Fault Attacks on RSA Public Keys: Left-To-Right Implementations are also Vulnerable

Alexandre Berzati (1, 2) , Cécile Canovas (1) , Jean-Guillaume Dumas (3) , Louis Goubin (2)

1 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information
2 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation
3 CASYS - Calculs Algébriques et Systèmes Dynamiques

After attacking the RSA by injecting fault and corresponding countermeasures, works appear now about the need for protecting RSA public elements against fault attacks. We provide here an extension of a recent attack based on the public modulus corruption. The difficulty to decompose the "Left-To-Right" exponentiation into partial multiplications is overcome by modifying the public modulus to a number with known factorization. This fault model is justified here by a complete study of faulty prime numbers with a fixed size. The good success rate of this attack combined with its practicability raises the question of using faults for changing algebraic properties of finite field based cryptosystems.

Keywords: RSA; fault attacks; "Left-To-Right" exponentiation; number theory.; Left-To-Right" exponentiation; number theory

Domains: Cryptography and Security [cs.CR]

Alexandre Berzati, Cécile Canovas, Jean-Guillaume Dumas, Louis Goubin. Fault Attacks on RSA Public Keys: Left-To-Right Implementations are also Vulnerable. RSA Conference 2009 - Cryptographers' Track, Apr 2009, San Francisco, United States. pp.414--428, ⟨10.1007/978-3-642-00862-7_28⟩. ⟨hal-00348416v3⟩