Provably Secure Identity-based Encryption And Signature Over Ceclotomic Fields

Conventional public key cryptography issued a certificate and managed certifi-cates and keys via Certificate Authority,in which the process of management is complicated and possess very high computational complexity and storage com-plexity.However,identity-based cryptography is a type of public key cryptong-raphy with simple key management procedures.Compared with conventional public key infrastructure,public key cryptography simplify the process of key management based on certificate in it.To our knowledge,till now,the existing identity-based cryptography based on NTRU are all over power-of-2 cyclotomic rings,in which NTT algorithm can be implemented and multiplications can be done very fast.However,there are too many subfields in the corresponding cyclotomic fields,making these settings sensitive to subfield attacks.So,seeking constructions of IBE and IBS over more general fields is a meaningful work.Whether there are provably secure identity-based cryptography over more general fields is still open.In this thesis,with the help of the results of Collision Resistance Preimage Sampleable Functions(CRPSF)over cyclotomic fields,we give concrete construc-tions of provably secure identity-based encryption schemes(IBE)and identity-based signature schemes(IBS)based on NTRU over any cyclotomic field.Our IBE schemes are provably secure under adaptive chosen-plaintext and adaptive chosen-identity attacks,meanwhile,our IBS schemes are existentially unforge-able against adaptively chosen message and adaptively chosen identity attacks for any probabilistic polynomial time(PPT)adversary in the random oracle model.The securities of IBE and IBS schemes are based on the worst-case approximate shortest independent vectors problem(SIVP)over corresponding ideal lattices,in which approxiamte parameters,respectively,are ?=O(n9.5)and ?'=O(n8).The secret key size of our IBE(IBS)scheme is short-only one(two)ring ele-ment(s).The ciphertext(signature)is also short-only two(three)ring elements.Meanwhile,as the case of NTRUEncrypt,our IBE scheme could encrypt n bits in each encryption process.These properties may make our scheme have more advantages in theory.