A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Encryption-Scheme Security in the Presence of Key-Dependent Messages
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
CSF '07 Proceedings of the 20th IEEE Computer Security Foundations Symposium
Security under key-dependent inputs
Proceedings of the 14th ACM conference on Computer and communications security
Circular-Secure Encryption from Decision Diffie-Hellman
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
OAEP Is Secure under Key-Dependent Messages
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On the (Im)Possibility of Key Dependent Encryption
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Simultaneous Hardcore Bits and Cryptography against Memory Attacks
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Public-Key Cryptosystems Resilient to Key Leakage
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Towards key-dependent message security in the standard model
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Circular and leakage resilient public-key encryption under subgroup indistinguishability
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
On symmetric encryption and point obfuscation
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Soundness of formal encryption in the presence of key-cycles
ESORICS'05 Proceedings of the 10th European conference on Research in Computer Security
Bounded key-dependent message security
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Key-dependent message security: generic amplification and completeness
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Randomly encoding functions: a new cryptographic paradigm
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Authenticated and misuse-resistant encryption of key-dependent data
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Key-dependent message security for division function: discouraging anonymous credential sharing
ProvSec'11 Proceedings of the 5th international conference on Provable security
Ciphers that securely encipher their own keys
Proceedings of the 18th ACM conference on Computer and communications security
Circular and KDM security for identity-based encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
On the circular security of bit-encryption
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Randomness-Dependent message security
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Hi-index | 0.00 |
We show how to achieve public-key encryption schemes that can securely encrypt nonlinear functions of their own secret key. Specifically, we show that for any constant d ε N, there exists a public-key encryption scheme that can securely encrypt any function f of its own secret key, assuming f can be expressed as a polynomial of total degree d. Such a scheme is said to be key-dependent message (KDM) secure w.r.t. degree-d polynomials. We also show that for any constants c, e, there exists a public-key encryption scheme that is KDM secure w.r.t. all Turing machines with description size c log λ and running time λe, where λ is the security parameter. The security of such public-key schemes can be based either on the standard decision Diffie-Hellman (DDH) assumption or on the learning with errors (LWE) assumption (with certain parameters (settings). In the case of functions that can be expressed as degree-d polynomials, we show that the resulting schemes are also secure with respect to key cycles of any length. Specifically, for any polynomial number n of key pairs, our schemes can securely encrypt a degree-d polynomial whose variables are the collection of coordinates of all n secret keys. Prior to this work, it was not known how to achieve this for nonlinear functions. Our key idea is a general transformation that amplifies KDM security. The transformation takes an encryption scheme that is KDM secure w.r.t. some functions even when the secret keys are weak (i.e. chosen from an arbitrary distribution with entropy k), and outputs a scheme that is KDM secure w.r.t. a richer class of functions. The resulting scheme may no longer be secure with weak keys. Thus, in some sense, this transformation converts security with weak keys into amplified KDM security.