Automating Fast and Secure Translations from Type-I to Type-III Pairing Schemes

Abstract

Pairing-based cryptography has exploded over the last decade, as this algebraic setting offers good functionality and efficiency. However, there is a huge security gap between how schemes are usually analyzed in the academic literature and how they are typically implemented. The issue at play is that there exist multiple types of pairings: Type-I called "symmetric" is typically how schemes are presented and proven secure in the literature, because it is simpler and the complexity assumptions can be weaker; however, Type-III called "asymmetric" is typically the most efficient choice for an implementation in terms of bandwidth and computation time. There are two main complexities when moving from one pairing type to another. First, the change in algebraic setting invalidates the original security proof. Second, there are usually multiple (possibly thousands) of ways to translate from a Type-I to a Type-III scheme, and the "best" translation may depend on the application. Our contribution is the design, development and evaluation of a new software tool, Auto-Group+, that automatically translates from Type-I to Type-III pairings. The output of Au-toGroup+ is: (1) "secure" provided the input is "secure" and (2) optimal based on the user's efficiency constraints (excluding software and run-time errors). Prior automation work for pairings was either not guaranteed to be secure or only partially automated and impractically slow. This work addresses the pairing security gap by realizing a fast and secure translation tool.

Fast and Scalable Bilinear-Type Conversion Method for Large Scale Crypto Schemes

“…Given several kinds of constraints and a metric implemented into an objective function, it searches for a solution that minimizes the function value subject to the constraints. The idea of encoding computational constraints into an objective function follows from previous works [20,22]. Our novelty is the encoding method that allows one to use Integer Programming that fits well to our optimization problem with various constraints.…”

“…As vast number of schemes have been built over Type-I groups, e.g, [9][10][11][12][13][14][15], bilinear-type conversion methods that translate schemes designed for Type-I groups into ones that work over Type-III groups have been developed [16][17][18][19][20][21][22]. Recall that cryptographic schemes designed over Type-I groups do not necessarily work over Type-III groups due to the presence of symmetric pairings, e(X, X ).…”

“…Automated conversion methods in the literature [20][21][22] are only for small-scale schemes consisting of up to tens of group operations. To follow the secure conversion framework introduced in [21], one needs to convert not only the algorithms in the target scheme but those that appear in security proofs.…”

Improved functional proxy re-encryption schemes for secure cloud data sharing

“…To further demonstrate our schemes efficiency, we roughly evaluated our scheme's practical performance according to implementation in [1]. We give the performance comparison results for GA07B, LZD+, WCW and Our schemes in Fig.…”

“…We give the performance comparison results for GA07B, LZD+, WCW and Our schemes in Fig. 6,7 ,8,9,10, 11, 12, according to the efficiency benchmark of SS156 and BN256 groups [1] implemented in the highly efficient RELIC cryptographic toolkit version 0.4 [2](using the GMP library [12] for big number operations and the default configuration options for prime field arithmetic ), measured on a standard workstation, which is 2.4GHz Intel Core i5 processor and 8GB of RAM (1067MHz DDR3) running Mac OS X Lion version 10.7.5. We have neglected some operations such as the computation cost of one-time symmetric encryption, one-time symmetric decryption and one-time checking for the decryption results' validity, one-time signature and verification.…”