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Anonymous Signcryption in Ring Signature Scheme Over Elliptic Curve Cryptosystem

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Anonymous Signcryption in Ring Signature Scheme Over Elliptic Curve Cryptosystem Anonymous signcryption in ring signature scheme over elliptic curve cryptosystem Yu Fang Chung1 Zhen Yu Wu2 Feipei Lai1&3 Tzer Shyong Chen4 1 Electrical Engineering Department, National Taiwan University, Taipei, Taiwan 2 Computer Science and Information Engineering Department, National Cheng-Kung University, Tainan, Taiwan 3 Computer Science and Information Engineering Department, National Taiwan University, Taipei, Taiwan 4 Information Management Department, Tunghai University, Taichung, Taiwan E-Mail: [email protected] Abstract designed to meet different needs. This work focuses on the application of the combination of ring This study presents an anonymous signcryption signatures and signcryption. scheme based on the elliptic curve cryptosystem, The ring signature scheme [2] was developed by R. which combines the properties of elliptic curve Rivest et al. in 2001, which was created from the cryptosystem and ring signature. While the signers are concept of “How to leak a secret.” Ring signature was endowed with anonymity through the technique of a special group signature without want of creating a ring signature, the elliptic curve cryptosystem achieves group; in spite of the management of an administrator, the advantages of high security, low computation load, a signer only required randomly choosing a portion of and small bandwidth requirements. To integrate the the public keys of members and then creating a ring advantages of these two applications, the resulting signature through his private key. Such a signature system reaches a highly secure and efficient method significantly lowered the complexity of the anonymous signcryption scheme. Signcryption makes mutual authentication process, to achieve the greatest a session key unnecessary to be established in advance advantage that allows then signer to remain anonymity for each session; hence, transmission load is reduced, thus to protect the privacy of a signer. and efficiency of performance and transmission is Signcryption, a kind of public key cryptosystem, enhanced. succeeds in simultaneously encrypting the message while digitally signing. Compared with the traditional Keywords: Signcryption, elliptic curve cryptosystem, systems like PGP that executes signing and encrypting ring signature, and anonymity. a message in sequential procedures, such a characteristic makes signcryption system securer and more efficient. To be specific, the efficiency of 1. Introduction performance based on the signcryption system can be Advances in cryptography provide information enhanced atout 50% to 90% than the traditional ones. security on the Internet. Encryption systems ensure In 1997, Zheng [5] introduced the conception of confidentiality of message transmission, while digital- the signcryption. From then on, many researchers had signature techniques ensure authenticity and integrity addressed and discussed many variations of of information. These factors play a significant role in signcryption schemes [6-8]. Such as Lee and Mao information security. Conventional handwritten presented a signcryption scheme based on RSA [6] signatures are increasingly being replaced by digital and proposed security proofs in the random oracle signatures, which are widely used in the internet model aimed at privacy and unforgeability. Libert and society. Since W. Diffie and M. Hellman initially Quisquater presented an ID-based signcrytpion using proposed the digital signature method in 1976 [1], bilinear pairing [7]. Additionally, Yum and Lee scholars later developed various digital signature proposed the new signcryption schemes based on methods, including RSA, ElGamal, and DSS, which KCDSA [8]. form the basis of the methods presented in this study. Nevertheless, the schemes above-mentioned However, in practice people have different disabled to complete the requirement of anonymity for requirements with regard to digital signatures. Various signers. Anonymous signcryption is useful in cases digital signatures, such as group signatures, ring where the identity of a sender must remain secret, yet signatures [2], blind signatures, proxy signatures [3], the message must be verifiable. Thus, in Section 2, threshold signatures [4] and signcryption [5], had been there develops an anonymous signcryption scheme based on the elliptic curve cryptosystem, which Step 4: Signer Ui calculates ci = H(m || xi-1) and combines the pros of ring signature scheme. The si = k - dici (mod q). application of elliptic curve cryptosystem can make Step 5: Signer Ui encrypts the message m following performance rise efficiently. As to the establishment of m’=Exe(m) using the symmetric secret key xe. security, the proposed scheme possesses not only Step 6: Signer Ui sends the encrypted text confidentiality but also characteristics like σ =(m’, c , s , s , …, s , R) to the verifier U . unforgeability, anonymity, and undeniability. 