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Secure Obfuscation for Encrypted Signatures

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Satoshi Hada
Satoshi Hada

Eurocrypt 2010

TechnologyEducation
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Secure Obfuscation for Encrypted Signatures Eurocrypt 2010 (May 31) Satoshi Hada IBM Research - Tokyo
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The purpose of obfuscation is to hide private information contained in programs while preserving the functionality. byte[] signcrypt(byte[] m){ byte[] key } Obfuscator Before Obfuscation After Obfuscation 2 1 # The obfuscated program preserves the functionality Functionality ,[object Object],[object Object],Virtual Black-box Property Requirement Name
Summary: a new positive result on program obfuscation ,[object Object],Sign Encrypt Alice’s private signing key Bob’s public encryption key m c σ Message Ciphertext Encrypted Signature We can obfuscate this program NOTE: The message is not encrypted.
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Motivation: only a few positive results are known and we should look for more positive results. ,[object Object],[object Object],Negative ,[object Object],[object Object],[object Object],Positive Results Type
Motivation: To use signcryption for Webmail services, service providers need to store users’ private signing keys and execute signcryption on servers. Key leakage is a serious security issue. Alice’s Web Browser Bob’s Web Browser Server Server Key leakage is a serious security issue!! Standard browsers have no capability of signcryption Signcrypt@ Server
A solution is to obfuscate the signcryption program so that the private signing key can not be abused. Server Server We can obfuscate this program Alice’s Web Browser Bob’s Web Browser Signcrypt@ Server
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The basic idea is to design a pair of signature and encryption schemes such that the following two are functionally equivalent: Sign Encrypt m c σ Encrypt Alice’s signing key Bob’s encryption key Sign Obfuscated programs Encrypted Alice’s signing key Encrypted Signature (to be obfuscated) Message Ciphertext ,[object Object],[object Object],Obfuscator The virtual black-box property reduces to the security of encryption.
Example : We realize the basic idea using the BLS signature scheme ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example: Encrypted signature program ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Sign Encrypt
Example: Obfuscation (initial attempt) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Before Obfuscation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Obfuscation After Obfuscation Output is randomly generated Output is fixed for each message Encrypted signing key
Example: Obfuscation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Obfuscation After Obfuscation The output distributions are identical ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Before Obfuscation Randomization was added
Main Result: We can securely obfuscate an encrypted signature scheme in the standard model ,[object Object],[object Object],[object Object],[object Object],2 1 # Theorem 2: Waters’s signature scheme is existentially unforgeable (EU) against chosen message attacks under the decisional bilinear Diffie-Hellman (DBDH) assumption. Waters’s signature scheme (Eurocrypt’05) Theorem 3: Linear encryption scheme is IND-CPA under the decisional linear (DL) assumption. Linear encryption scheme (Crypto’04) Security (in the standard model) Building Block
Main Result: The security of Waters’s signature scheme is preserved even when adversaries are given obfuscated encrypted signature programs Def 3: A signature scheme is EU against adversaries having signing oracle Def 5: A signature scheme is EU against adversaries having signing oracle and obfuscated encrypted signature program trivial Thm 1 Thm 1: if the obfuscator satisfies the VBP, then Def 4 implies Def 5. Thm 2: Waters’s signature scheme satisfies Def 3 under DBDH Corollary 1: Waters’s signature scheme satisfies Def 5 under DL and DBDH trivial Thms 1& 4 Abstract Concrete Stronger Security
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
We can use encrypted signature as a building block to construct a secure signcryption scheme. Using our proposed obfuscation, we can obfuscate the signcryption scheme. Sign Encrypt Alice’s private signing key Bob’s public encryption key m c σ Message Ciphertext Encrypted Signature (Hybrid) Encrypt m EncryptedSignature-then-Encryption (EStE) ,[object Object],[object Object],[object Object]
There are some attacks that our proposed obfuscation cannot prevent. ,[object Object],[object Object],[object Object],Attacks we can prevent ,[object Object],[object Object],[object Object],[object Object],Attack we cannot prevent Attacks Type
Generalization: we can apply the basic idea to other signature schemes We can generalize our construction to clarify the properties that a pair of encryption and signature schemes should satisfy so that the encrypted signature can be securely obfuscated NO YES Pairing-based CRYPTO’02 Lysyanskaya’s unique signature scheme 1 CRYPTO’89 Undeniable signature scheme by Chaum and Antwerpen 3 J. ACM 2004 DDH-based Pseudoranom functions (MAC) 4 5 2 # PKC’02 Dodis’s verifiable random function JoC 1991 Schnorr’s signature scheme Reference Scheme

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Secure Obfuscation for Encrypted Signatures

  • 1. Secure Obfuscation for Encrypted Signatures Eurocrypt 2010 (May 31) Satoshi Hada IBM Research - Tokyo
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  • 7. Motivation: To use signcryption for Webmail services, service providers need to store users’ private signing keys and execute signcryption on servers. Key leakage is a serious security issue. Alice’s Web Browser Bob’s Web Browser Server Server Key leakage is a serious security issue!! Standard browsers have no capability of signcryption Signcrypt@ Server
  • 8. A solution is to obfuscate the signcryption program so that the private signing key can not be abused. Server Server We can obfuscate this program Alice’s Web Browser Bob’s Web Browser Signcrypt@ Server
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  • 16. Main Result: The security of Waters’s signature scheme is preserved even when adversaries are given obfuscated encrypted signature programs Def 3: A signature scheme is EU against adversaries having signing oracle Def 5: A signature scheme is EU against adversaries having signing oracle and obfuscated encrypted signature program trivial Thm 1 Thm 1: if the obfuscator satisfies the VBP, then Def 4 implies Def 5. Thm 2: Waters’s signature scheme satisfies Def 3 under DBDH Corollary 1: Waters’s signature scheme satisfies Def 5 under DL and DBDH trivial Thms 1& 4 Abstract Concrete Stronger Security
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  • 20. Generalization: we can apply the basic idea to other signature schemes We can generalize our construction to clarify the properties that a pair of encryption and signature schemes should satisfy so that the encrypted signature can be securely obfuscated NO YES Pairing-based CRYPTO’02 Lysyanskaya’s unique signature scheme 1 CRYPTO’89 Undeniable signature scheme by Chaum and Antwerpen 3 J. ACM 2004 DDH-based Pseudoranom functions (MAC) 4 5 2 # PKC’02 Dodis’s verifiable random function JoC 1991 Schnorr’s signature scheme Reference Scheme