Paper 2011/024
Secure evaluation of polynomial using privacy ring homomorphisms
Alexander Rostovtsev, Alexey Bogdanov, and Mikhail Mikhaylov
Abstract
Method of secure evaluation of polynomial y=F(x_1, …, x_k) over some rings on untrusted computer is proposed. Two models of untrusted computer are considered: passive and active. In passive model untrusted computer correctly computes polynomial F and tries to know secret input (x_1, …, x_k) and output y. In active model untrusted computer tries to know input and output and tries to change correct output y so that this change cannot be determined. Secure computation is proposed by using onetime privacy ring homomorphism Z/nZ > Z/nZ[z]/(f(z)), n = pq, generated by trusted computer. In the case of active model secret check point v = F(u_1, …, u_k) is used. Trusted computer generates polynomial f(z)=(zt)(z+t), t in Z/nZ, and input X_i(z) in Z/nZ[z]/(f(z)) such that X_i(t)=x_i (mod n) for passive model, and f(z)=(zt_1)(zt_2)(zt_3), t_i in Z/nZ and input X_i(z) in Z/nZ[z]/(f(z)) such that X_i(t_1)=x_i (mod n), X_i(t_2)= u_i (mod n) for active model. Untrusted computer computes function Y(z) = F(X_1(z), …, X_k(z)) in the ring Z/nZ[z]/(f(z)). For passive model trusted computer determines secret output y=Y(t) (mod n). For active model trusted computer checks that Y(t_2)=v (mod n), then determines correct output y=Y(t_1) (mod n).
Metadata
 Available format(s)
 Category
 Cryptographic protocols
 Publication info
 Published elsewhere. Unknown where it was published
 Keywords
 elliptic curve cryptosystemfactoringpublickey cryptography
 Contact author(s)
 rostovtsev @ ssl stu neva ru
 History
 20110114: received
 Short URL
 https://ia.cr/2011/024
 License

CC BY
BibTeX
@misc{cryptoeprint:2011/024, author = {Alexander Rostovtsev and Alexey Bogdanov and Mikhail Mikhaylov}, title = {Secure evaluation of polynomial using privacy ring homomorphisms}, howpublished = {Cryptology ePrint Archive, Paper 2011/024}, year = {2011}, note = {\url{https://eprint.iacr.org/2011/024}}, url = {https://eprint.iacr.org/2011/024} }