Hybrid Position-Residues Number System

Karim Bigou (1) , Arnaud Tisserand (1)

1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources

We propose an hybrid representation of large integers , or prime field elements, combining both positional and residue number systems (RNS). Our hybrid position-residues (HPR) number system mixes a high-radix positional representation and digits represented in RNS. RNS offers an important source of parallelism for addition, subtraction and multiplication operations. But, due to its non-positional property, it makes comparisons and modular reductions more costly than in a positional number system. HPR offers various trade-offs between internal parallelism and the efficiency of operations requiring position information. Our current application domain is asymmetric cryptography where HPR significantly reduces the cost of some modular operations compared to state-of-the-art RNS solutions. Index Terms—number representation; large integer; finite field; modular arithmetic; residue number system.

Mots clés: number representation; large integer; finite field; modular arithmetic; residue number system

Domaines: Arithmétique des ordinateurs; Cryptographie et sécurité [cs.CR]

Karim Bigou, Arnaud Tisserand. Hybrid Position-Residues Number System. ARITH: 23rd Symposium on Computer Arithmetic, Jul 2016, Santa Clara, CA, United States. ⟨hal-01314232⟩