1 1 2 n v This paper is organized as follows. Section 1 Verification of signcryption text introduces the history of signature techniques, On receiving the encrypted text concerning for different achievements. Section 2 σ =(m’, c1, s1, s2, …, sn, R), the verifier Uv performs presents the proposed signcryption scheme that is the following steps to verify. based on ring signature. Section 3 discusses the Step 1: Let (xr, yr) = R, verifier Uv calculates security of the system. Section 4 is the analysis of (xd, yd) = dvR and m”= Exd (m’). performance from the angle of efficiency. Conclusions Step 2: Let t=1,2,…,n-1, Verifier Uv calculates (xt, yt) are finally drawn in Section 5. = Tt = stP + ctQt and ct+1 = H(m” || xt). Step 3: Verifier Uv calculates (xn, yn) = Tn = snP + cnQn 2. Proposed anonymous ECC-based and c ’ = H(m” || x ). signcryption scheme 1 n Step 4: Once Verifier Uv confirms c1’ = c1 then σ =(m’, c , s , s , …, s , R) is a valid anonymous The elliptic curve cryptosystem (ECC) has the 1 1 2 n signcryption text from the group A = (U , U , …, advantages of high security, low computation load, 1 2 U ); otherwise, reject the encrypted text. and small bandwidth requirement, while the ring n signature protects the signer with anonymity. To Conversion of signcryption text to standard integrate elliptic curve cryptosystem and ring signature signature herein, the resulting system can achieve a highly On receiving signcryption text secure and efficient anonymous signcryption method. σ =(m’, c1, s1, s2, …, sn, R), the verifier Uv applies the The process comprises four steps, namely system verification process in the above to confirm the construction, generation of signcryption text, validity of signcryption text σ. Thus, m” denotes the verification of signcryption text, and conversion of signed message from a group, and σ’ = (m”, c1, s1, signcryption text to standard signature. s2, …, sn) indicates the standard ring signature converted from σ which is an ECC-based ring System construction signature. Only verifier Uv can perform the signature Let q denote a large prime number, E denote an conversion process. Any third party can verify the elliptic curve, P denote a base point on the elliptic validity of the converted signature. curve E with order q and H denote a dispersed row function for resisting collision, where q, E, P, and H 3. Analysis of security are public parameters, and Zq is a finite field with q elements. This method combines the ECC-based system, ring Let a group member set be A = (U , U , …, U ) 1 2 n signature and symmetric encryption, reaching the under the ECC, the private keys of U , U , …, U are 1 2 n characteristics such as confidentiality, unforgeability, d , d , …, d respectively. The corresponding public 1 2 n anonymity, and undeniability. The difficulty for keys Q , Q , …, Q satisfies Q = d P, where i=1,2,…,n. 1 2 n i i solving the elliptic curve discrete logarithm problem The private and public keys of verifier U are d and v v (ECDLP) is currently regarded as a hard enough Q = d P, respectively. v v problem to the security protocols. Generation of signcryption text Confidentiality Let a member U in A send the signcryption text of the i Message m is sent in ciphertext form so that it can message m to verifier U The process of generating v only be decrypted by those with a secret session key. signcryption text is as follows. As to the session key, it is encrypted using the public Step 1: Signer Ui randomly selects k " R [1 , q ! 1 ] and keys of the verifiers before it is sent to the verifiers. So r "R [1, q !1] far an ECC-based public key infrastructure remains Step 2: Signer Ui calculates (xi, yi) = Ti = kP, s e c ure, thus only verifier Uv can obtain the message m (xr, yr) = R = rP, and (xe, ye) = Te = rQv. from the ciphertext. Step 3:When t=1 and t-1=n, let t=i+1, i+2,…,n,1,…,i-1, Unforgeability signer U selects s t " R [ 1 , q !a1n]d calculates c i t An ECC-based ring signature is unforgeable in the = H(m || x ) and (x , y ) = T = s P + c Q . t-1 t t t t t t random oracle mode. In a random oracle mode, consider the ring signature algorithm SIG of the proposed method along with the dispersed row output of the previous similar requests. Under this function H as an oracle. method, B needs only perform an addition operation Concerning a ring signature algorithm SIG, if a on the two ends to obtain the desired value of Q, forged algorithm A that employs the public keys which also forces A to compute s such that it satisfies Q1, Q2, …, Qn as inputs, but without knowledge about Q =sP in the final forgery process to seal the gap. any corresponding private key. Using polynomial B cannot determine which request was applied by sequence requests to SIG and H, the algorithm A can A to the final forgery of signature, and can only guess forge the ring signature for a message m with a non- from it. However, B can only attempt two guesses.
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