosystem (the term Identity Based Cryptography refers to this set of algorithms whereas the term Identity Based Cryptosystem refers to a specific algorithm) was introduced by Boneh and Franklin (Boneh, et.al.,2001). An Identity Based Encryption or IBE (the term IBE is used to denote a specific Identity Based Cryptosystem) scheme has the following four algorithms: Setup, KeyDer, Enc and Dec. This chapter discusses the algorithms of the IBE schemes and compares them based on the implementation efficiency. An extention to the basic IBE scheme is the Hierarchical IBE proposed by Horwitz and Lynn(Horwitz, et.al., 2001). In contrast to the basic standard model of IBE, a Random Oracle Model (Bellare, et.al.,1993) may be used where proofs of security are obtained by replacing hash functions with “Random Oracles” that output truly random values for every distinct output. This chapter discusses IBE schemes based on the Random Oracle Model IBEs and compares them with the standard model IBE. An extension of the above schemes with multiple Trusted Authorities(TAs) instead of a single TA is also possible. An architecture for the implementation of the IBE is discussed along with the security of the various schemes.