Prime numbers and computer methods for factorization
Prime numbers and computer methods for factorization
Faster primality testing (extended abstract)
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Implementation of fast RSA key generation on smart cards
Proceedings of the 2002 ACM symposium on Applied computing
Handbook of Applied Cryptography
Handbook of Applied Cryptography
On Generation of Probable Primes By Incremental Search
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Efficient Generation of Shared RSA Keys (Extended Abstract)
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Prime Number Generation
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Efficient Generation of Prime Numbers
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
A note on efficient implementation of prime generation algorithms in small portable devices
Computer Networks: The International Journal of Computer and Telecommunications Networking
Fast generation of prime numbers on portable devices: an update
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
On the Implementation of a Fast Prime Generation Algorithm
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
A New Side-Channel Attack on RSA Prime Generation
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
RSA moduli with a predetermined portion: techniques and applications
ISPEC'08 Proceedings of the 4th international conference on Information security practice and experience
Analyzing standards for RSA integers
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Fast generation of prime numbers on portable devices: an update
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
RSA key generation: new attacks
COSADE'12 Proceedings of the Third international conference on Constructive Side-Channel Analysis and Secure Design
Generating provable primes efficiently on embedded devices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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The generation of prime numbers underlies the use of most public-key cryptosystems, essentially as a primitive needed for the creation of RSA key pairs. Surprisingly enough, despite decades of intense mathematical studies on primality testing and an observed progressive intensification of cryptography, prime number generation algorithms remain scarcely investigated and most real-life implementations are of dramatically poor performance. We show simple techniques that substantially improve all algorithms previously suggested or extend their capabilities. We derive fast implementations on appropriately equipped portable devices like smart-cards embedding a cryptographic coprocessor. This allows onboard generation of RSA keys featuring a very attractive (average) processing time. Our motivation here is to help transferring this task from terminals where this operation usually took place so far, to portable devices themselves in near future for more confidence, security, and compliance with network-scaled distributed protocols such as electronic cash or mobile commerce.