On Using RSA/ECC Coprocessor for Ideal Lattice-Based Key Exchange

Aurélien Greuet (1) , Simon Montoya (1, 2) , Guénaël Renault (3, 2)

1 Idemia
2 GRACE - Geometry, arithmetic, algorithms, codes and encryption
3 ANSSI - Agence nationale de la sécurité des systèmes d'information

Polynomial multiplication is one of the most costly operations of ideal lattice-based cryptosystems. In this work, we study its optimizations when one of the operands has coefficients close to 0. We focus on this structure since it is at the core of lattice-based Key Encapsulation Mechanisms submitted to the NIST call for post-quantum cryptography. In particular, we propose optimization of this operation for embedded devices by using a RSA/ECC coprocessor that provides efficient and secure large-integer arithmetic. In this context, we compare Kronecker Substitution, already studied in [AHH + 19], with two specific algorithms that we introduce: KSV, a variant of this substitution, and an adaptation of the schoolbook multiplication, denoted Shift&Add. All these algorithms rely on the transformation of polynomial multiplication to large-integer arithmetic. Then, thanks to these algorithms, existing secure coprocessors dedicated to large-integer can be re-purposed in order to speed-up post-quantum schemes. The efficiency of these algorithms depends on the component specifications and the cryptosystem parameters set. Thus, we establish a methodology to determine which algorithm to use, for a given component, by only implementing basic large-integer operations. Moreover, the three algorithms are assessed on a chip ensuring that the theoretical methodology matches with practical results.

Domaines: Cryptographie et sécurité [cs.CR]

Aurélien Greuet, Simon Montoya, Guénaël Renault. On Using RSA/ECC Coprocessor for Ideal Lattice-Based Key Exchange. COSADE 2021, Oct 2021, Lugano, Switzerland. ⟨10.1007/978-3-030-89915-8_10⟩. ⟨hal-03330066⟩